Lucky and even lucky numbers
You are encouraged to solve this task according to the task description, using any language you may know.
Note that in the following explanation list indices are assumed to start at one.
- Definition of lucky numbers
Lucky numbers are positive integers that are formed by:
- Form a list of all the positive odd integers > 0
- Return the first number from the list (which is 1).
- (Loop begins here)
- Note then return the second number from the list (which is 3).
- Discard every third, (as noted), number from the list to form the new list
- (Expanding the loop a few more times...)
- Note then return the third number from the list (which is 7).
- Discard every 7th, (as noted), number from the list to form the new list
- Note then return the 4th number from the list (which is 9).
- Discard every 9th, (as noted), number from the list to form the new list
- Take the 5th, i.e. 13. Remove every 13th.
- Take the 6th, i.e. 15. Remove every 15th.
- Take the 7th, i.e. 21. Remove every 21th.
- Take the 8th, i.e. 25. Remove every 25th.
- (Rule for the loop)
- Note the th, which is .
- Remove every th.
- Increment .
- Definition of even lucky numbers
This follows the same rules as the definition of lucky numbers above except for the very first step:
- Form a list of all the positive even integers > 0
- Return the first number from the list (which is 2).
- (Loop begins here)
- Note then return the second number from the list (which is 4).
- Discard every 4th, (as noted), number from the list to form the new list
- (Expanding the loop a few more times...)
- Note then return the third number from the list (which is 6).
- Discard every 6th, (as noted), number from the list to form the new list
- Take the 4th, i.e. 10. Remove every 10th.
- Take the 5th, i.e. 12. Remove every 12th.
- (Rule for the loop)
- Note the th, which is .
- Remove every th.
- Increment .
- Task requirements
- Write one or two subroutines (functions) to generate lucky numbers and even lucky numbers
- Write a command-line interface to allow selection of which kind of numbers and which number(s). Since input is from the command line, tests should be made for the common errors:
- missing arguments
- too many arguments
- number (or numbers) aren't legal
- misspelled argument (lucky or evenLucky)
- The command line handling should:
- support mixed case handling of the (non-numeric) arguments
- support printing a particular number
- support printing a range of numbers by their index
- support printing a range of numbers by their values
- The resulting list of numbers should be printed on a single line.
The program should support the arguments:
what is displayed (on a single line) argument(s) (optional verbiage is encouraged) ╔═══════════════════╦════════════════════════════════════════════════════╗ ║ j ║ Jth lucky number ║ ║ j , lucky ║ Jth lucky number ║ ║ j , evenLucky ║ Jth even lucky number ║ ║ ║ ║ ║ j k ║ Jth through Kth (inclusive) lucky numbers ║ ║ j k lucky ║ Jth through Kth (inclusive) lucky numbers ║ ║ j k evenLucky ║ Jth through Kth (inclusive) even lucky numbers ║ ║ ║ ║ ║ j -k ║ all lucky numbers in the range j ──► |k| ║ ║ j -k lucky ║ all lucky numbers in the range j ──► |k| ║ ║ j -k evenLucky ║ all even lucky numbers in the range j ──► |k| ║ ╚═══════════════════╩════════════════════════════════════════════════════╝ where |k| is the absolute value of k
Demonstrate the program by:
- showing the first twenty lucky numbers
- showing the first twenty even lucky numbers
- showing all lucky numbers between 6,000 and 6,100 (inclusive)
- showing all even lucky numbers in the same range as above
- showing the 10,000th lucky number (extra credit)
- showing the 10,000th even lucky number (extra credit)
- See also
- This task is related to the Sieve of Eratosthenes task.
- OEIS Wiki Lucky numbers.
- Sequence A000959 lucky numbers on The On-Line Encyclopedia of Integer Sequences.
- Sequence A045954 even lucky numbers or ELN on The On-Line Encyclopedia of Integer Sequences.
- Entry lucky numbers on The Eric Weisstein's World of Mathematics.
11l
-V NoValue = 0
F initLuckyNumbers(nelems, evenlucky, limit = -1)
[Int] result
L(i) 0 .< nelems
V k = i
L(j) (result.len - 1 .< 0).step(-1)
k = k * result[j] I/ (result[j] - 1)
V n = 2 * k + 1 + evenlucky
I limit != -1 & n > limit
L.break
result.append(n)
R result
F name(evenlucky)
R [‘Lucky’, ‘Even lucky’][evenlucky]
F printSingle(j, evenlucky)
V luckySeq = initLuckyNumbers(j, evenlucky)
print(name(evenlucky)‘ number at index ’j‘ is ’luckySeq[j - 1])
F printRange(j, k, evenlucky)
V luckySeq = initLuckyNumbers(k, evenlucky)
print(name(evenlucky)‘ numbers at indexes ’j‘ to ’k‘ are: ’, end' ‘’)
L(idx) j - 1 .< k
I idx != j - 1
print(‘, ’, end' ‘’)
print(luckySeq[idx], end' ‘’)
print()
F printInRange(j, k, evenlucky)
V luckySeq = initLuckyNumbers(k, evenlucky, k)
print(name(evenlucky)‘ numbers between ’j‘ to ’k‘ are: ’, end' ‘’)
V first = 1B
L(val) luckySeq
I val > j
I first
first = 0B
E
print(‘, ’, end' ‘’)
print(val, end' ‘’)
print()
F process_args(args)
assert(args.len C 1..3, ‘Wrong number of arguments’)
// First argument: "j" value.
V j = Int(args[0])
V k = NoValue
// Second argument: "k" value or a comma.
I args.len > 1
I args[1] == ‘,’
// Must be followed by the kind of lucky number.
assert(args.len == 3, ‘Missing kind argument’)
E
k = Int(args[1])
assert(k != 0, ‘Expected a non null number’)
V evenlucky = 0
// Third argument: number kind.
I args.len == 3
V kind = args[2].lowercase()
assert(kind C (‘lucky’, ‘evenlucky’), ‘Wrong kind’)
I kind == ‘evenlucky’
evenlucky = 1
I k == NoValue
// Print jth value.
printSingle(j, evenlucky)
E I k > 0
// Print jth to kth values.
printRange(j, k, evenlucky)
E
// Print values in range j..(-k).
printInRange(j, -k, evenlucky)
:start:
I 1B
L(args) [‘1 20’, ‘1 20 evenlucky’, ‘6000 -6100’, ‘6000 -6100 evenlucky’, ‘10000’, ‘10000 , lucky’, ‘10000 , evenlucky’]
print(‘Command line arguments: ’args)
process_args(args.split(‘ ’))
print()
E
process_args(:argv[1..])
- Output:
Command line arguments: 1 20 Lucky numbers at indexes 1 to 20 are: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79 Command line arguments: 1 20 evenlucky Even lucky numbers at indexes 1 to 20 are: 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76 Command line arguments: 6000 -6100 Lucky numbers between 6000 to 6100 are: 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093 Command line arguments: 6000 -6100 evenlucky Even lucky numbers between 6000 to 6100 are: 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092 Command line arguments: 10000 Lucky number at index 10000 is 115591 Command line arguments: 10000 , lucky Lucky number at index 10000 is 115591 Command line arguments: 10000 , evenlucky Even lucky number at index 10000 is 111842
C
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#define LUCKY_SIZE 60000
int luckyOdd[LUCKY_SIZE];
int luckyEven[LUCKY_SIZE];
void compactLucky(int luckyArray[]) {
int i, j, k;
for (i = 0; i < LUCKY_SIZE; i++) {
if (luckyArray[i] == 0) {
j = i;
break;
}
}
for (j = i + 1; j < LUCKY_SIZE; j++) {
if (luckyArray[j] > 0) {
luckyArray[i++] = luckyArray[j];
}
}
for (; i < LUCKY_SIZE; i++) {
luckyArray[i] = 0;
}
}
void initialize() {
int i, j;
// unfiltered
for (i = 0; i < LUCKY_SIZE; i++) {
luckyEven[i] = 2 * i + 2;
luckyOdd[i] = 2 * i + 1;
}
// odd filter
for (i = 1; i < LUCKY_SIZE; i++) {
if (luckyOdd[i] > 0) {
for (j = luckyOdd[i] - 1; j < LUCKY_SIZE; j += luckyOdd[i]) {
luckyOdd[j] = 0;
}
compactLucky(luckyOdd);
}
}
// even filter
for (i = 1; i < LUCKY_SIZE; i++) {
if (luckyEven[i] > 0) {
for (j = luckyEven[i] - 1; j < LUCKY_SIZE; j += luckyEven[i]) {
luckyEven[j] = 0;
}
compactLucky(luckyEven);
}
}
}
void printBetween(size_t j, size_t k, bool even) {
int i;
if (even) {
if (luckyEven[j] == 0 || luckyEven[k] == 0) {
fprintf(stderr, "At least one argument is too large\n");
exit(EXIT_FAILURE);
}
printf("Lucky even numbers between %d and %d are:", j, k);
for (i = 0; luckyEven[i] != 0; i++) {
if (luckyEven[i] > k) {
break;
}
if (luckyEven[i] > j) {
printf(" %d", luckyEven[i]);
}
}
} else {
if (luckyOdd[j] == 0 || luckyOdd[k] == 0) {
fprintf(stderr, "At least one argument is too large\n");
exit(EXIT_FAILURE);
}
printf("Lucky numbers between %d and %d are:", j, k);
for (i = 0; luckyOdd[i] != 0; i++) {
if (luckyOdd[i] > k) {
break;
}
if (luckyOdd[i] > j) {
printf(" %d", luckyOdd[i]);
}
}
}
printf("\n");
}
void printRange(size_t j, size_t k, bool even) {
int i;
if (even) {
if (luckyEven[k] == 0) {
fprintf(stderr, "The argument is too large\n");
exit(EXIT_FAILURE);
}
printf("Lucky even numbers %d to %d are:", j, k);
for (i = j - 1; i < k; i++) {
printf(" %d", luckyEven[i]);
}
} else {
if (luckyOdd[k] == 0) {
fprintf(stderr, "The argument is too large\n");
exit(EXIT_FAILURE);
}
printf("Lucky numbers %d to %d are:", j, k);
for (i = j - 1; i < k; i++) {
printf(" %d", luckyOdd[i]);
}
}
printf("\n");
}
void printSingle(size_t j, bool even) {
if (even) {
if (luckyEven[j] == 0) {
fprintf(stderr, "The argument is too large\n");
exit(EXIT_FAILURE);
}
printf("Lucky even number %d=%d\n", j, luckyEven[j - 1]);
} else {
if (luckyOdd[j] == 0) {
fprintf(stderr, "The argument is too large\n");
exit(EXIT_FAILURE);
}
printf("Lucky number %d=%d\n", j, luckyOdd[j - 1]);
}
}
void help() {
printf("./lucky j [k] [--lucky|--evenLucky]\n");
printf("\n");
printf(" argument(s) | what is displayed\n");
printf("==============================================\n");
printf("-j=m | mth lucky number\n");
printf("-j=m --lucky | mth lucky number\n");
printf("-j=m --evenLucky | mth even lucky number\n");
printf("-j=m -k=n | mth through nth (inclusive) lucky numbers\n");
printf("-j=m -k=n --lucky | mth through nth (inclusive) lucky numbers\n");
printf("-j=m -k=n --evenLucky | mth through nth (inclusive) even lucky numbers\n");
printf("-j=m -k=-n | all lucky numbers in the range [m, n]\n");
printf("-j=m -k=-n --lucky | all lucky numbers in the range [m, n]\n");
printf("-j=m -k=-n --evenLucky | all even lucky numbers in the range [m, n]\n");
}
void process(int argc, char *argv[]) {
bool evenLucky = false;
int j = 0;
int k = 0;
bool good = false;
int i;
for (i = 1; i < argc; ++i) {
if ('-' == argv[i][0]) {
if ('-' == argv[i][1]) {
// long args
if (0 == strcmp("--lucky", argv[i])) {
evenLucky = false;
} else if (0 == strcmp("--evenLucky", argv[i])) {
evenLucky = true;
} else {
fprintf(stderr, "Unknown long argument: [%s]\n", argv[i]);
exit(EXIT_FAILURE);
}
} else {
// short args
if ('j' == argv[i][1] && '=' == argv[i][2] && argv[i][3] != 0) {
good = true;
j = atoi(&argv[i][3]);
} else if ('k' == argv[i][1] && '=' == argv[i][2]) {
k = atoi(&argv[i][3]);
} else {
fprintf(stderr, "Unknown short argument: [%s]\n", argv[i]);
exit(EXIT_FAILURE);
}
}
} else {
fprintf(stderr, "Unknown argument: [%s]\n", argv[i]);
exit(EXIT_FAILURE);
}
}
if (!good) {
help();
exit(EXIT_FAILURE);
}
if (k > 0) {
printRange(j, k, evenLucky);
} else if (k < 0) {
printBetween(j, -k, evenLucky);
} else {
printSingle(j, evenLucky);
}
}
void test() {
printRange(1, 20, false);
printRange(1, 20, true);
printBetween(6000, 6100, false);
printBetween(6000, 6100, true);
printSingle(10000, false);
printSingle(10000, true);
}
int main(int argc, char *argv[]) {
initialize();
//test();
if (argc < 2) {
help();
return 1;
}
process(argc, argv);
return 0;
}
- Output:
LuckyNumbers.exe -j=1 -k=20 Lucky numbers 1 to 20 are: 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 LuckyNumbers.exe -j=1 -k=20 --evenLucky Lucky even numbers 1 to 20 are: 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76 LuckyNumbers.exe -j=6000 -k=-6100 Lucky numbers between 6000 and 6100 are: 6009 6019 6031 6049 6055 6061 6079 6093 LuckyNumbers.exe -j=6000 -k=-6100 --evenLucky Lucky even numbers between 6000 and 6100 are: 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092 LuckyNumbers.exe -j=10000 Lucky number 10000=115591 LuckyNumbers.exe -j=10000 --evenLucky Lucky even number 10000=111842
C++
#include <algorithm>
#include <iostream>
#include <iterator>
#include <vector>
const int luckySize = 60000;
std::vector<int> luckyEven(luckySize);
std::vector<int> luckyOdd(luckySize);
void init() {
for (int i = 0; i < luckySize; ++i) {
luckyEven[i] = i * 2 + 2;
luckyOdd[i] = i * 2 + 1;
}
}
void filterLuckyEven() {
for (size_t n = 2; n < luckyEven.size(); ++n) {
int m = luckyEven[n - 1];
int end = (luckyEven.size() / m) * m - 1;
for (int j = end; j >= m - 1; j -= m) {
std::copy(luckyEven.begin() + j + 1, luckyEven.end(), luckyEven.begin() + j);
luckyEven.pop_back();
}
}
}
void filterLuckyOdd() {
for (size_t n = 2; n < luckyOdd.size(); ++n) {
int m = luckyOdd[n - 1];
int end = (luckyOdd.size() / m) * m - 1;
for (int j = end; j >= m - 1; j -= m) {
std::copy(luckyOdd.begin() + j + 1, luckyOdd.end(), luckyOdd.begin() + j);
luckyOdd.pop_back();
}
}
}
void printBetween(size_t j, size_t k, bool even) {
std::ostream_iterator<int> out_it{ std::cout, ", " };
if (even) {
size_t max = luckyEven.back();
if (j > max || k > max) {
std::cerr << "At least one are is too big\n";
exit(EXIT_FAILURE);
}
std::cout << "Lucky even numbers between " << j << " and " << k << " are: ";
std::copy_if(luckyEven.begin(), luckyEven.end(), out_it, [j, k](size_t n) {
return j <= n && n <= k;
});
} else {
size_t max = luckyOdd.back();
if (j > max || k > max) {
std::cerr << "At least one are is too big\n";
exit(EXIT_FAILURE);
}
std::cout << "Lucky numbers between " << j << " and " << k << " are: ";
std::copy_if(luckyOdd.begin(), luckyOdd.end(), out_it, [j, k](size_t n) {
return j <= n && n <= k;
});
}
std::cout << '\n';
}
void printRange(size_t j, size_t k, bool even) {
std::ostream_iterator<int> out_it{ std::cout, ", " };
if (even) {
if (k >= luckyEven.size()) {
std::cerr << "The argument is too large\n";
exit(EXIT_FAILURE);
}
std::cout << "Lucky even numbers " << j << " to " << k << " are: ";
std::copy(luckyEven.begin() + j - 1, luckyEven.begin() + k, out_it);
} else {
if (k >= luckyOdd.size()) {
std::cerr << "The argument is too large\n";
exit(EXIT_FAILURE);
}
std::cout << "Lucky numbers " << j << " to " << k << " are: ";
std::copy(luckyOdd.begin() + j - 1, luckyOdd.begin() + k, out_it);
}
}
void printSingle(size_t j, bool even) {
if (even) {
if (j >= luckyEven.size()) {
std::cerr << "The argument is too large\n";
exit(EXIT_FAILURE);
}
std::cout << "Lucky even number " << j << "=" << luckyEven[j - 1] << '\n';
} else {
if (j >= luckyOdd.size()) {
std::cerr << "The argument is too large\n";
exit(EXIT_FAILURE);
}
std::cout << "Lucky number " << j << "=" << luckyOdd[j - 1] << '\n';
}
}
void help() {
std::cout << "./lucky j [k] [--lucky|--evenLucky]\n";
std::cout << "\n";
std::cout << " argument(s) | what is displayed\n";
std::cout << "==============================================\n";
std::cout << "-j=m | mth lucky number\n";
std::cout << "-j=m --lucky | mth lucky number\n";
std::cout << "-j=m --evenLucky | mth even lucky number\n";
std::cout << "-j=m -k=n | mth through nth (inclusive) lucky numbers\n";
std::cout << "-j=m -k=n --lucky | mth through nth (inclusive) lucky numbers\n";
std::cout << "-j=m -k=n --evenLucky | mth through nth (inclusive) even lucky numbers\n";
std::cout << "-j=m -k=-n | all lucky numbers in the range [m, n]\n";
std::cout << "-j=m -k=-n --lucky | all lucky numbers in the range [m, n]\n";
std::cout << "-j=m -k=-n --evenLucky | all even lucky numbers in the range [m, n]\n";
}
int main(int argc, char **argv) {
bool evenLucky = false;
int j = 0;
int k = 0;
// skip arg 0, because that is just the executable name
if (argc < 2) {
help();
exit(EXIT_FAILURE);
}
bool good = false;
for (int i = 1; i < argc; ++i) {
if ('-' == argv[i][0]) {
if ('-' == argv[i][1]) {
// long args
if (0 == strcmp("--lucky", argv[i])) {
evenLucky = false;
} else if (0 == strcmp("--evenLucky", argv[i])) {
evenLucky = true;
} else {
std::cerr << "Unknown long argument: [" << argv[i] << "]\n";
exit(EXIT_FAILURE);
}
} else {
// short args
if ('j' == argv[i][1] && '=' == argv[i][2] && argv[i][3] != 0) {
good = true;
j = atoi(&argv[i][3]);
} else if ('k' == argv[i][1] && '=' == argv[i][2]) {
k = atoi(&argv[i][3]);
} else {
std::cerr << "Unknown short argument: " << argv[i] << '\n';
exit(EXIT_FAILURE);
}
}
} else {
std::cerr << "Unknown argument: " << argv[i] << '\n';
exit(EXIT_FAILURE);
}
}
if (!good) {
help();
exit(EXIT_FAILURE);
}
init();
filterLuckyEven();
filterLuckyOdd();
if (k > 0) {
printRange(j, k, evenLucky);
} else if (k < 0) {
printBetween(j, -k, evenLucky);
} else {
printSingle(j, evenLucky);
}
return 0;
}
- Output:
>LuckyNumbers.exe -j=1 -k=20 Lucky numbers 1 to 20 are: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, >LuckyNumbers.exe -j=1 -k=20 --evenLucky Lucky even numbers 1 to 20 are: 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76, >LuckyNumbers.exe -j=6000 -k=-6100 Lucky numbers between 6000 and 6100 are: 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093, >LuckyNumbers.exe -j=6000 -k=-6100 --evenLucky Lucky even numbers between 6000 and 6100 are: 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092, >LuckyNumbers.exe -j=10000 Lucky number 10000=115591 >LuckyNumbers.exe -j=10000 --evenLucky Lucky even number 10000=111842
D
import std.algorithm;
import std.concurrency;
import std.conv;
import std.getopt;
import std.range;
import std.stdio;
auto lucky(bool even, int nmax=200_000) {
import std.container.array;
int start = even ? 2 : 1;
return new Generator!int({
auto ln = make!(Array!int)(iota(start,nmax,2));
// yield the first number
yield(ln[0]);
int n=1;
for(; n<ln.length/2+1; n++) {
yield(ln[n]);
int step = ln[n]-1;
// remove the non-lucky numbers related to the current lucky number
for (int i=step; i<ln.length; i+=step) {
ln.linearRemove(ln[].drop(i).take(1));
}
}
// yield all remaining values
foreach(val; ln[n..$]) {
yield(val);
}
});
}
void help(Option[] opt) {
defaultGetoptPrinter("./lucky j [k] [--lucky|--evenLucky]", opt);
writeln;
writeln(" argument(s) | what is displayed");
writeln("==============================================");
writeln("-j=m | mth lucky number");
writeln("-j=m --lucky | mth lucky number");
writeln("-j=m --evenLucky | mth even lucky number");
writeln("-j=m -k=n | mth through nth (inclusive) lucky numbers");
writeln("-j=m -k=n --lucky | mth through nth (inclusive) lucky numbers");
writeln("-j=m -k=n --evenLucky | mth through nth (inclusive) even lucky numbers");
writeln("-j=m -k=-n | all lucky numbers in the range [m, n]");
writeln("-j=m -k=-n --lucky | all lucky numbers in the range [m, n]");
writeln("-j=m -k=-n --evenLucky | all even lucky numbers in the range [m, n]");
}
void main(string[] args) {
int j;
int k;
bool evenLucky = false;
void luckyOpt() {
evenLucky = false;
}
auto helpInformation = getopt(
args,
std.getopt.config.passThrough,
std.getopt.config.required,
"j", "The starting point to generate lucky numbers", &j,
"k", "The ending point for generating lucky numbers", &k,
"lucky", "Specify to generate a list of lucky numbers", &luckyOpt,
"evenLucky", "Specify to generate a list of even lucky numbers", &evenLucky
);
if (helpInformation.helpWanted) {
help(helpInformation.options);
return;
}
if (k>0) {
lucky(evenLucky).drop(j-1).take(k-j+1).writeln;
} else if (k<0) {
auto f = (int a) => j<=a && a<=-k;
lucky(evenLucky, -k).filter!f.writeln;
} else {
lucky(evenLucky).drop(j-1).take(1).writeln;
}
}
- Output:
.\lucky_and_even_lucky_numbers.exe -j=1 -k=20 [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] .\lucky_and_even_lucky_numbers.exe -j=1 -k=20 --evenLucky [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] .\lucky_and_even_lucky_numbers.exe -j=6000 -k=-6100 [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] .\lucky_and_even_lucky_numbers.exe -j=6000 -k=-6100 --evenLucky [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092] .\lucky_and_even_lucky_numbers.exe -j=10000 [115591] .\lucky_and_even_lucky_numbers.exe -j=10000 --evenLucky [111842]
F#
The functions
// Odd and Even Lucky Numbers. Nigel Galloway: October 3rd., 2020
let rec fN i g e l=seq{yield! i|>Seq.skip g|>Seq.take(e-g-1)
let n=Seq.chunkBySize e i|>Seq.collect(Seq.take(e-1)) in yield! fN n (e-1) (Seq.item l n) (l+1)}
let oLuck,eLuck=let rec fG g=seq{yield g; yield! fG(g+2)} in (fN(fG 1) 0 3 2,fN(fG 2) 0 4 2)
The task
Using a fsi console:
- Output:
> oLuck|>Seq.take 20|>Seq.iter(printf "%d "); printfn "";; 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 > eLuck|>Seq.take 20|>Seq.iter(printf "%d "); printfn "";; 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76 > oLuck|>Seq.skipWhile(fun n->n<6000)|>Seq.takeWhile(fun n->n<6100)|>Seq.iter(printf "%d "); printfn "";; 6009 6019 6031 6049 6055 6061 6079 6093 > eLuck|>Seq.skipWhile(fun n->n<6000)|>Seq.takeWhile(fun n->n<6100)|>Seq.iter(printf "%d "); printfn "";; 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092
FreeBASIC
Const luckyMax = 120000
Dim Shared As Integer lucky(luckyMax - 1)
Sub RemoveElement(arr() As Integer, index As Integer)
If index < Lbound(arr) Or index > Ubound(arr) Then
Print "Index out of bounds"
Exit Sub
End If
For i As Integer = index To Ubound(arr) - 1
arr(i) = arr(i + 1)
Next i
Redim Preserve arr(Lbound(arr) To Ubound(arr) - 1)
End Sub
Sub filterLucky(lucky() As Integer)
Dim As Integer n, m, p
Dim As Integer dellucky()
For n = 2 To Ubound(lucky)
Redim dellucky(1 To 1)
For m = lucky(n) To Ubound(lucky) Step lucky(n)
dellucky(Ubound(dellucky)) = m
Redim Preserve dellucky(1 To Ubound(dellucky) + 1)
Next m
For p = Ubound(dellucky) - 1 To 1 Step -1
RemoveElement (lucky(), dellucky(p))
Next p
Next n
End Sub
Const helptxt = _
" argument(s) | what is displayed " & Chr(10) & _
"=======================================" & Chr(10) & _
" j | jth lucky number " & Chr(10) & _
" j [,] lucky | jth lucky number " & Chr(10) & _
" j [,] evenLucky | jth even lucky number" & Chr(10) & _
" j k | jth through kth (inclusive) lucky numbers" & Chr(10) & _
" j k lucky | jth through kth (inclusive) lucky numbers" & Chr(10) & _
" j k evenLucky | jth through kth (inclusive) even lucky numbers" & Chr(10) & _
" j -k | all lucky numbers in the range j to k" & Chr(10) & _
" j -k lucky | all lucky numbers in the range j to k" & Chr(10) & _
" j -k evenLucky | all even lucky numbers in the range j to k "
Sub fatal(msg As String)
Print msg; Chr(10)
Print helptxt
Sleep
End
End Sub
Sub process(cl() As String)
If Ubound(cl) = 2 And cl(2) = "," Then cl(2) = ""
Dim As Integer i, j
Dim As Integer k, m, n
Dim As Boolean single_ = true, range = true, oddluck = true
For i = 1 To Ubound(cl)
Dim As String cli = cl(i)
If Val(cli) <> 0 Or cli = "0" Then
n = Valint(cli)
If i > 2 Then fatal("too many numbers")
If i = 1 Then
If n < 1 Then fatal("first argument must be a positive integer")
j = n
Else
single_ = False
If n < 0 Then
range = False
n = -n
End If
If n < j Then fatal("second argument cannot be less than first")
k = n
End If
Else
Select Case Lcase(cli)
Case "lucky"
oddluck = true
Case "evenlucky"
oddluck = False
Case Else
fatal("unrecognised " & cli)
End Select
If i <> Ubound(cl) Then fatal(cli & " must be last parameter")
End If
Next
If oddluck Then
For i = 1 To luckyMax
lucky(i) = 2 * i - 1
Next
Else
For i = 1 To luckyMax
lucky(i) = 2 * i
Next
End If
filterLucky(lucky())
Dim As String evenstr = Iif(oddluck, "", "even ")
If single_ Then
If j > Ubound(lucky) Then fatal("the argument, " & j & ", is too big")
Print "Lucky " & evenstr & "number " & j & " = " & lucky(j)
Elseif range Then
If k > Ubound(lucky) Then fatal("the argument, " & k & ", is too big")
Print "Lucky " & evenstr & "numbers " & j & " to " & k & !" are: \n";
For i = j To k '- 1
Print lucky(i);
Next
Print
Else
If j > lucky(Ubound(lucky) - 1) Then
fatal("start of range is too big")
Elseif k > lucky(Ubound(lucky) - 1) Then
fatal("end of range is too big")
End If
m = 0
While lucky(m) < j
m += 1
Wend
n = m
While lucky(n) <= k
n += 1
Wend
Print "Lucky " & evenstr & "numbers between " & j & " and " & k & !" are: \n";
For i = m To n - 1
Print lucky(i);
Next
Print
End If
End Sub
Sub main()
Dim As String nargs = Command(-1)
If Len(nargs) < 1 Then
Dim As String tests(1 To 8) = {"1 20", "1 20 evenLucky", "20 lucky", "20 evenLucky", "6000 -6100", "6000 -6100 evenLucky", "10000 lucky", "10000 evenLucky"}
Dim As String testArgs()
For t As Integer = 1 To Ubound(tests)
Dim As Integer numArgs = 0
Dim As String test = tests(t)
Dim As Integer posic = 1
While posic <= Len(test)
Dim As Integer nextPos = Instr(posic, test, " ")
If nextPos = 0 Then nextPos = Len(test) + 1
numArgs += 1
Redim Preserve testArgs(1 To numArgs)
testArgs(numArgs) = Mid(test, posic, nextPos - posic)
posic = nextPos + 1
Wend
Print
process(testArgs())
Next
Print "tests complete"
Exit Sub
Else
Dim As String testArgs()
Dim As Integer numArgs = 1
Do
Dim As String arg = Command(numArgs)
If Len(arg) = 0 Then Exit Do
Redim Preserve testArgs(numArgs)
testArgs(numArgs) = Command(numArgs)
numArgs += 1
Loop
process(testArgs())
End If
End Sub
main()
Sleep
- Output:
Lucky numbers 1 to 20 are: 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 Lucky even numbers 1 to 20 are: 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76 Lucky number 20 = 79 Lucky even number 20 = 76 Lucky numbers between 6000 and 6100 are: 6009 6019 6031 6049 6055 6061 6079 6093 Lucky even numbers between 6000 and 6100 are: 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092 Lucky number 10000 = 115591 Lucky even number 10000 = 111842 tests complete
Go
package main
import (
"fmt"
"log"
"os"
"strconv"
"strings"
)
const luckySize = 60000
var luckyOdd = make([]int, luckySize)
var luckyEven = make([]int, luckySize)
func init() {
for i := 0; i < luckySize; i++ {
luckyOdd[i] = i*2 + 1
luckyEven[i] = i*2 + 2
}
}
func filterLuckyOdd() {
for n := 2; n < len(luckyOdd); n++ {
m := luckyOdd[n-1]
end := (len(luckyOdd)/m)*m - 1
for j := end; j >= m-1; j -= m {
copy(luckyOdd[j:], luckyOdd[j+1:])
luckyOdd = luckyOdd[:len(luckyOdd)-1]
}
}
}
func filterLuckyEven() {
for n := 2; n < len(luckyEven); n++ {
m := luckyEven[n-1]
end := (len(luckyEven)/m)*m - 1
for j := end; j >= m-1; j -= m {
copy(luckyEven[j:], luckyEven[j+1:])
luckyEven = luckyEven[:len(luckyEven)-1]
}
}
}
func printSingle(j int, odd bool) error {
if odd {
if j >= len(luckyOdd) {
return fmt.Errorf("the argument, %d, is too big", j)
}
fmt.Println("Lucky number", j, "=", luckyOdd[j-1])
} else {
if j >= len(luckyEven) {
return fmt.Errorf("the argument, %d, is too big", j)
}
fmt.Println("Lucky even number", j, "=", luckyEven[j-1])
}
return nil
}
func printRange(j, k int, odd bool) error {
if odd {
if k >= len(luckyOdd) {
return fmt.Errorf("the argument, %d, is too big", k)
}
fmt.Println("Lucky numbers", j, "to", k, "are:")
fmt.Println(luckyOdd[j-1 : k])
} else {
if k >= len(luckyEven) {
return fmt.Errorf("the argument, %d, is too big", k)
}
fmt.Println("Lucky even numbers", j, "to", k, "are:")
fmt.Println(luckyEven[j-1 : k])
}
return nil
}
func printBetween(j, k int, odd bool) error {
var r []int
if odd {
max := luckyOdd[len(luckyOdd)-1]
if j > max || k > max {
return fmt.Errorf("at least one argument, %d or %d, is too big", j, k)
}
for _, num := range luckyOdd {
if num < j {
continue
}
if num > k {
break
}
r = append(r, num)
}
fmt.Println("Lucky numbers between", j, "and", k, "are:")
fmt.Println(r)
} else {
max := luckyEven[len(luckyEven)-1]
if j > max || k > max {
return fmt.Errorf("at least one argument, %d or %d, is too big", j, k)
}
for _, num := range luckyEven {
if num < j {
continue
}
if num > k {
break
}
r = append(r, num)
}
fmt.Println("Lucky even numbers between", j, "and", k, "are:")
fmt.Println(r)
}
return nil
}
func main() {
nargs := len(os.Args)
if nargs < 2 || nargs > 4 {
log.Fatal("there must be between 1 and 3 command line arguments")
}
filterLuckyOdd()
filterLuckyEven()
j, err := strconv.Atoi(os.Args[1])
if err != nil || j < 1 {
log.Fatalf("first argument, %s, must be a positive integer", os.Args[1])
}
if nargs == 2 {
if err := printSingle(j, true); err != nil {
log.Fatal(err)
}
return
}
if nargs == 3 {
k, err := strconv.Atoi(os.Args[2])
if err != nil {
log.Fatalf("second argument, %s, must be an integer", os.Args[2])
}
if k >= 0 {
if j > k {
log.Fatalf("second argument, %d, can't be less than first, %d", k, j)
}
if err := printRange(j, k, true); err != nil {
log.Fatal(err)
}
} else {
l := -k
if j > l {
log.Fatalf("second argument, %d, can't be less in absolute value than first, %d", k, j)
}
if err := printBetween(j, l, true); err != nil {
log.Fatal(err)
}
}
return
}
var odd bool
switch lucky := strings.ToLower(os.Args[3]); lucky {
case "lucky":
odd = true
case "evenlucky":
odd = false
default:
log.Fatalf("third argument, %s, is invalid", os.Args[3])
}
if os.Args[2] == "," {
if err := printSingle(j, odd); err != nil {
log.Fatal(err)
}
return
}
k, err := strconv.Atoi(os.Args[2])
if err != nil {
log.Fatal("second argument must be an integer or a comma")
}
if k >= 0 {
if j > k {
log.Fatalf("second argument, %d, can't be less than first, %d", k, j)
}
if err := printRange(j, k, odd); err != nil {
log.Fatal(err)
}
} else {
l := -k
if j > l {
log.Fatalf("second argument, %d, can't be less in absolute value than first, %d", k, j)
}
if err := printBetween(j, l, odd); err != nil {
log.Fatal(err)
}
}
}
- Output:
$ ./lucky 1 20 Lucky numbers 1 to 20 are: [1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79] $ ./lucky 1 20 evenLucky Lucky even numbers 1 to 20 are: [2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76] $ ./lucky 6000 -6100 Lucky numbers between 6000 and 6100 are: [6009 6019 6031 6049 6055 6061 6079 6093] $ ./lucky 6000 -6100 evenLucky Lucky even numbers between 6000 and 6100 are: [6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092] $ ./lucky 10000 , lucky Lucky number 10000 = 115591 $ ./lucky 10000 , evenLucky Lucky even number 10000 = 111842
Haskell
Haskell is a very nice language for this problem because it is a lazy language. Here regular expressions and data types are used.
import System.Environment
import Text.Regex.Posix
data Lucky = Lucky | EvenLucky
helpMessage :: IO ()
helpMessage = do
putStrLn " what is displayed (on a single line)"
putStrLn " argument(s) (optional verbiage is encouraged)"
putStrLn "======================|==================================================="
putStrLn " j | Jth lucky number "
putStrLn " j , lucky | Jth lucky number "
putStrLn " j , evenLucky | Jth even lucky number "
putStrLn " "
putStrLn " j k | Jth through Kth (inclusive) lucky numbers "
putStrLn " j k lucky | Jth through Kth (inclusive) lucky numbers "
putStrLn " j k evenlucky | Jth through Kth (inclusive) even lucky numbers "
putStrLn " "
putStrLn " j -k | all lucky numbers in the range j -> |k| "
putStrLn " j -k lucky | all lucky numbers in the range j -> |k| "
putStrLn " j -k evenlucky | all even lucky numbers in the range j -> |k| "
putStrLn "======================|==================================================="
oddNumbers :: [Int]
oddNumbers = filter odd [1..]
evenNumbers :: [Int]
evenNumbers = filter even [1..]
luckyNumbers :: [Int] -> [Int]
luckyNumbers xs =
let i = 3 in
sieve i xs
where
sieve i (ln:s:xs) =
ln : sieve (i + 1) (s : [x | (n, x) <- zip [i..] xs, rem n s /= 0])
nth :: Int -> Lucky -> Int
nth j Lucky = luckyNumbers oddNumbers !! (j-1)
nth j EvenLucky = luckyNumbers evenNumbers !! (j-1)
range :: Int -> Int -> Lucky -> [Int]
range x x2 Lucky = drop (x-1) (take x2 (luckyNumbers oddNumbers))
range x x2 EvenLucky = drop (x-1) (take x2 (luckyNumbers evenNumbers))
interval :: Int -> Int -> Lucky -> [Int]
interval x x2 Lucky = dropWhile (<x) (takeWhile (<=x2) (luckyNumbers oddNumbers))
interval x x2 EvenLucky = dropWhile (<x) (takeWhile (<=x2) (luckyNumbers evenNumbers))
lucky :: [String] -> Lucky
lucky xs =
if "evenLucky" `elem` xs
then EvenLucky
else Lucky
readn :: String -> Int
readn s = read s :: Int
isInt :: String -> Bool
isInt s = not (null (s =~ "-?[0-9]{0,10}" :: String))
main :: IO ()
main = do
args <- getArgs
if head args == "--help" || null args
then
helpMessage
else
let l = lucky args in
case map readn (filter isInt args) of
[] -> do
putStrLn "Invalid input, missing arguments"
putStrLn "Type --help"
[x] -> print (nth x l)
[x, x2] -> if x2 > 0
then print (range x x2 l)
else print (interval x (-x2) l)
_ -> do
putStrLn "Invalid input, wrong number of arguments"
putStrLn "Type --help"
- Output:
$ luckyNumbers 1 20 [1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79] $ luckyNumbers 1 20 evenLucky [2,4,6,10,12,18,20,22,26,34,36,42,44,50,52,54,58,68,70,76] $ luckyNumbers 6000 -6100 lucky [6009,6019,6031,6049,6055,6061,6079,6093] $ luckyNumbers 6000 -6100 evenLucky [6018,6020,6022,6026,6036,6038,6050,6058,6074,6090,6092] $ luckyNumbers 10000 115591 $ luckyNumbers 10000 evenLucky 111842
J
Not going for extra credit because I want to encourage functional reactive "types" in J. (Note that FRP, along with an ML typed compiler, would probably remove the motivation for the while loop in this implementation.)
Implementation:
luckySeq=:3 :0
1 luckySeq y
:
len=.0
nth=.0
seq=.x+2*i.4*y
while. len~:#seq do.
len=. #seq
nth=. nth+1
seq=. nth exclude seq
end.
)
exclude=: ] #~ 1 - #@] $ -@{ {. 1:
lucky=:''
evenLucky=:0
program=:3 :0
range=: |y-.0
seq=. (1+0 e.y) luckySeq >./range
if. 0><./y do.
(#~ e.&(thru/range)) seq
else.
(<:thru/range) { seq
end.
)
thru=: <./ + i.@(+*)@-~
Task:
program 1 20
1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79
program 1 20,evenLucky
2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76
program 6000,-6100
6009 6019 6031 6049 6055 6061 6079 6093
program 6000,-6100,evenLucky
6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092
Note that I've used the J command line rather than a unix or windows command line. This is because J is portable to a wide variety of environments (including phones) and there's no reliably common command line that exists across all these environments. Therefore, J must provide its own, and J's command line requires some slight syntax changes from the suggestions implicit in this task.
Java
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
public class LuckyNumbers {
private static int MAX = 200000;
private static List<Integer> luckyEven = luckyNumbers(MAX, true);
private static List<Integer> luckyOdd = luckyNumbers(MAX, false);
public static void main(String[] args) {
// Case 1 and 2
if ( args.length == 1 || ( args.length == 2 && args[1].compareTo("lucky") == 0 ) ) {
int n = Integer.parseInt(args[0]);
System.out.printf("LuckyNumber(%d) = %d%n", n, luckyOdd.get(n-1));
}
// Case 3
else if ( args.length == 2 && args[1].compareTo("evenLucky") == 0 ) {
int n = Integer.parseInt(args[0]);
System.out.printf("EvenLuckyNumber(%d) = %d%n", n, luckyEven.get(n-1));
}
// Case 4 through 9
else if ( args.length == 2 || args.length == 3 ) {
int j = Integer.parseInt(args[0]);
int k = Integer.parseInt(args[1]);
// Case 4 and 5
if ( ( args.length == 2 && k > 0 ) || (args.length == 3 && k > 0 && args[2].compareTo("lucky") == 0 ) ) {
System.out.printf("LuckyNumber(%d) through LuckyNumber(%d) = %s%n", j, k, luckyOdd.subList(j-1, k));
}
// Case 6
else if ( args.length == 3 && k > 0 && args[2].compareTo("evenLucky") == 0 ) {
System.out.printf("EvenLuckyNumber(%d) through EvenLuckyNumber(%d) = %s%n", j, k, luckyEven.subList(j-1, k));
}
// Case 7 and 8
else if ( ( args.length == 2 && k < 0 ) || (args.length == 3 && k < 0 && args[2].compareTo("lucky") == 0 ) ) {
int n = Collections.binarySearch(luckyOdd, j);
int m = Collections.binarySearch(luckyOdd, -k);
System.out.printf("Lucky Numbers in the range %d to %d inclusive = %s%n", j, -k, luckyOdd.subList(n < 0 ? -n-1 : n, m < 0 ? -m-1 : m+1));
}
// Case 9
else if ( args.length == 3 && k < 0 && args[2].compareTo("evenLucky") == 0 ) {
int n = Collections.binarySearch(luckyEven, j);
int m = Collections.binarySearch(luckyEven, -k);
System.out.printf("Even Lucky Numbers in the range %d to %d inclusive = %s%n", j, -k, luckyEven.subList(n < 0 ? -n-1 : n, m < 0 ? -m-1 : m+1));
}
}
}
private static List<Integer> luckyNumbers(int max, boolean even) {
List<Integer> luckyList = new ArrayList<>();
for ( int i = even ? 2 : 1 ; i <= max ; i += 2 ) {
luckyList.add(i);
}
int start = 1;
boolean removed = true;
while ( removed ) {
removed = false;
int increment = luckyList.get(start);
List<Integer> remove = new ArrayList<>();
for ( int i = increment-1 ; i < luckyList.size() ; i += increment ) {
remove.add(0, i);
removed = true;
}
for ( int i : remove ) {
luckyList.remove(i);
}
start++;
}
return luckyList;
}
}
- Output:
C:\My_Data\software\EclipseOxygenProjects\Rosetta Code\bin>java LuckyNumbers 1 20 LuckyNumber(1) through LuckyNumber(20) = [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] C:\My_Data\software\EclipseOxygenProjects\Rosetta Code\bin>java LuckyNumbers 1 20 evenLucky EvenLuckyNumber(1) through EvenLuckyNumber(20) = [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] C:\My_Data\software\EclipseOxygenProjects\Rosetta Code\bin>java LuckyNumbers 6000 -6100 Lucky Numbers in the range 6000 to 6100 inclusive = [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] C:\My_Data\software\EclipseOxygenProjects\Rosetta Code\bin>java LuckyNumbers 6000 -6100 evenLucky Even Lucky Numbers in the range 6000 to 6100 inclusive = [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092] C:\My_Data\software\EclipseOxygenProjects\Rosetta Code\bin>java LuckyNumbers 10000 LuckyNumber(10000) = 115591 C:\My_Data\software\EclipseOxygenProjects\Rosetta Code\bin>java LuckyNumbers 10000 evenLucky EvenLuckyNumber(10000) = 111842
JavaScript
First: the function.
function luckyNumbers(opts={}) {
/**************************************************************************\
| OPTIONS |
|**************************************************************************|
| even ...... boolean ............. return even/uneven numbers |
| (default: false) |
| |
| nth ....... number ............... return nth number |
| |
| through ... number ............... return numbers from #1 to number |
| OR array[from, to] ... return numbers on index |
| from array[from] to array[to] |
| |
| range ..... array[from, to] ...... return numbers between from and to |
\**************************************************************************/
opts.even = opts.even || false;
if (typeof opts.through == 'number') opts.through = [0, opts.through];
let out = [],
x = opts.even ? 2 : 1,
max = opts.range ? opts.range[1] * 3
: opts.through ? opts.through[1] * 12
: opts.nth ? opts.nth * 15
: 2000;
for (x; x <= max; x = x+2) out.push(x); // fill
for (x = 1; x < Math.floor(out.length / 2); x++) { // sieve
let i = out.length;
while (i--)
(i+1) % out[x] == 0 && out.splice(i, 1);
}
if (opts.nth) return out[opts.nth-1];
if (opts.through) return out.slice(opts.through[0], opts.through[1]);
if (opts.range) return out.filter(function(val) {
return val >= opts.range[0] && val <= opts.range[1];
});
return out;
}
/* TESTING */
// blank
console.log( luckyNumbers() );
// showing the first twenty lucky numbers
console.log( luckyNumbers({through: 20}) );
// showing the first twenty even lucky numbers
console.log( luckyNumbers({even: true, through: 20}) );
// showing all lucky numbers between 6,000 and 6,100 (inclusive)
console.log( luckyNumbers({range: [6000, 6100]}) );
// showing all even lucky numbers in the same range as above
console.log( luckyNumbers({even: true, range: [6000, 6100]}) );
// showing the 10,000th lucky number (extra credit)
console.log( luckyNumbers({nth: 10000}) );
// showing the 10,000th even lucky number (extra credit)
console.log( luckyNumbers({even: true, nth: 10000}) );
- Output:
> Array(276) [ 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, … ] > Array(20) [ 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, … ] > Array(20) [ 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, … ] > Array(8) [ 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093 ] > Array(11) [ 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, … ] > 115591 > 111842
And that's just pretty much it.
But now: our line interpreter!
We'll use an HTML-prompt here, because JavaScript actually doesn't have a command interface on it's own.
(function() {
document.write(`
<table>
<tr><th>argument(s)<br>space separated</th><th>gives</th></tr>
<tr><td>$j</td><td><i>j</i><sup>th</sup> lucky number</tr>
<tr><td>$j lucky</td><td><i>j</i><sup>th</sup> lucky number</tr>
<tr><td>$j evenLucky</td><td><i>j</i><sup>th</sup> even lucky number</tr>
<tr><td> </td><td> </td></tr>
<tr><td>$j $k</td><td><i>J</i><sup>th</sup> through <i>k</i><sup>th</sup> (inclusive) lucky numbers</td></tr>
<tr><td>$j $k lucky</td><td><i>J</i><sup>th</sup> through <i>k</i><sup>th</sup> (inclusive) lucky numbers</td></tr>
<tr><td>$j $k evenLucky</td><td><i>J</i><sup>th</sup> through <i>k</i><sup>th</sup> (inclusive) even lucky numbers</td></tr>
<tr><td> </td><td> </td></tr>
<tr><td>-$j</td><td>all lucky numbers in the range 1 .. |<i>j</i>|*</tr>
<tr><td>$j -$k</td><td>all lucky numbers in the range <i>j</i> .. |<i>k</i>|*</tr>
<tr><td>$j -$k lucky</td><td>all lucky numbers in the range <i>j</i> .. |<i>k</i>|*</tr>
<tr><td>$j -$k evenLucky</td><td>all even lucky numbers in the range <i>j</i> .. |<i>k</i>|*</tr>
</table>
<p>* where |<i>x</i>| is the absolute value of <i>x</i></p>
`);
let args = prompt('Enter a luckyNumbers argument string:').split(' '),
numbers = [],
strings = [],
obj = {}, // object to pass to our luckyNumbers function
msg = '';
for (let x = 0; x < args.length; x++) {
if (isNaN(parseInt(args[x]))) strings.push(args[x].toUpperCase());
else numbers.push(parseInt(args[x]));
}
// check strings
switch (true) {
case (strings.length > 1):
msg += 'Too many arguments.';
break;
case (strings.length == 0): break;
case (strings[0] != 'LUCKY' && strings[0] != 'EVENLUCKY'):
msg += `Unknown argument: ${strings[0]}.`;
break;
case (strings[0] == 'EVENLUCKY'): obj.even = true;
}
// check numbers
switch (true) {
case (numbers.length == 0):
msg += 'Missing number argument.';
break;
case (numbers.length > 2):
msg += 'Too many number arguments.';
break;
case (numbers.length == 1):
if (numbers[0] > 0) obj.nth = numbers[0];
else obj.through = Math.abs(numbers[0]);
break;
case (numbers.length == 2):
// both negative
if (numbers[0] < 0 && numbers[1] < 0) {
msg += 'Missing positive argument';
break;
}
// negative + positive
numbers.sort();
if (numbers[0] < 0 && numbers[1] > 0) {
obj.range = [numbers[1], Math.abs(numbers[0])];
break;
}
// both positive
if (numbers[0] > 0 && numbers[1] > 0) {
obj.through = [numbers[0]-1, numbers[1]];
}
}
if (msg.length > 0)
document.write(`<p>${msg}<br>Reload to try again</p>`);
else {
let res;
try { res = luckyNumbers(obj); }
catch (err) {
document.write(`<p>${err}<br>Reload to try again</p>`);
}
finally {
if (typeof res == 'object' ) res = res.join(', ');
document.write(`
<p>
<b>Input: </b>${args.join(' ')}<br>
<b>Result: </b>${res}
</p>
<p>Reload to continue</p>
`)
}
}
})();
Using the task demonstrations again, the I/O part looks like:
- Output:
Input: 1 20 Result: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79
Input: -20 evenLucky Result: 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76
Input: 6000 -6100 Result: 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093
Input: -6100 evenlucky 6000 Result: 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092
Input: 10000 Result: 115591
Input: Evenlucky 10000 Result: 111842
jq
Works with jq and jaq, the C and Rust implementions of jq
Also works with gojq, the Go implementation, but gojq requires a very large amount of memory to complete the last task (finding the 10,000th even lucky number).
The following program has been written to run using the C, Go and Rust implementations of jq and is therefore not as succinct as it would otherwise have been. Also, the mechanisms for passing in command-line parameters differ amongst the three implementations, so the program presented here expects the parameters to be presented on a single line as input. Thus a possible invocation would be:
JQ -Rrcf program.jq <<< '1 20'
The disadvantage of the sieve-based approach used below is the difficulty of choosing a sieve size that is on the one hand sufficient but on the other frugal. No claim is made for the algorithm used to determine the sieve size here other than it is reasonable for problems sufficiently similar to the ones solved here. However, if the sieve size turns out to be insufficient, an error condition will be raised.
# Preliminaries:
# This def can be omitted if using jq or gojq:
def range($a;$b;$c): $a | while(. < $b; .+$c);
# jaq does not support string interpolation so, for brevity:
def tos: tostring;
# The following def should be modified if an alternative mechanism for
# reading the parameter arguments is used:
def args: {args: [splits(" *")]};
def argsSize: .args|length;
# Input: an array
# Emit the items in the array until the condition on the items is met.
# The item for which the condition is first met is NOT emitted.
def emit_until(cond):
length as $length
| if $length == 0 or (.[0]|cond) then empty
else . as $in
| {i:0, ok: true}
| while(.ok;
.i+=1
| .ok = .i < $length and ($in[.i] | cond | not) )
| $in[.i]
end;
# input: a number or a string
# If the input is or can be converted to a number using tonumber, then return the number
# else return false.
def isnumber:
if type == "number" then .
elif type == "string" then tonumber? // false
else false
end;
# input: anything
# output: a boolean
def isinteger:
if type == "number" then . == floor
else isnumber as $x
| if $x then $x | (. == floor) else false end
end;
# mark and collapse
def removeEvery($n):
reduce range($n-1; length; $n) as $i (.; .[$i]=null)
| map(select(.));
# Input: {lucky}
def filterLucky:
(.lucky|length) as $length
| .n = 2
| until( .n >= $length;
.lucky[.n-1] as $m
| if $m then .lucky |= removeEvery($m) | .n += 1
else .n = $length
end )
| del(.n);
def printSingle($j):
if $j >= 1 + (.lucky|length) then "Argument is too big" | error
else
(if .odd then "Lucky number #" else "Lucky even number #" end)
+ ($j|tos) + " = " + (.lucky[$j-1]|tos)
end;
# like jq's range($j-1; $k)
def printRange($j; $k):
if $k >= (.lucky|length) then "Argument " + ($k|tos) + " is too big" | error
elif .odd
then "Lucky numbers " + ($j|tos) + " to " + ($k|tos) + " inclusive are:",
.lucky[$j-1:$k]
else "Lucky even numbers " + ($j|tos) + " to " + ($k|tos) + " inclusive are:",
.lucky[$j-1:$k]
end;
def printBetween($j; $k):
.lucky[-1] as $max
| if $j > $max or $k > $max
then "At least one argument is too big" | error
else
(if .odd
then "Lucky numbers between " + ($j|tos) + " and " + ($k|tos) + " are:"
else "Lucky even numbers between " + ($j|tos) + " and " + ($k|tos) + " are:"
end),
[.lucky | emit_until(. > $k) | select(. >= $j)]
end;
def odd:
if argsSize < 3 then true
else (.args[2] | tostring | ascii_downcase)
| if . == "lucky" or . == "odd" then true
elif . == "evenlucky" or . == "even" then false
else "Third argument " + (.args[2]|tos) + " is invalid" | error
end
end;
# Input: {odd}
def init($n):
if .odd
then .lucky = reduce range(0;$n) as $i (null; . + [$i*2 + 1])
else .lucky = reduce range(0;$n) as $i (null; . + [$i*2 + 2])
end;
# Emit {args, j, k, odd, single} or raise an error
def gatherArgs:
args
| if argsSize | (. < 1 or . > 3)
then "There must be between 1 and 3 command line arguments" | error
else .j = (.args[0] | isnumber )
| .k = (.args[1] | isnumber )
| .single = (argsSize == 1 or .args[1] == ",")
| .odd = odd
| if (.j | isinteger | not) or (.j < 1)
then "First argument " + (.args[0]|tos) + " must be a positive integer" | error
elif argsSize >= 2 and .args[1] != "," and (.k | isinteger | not)
then "Second argument " + (.args[1]|tos) + " must be an integer or ," | error
else .
end
| if .k and .k >= 0 and .j > .k
then "Second argument cannot be less than first" | error
else .
end
end ;
def start:
gatherArgs
| (if .k then (if .k > 0 then .k else null end) else .j end) as $size
| (if $size then ($size | . * (tostring|length|.*.)) else -.k end) as $size
| init($size)
| filterLucky
| if .single then printSingle(.j)
elif .k > 0 then printRange(.j; .k)
else .k |= - .
| if (.j > .k)
then "The second argument cannot be less in absolute value than first" | error
else printBetween(.j; .k)
end
end;
start
- Output:
Lucky numbers 1 to 20 inclusive are: [1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79] Lucky even numbers 1 to 20 inclusive are: [2,4,6,10,12,18,20,22,26,34,36,42,44,50,52,54,58,68,70,76] Lucky numbers between 6000 and 6100 are: [6009,6019,6031,6049,6055,6061,6079,6093] Lucky even numbers between 6000 and 6100 are: [6018,6020,6022,6026,6036,6038,6050,6058,6074,6090,6092] Lucky number #1000 = 8809 Lucky even number #10000 = 111842
Julia
This iterator for lucky numbers is semi-lazy: it completes one pass of the filter each iteration.
using Base, StringDistances
struct Lucky
start::Int
nmax::Int
Lucky(iseven, nmax) = new(iseven ? 2 : 1, nmax)
end
struct LuckyState
nextindex::Int
sequence::Vector{Int}
end
Base.eltype(iter::Lucky) = Int
function Base.iterate(iter::Lucky, state = LuckyState(1, collect(iter.start:2:iter.nmax)))
if length(state.sequence) < state.nextindex
return nothing
elseif state.nextindex == 1
return (iter.start, LuckyState(2, state.sequence))
end
result = state.sequence[state.nextindex]
newsequence = Vector{Int}()
for (i, el) in enumerate(state.sequence)
if i % result != 0
push!(newsequence, el)
end
end
(result, LuckyState(state.nextindex + 1, newsequence))
end
function luckyindex(j, wanteven, k=0)
topindex = max(j, k) + 4
luck = Lucky(wanteven, topindex * 20)
iter_result = iterate(luck)
while iter_result != nothing
(elem, state) = iter_result
iter_result = iterate(luck, state)
if iter_result != nothing && iter_result[2].nextindex > topindex
return iter_result[2].sequence[k > j ? (j:k) : j]
end
end
throw("Index $j out of range for nmax of $(luck.nmax).")
end
function luckyrange(j, k, wanteven)
topvalue = max(j, k)
luck = Lucky(wanteven, topvalue + 1)
iter_result = iterate(luck)
(elem, state) = iter_result # save next to last result
while iter_result != nothing
(elem, state) = iter_result
iter_result = iterate(luck, state)
end
filter(x -> (j <= x <= k), state.sequence)
end
function helpdisplay(exitlevel=1)
println("\n", PROGRAM_FILE, " j [-][k] [lucky|evenLucky]")
println("\tj: index wanted or a starting point (index or value)",
"\n\tk: optional ending point (index), \n\t-k: optional ending point (value)\n")
helpstring =
""" | Argument(s) | What is printed |
|--------------------------------------------------------------------------|
| j | jth lucky number (required argument) |
| j , lucky | jth lucky number |
| j , evenLucky | jth even lucky number |
| j k | jth through kth (inclusive) lucky numbers |
| j k lucky | jth through kth (inclusive) lucky numbers |
| j k evenLucky | jth through kth (inclusive) even lucky numbers |
| j -k | all lucky numbers in the value range [m, |k|] |
| j -k lucky | all lucky numbers in the value range [m, |k|] |
| j -k evenLucky | all even lucky numbers in the value range [m, |k|] |
|--------------------------------------------------------------------------|\n\n"""
println(helpstring)
exit(exitlevel)
end
function parsecommandline()
comma = false
evenLucky = false
range = false
j = k = 0
if length(ARGS) < 1
helpdisplay()
end
for (pos, arg) in enumerate(ARGS)
if pos == 1
j = tryparse(Int, arg)
if j == nothing
println("The first argument must be a positive integer.\n")
helpdisplay()
end
elseif pos == 2 || (pos == 3 && comma)
k = tryparse(Int, arg)
if k == nothing
k = 0
if arg == ","
comma = true
continue
elseif arg == "lucky"
continue
elseif arg == "evenLucky"
evenLucky = true
elseif compare(Hamming(), arg, "lucky") > 0.4 || compare(Hamming(), arg, "evenLucky") > 0.4
println("Did you misspell \"lucky\" or \"evenLucky\"? Check capitalization.\n")
helpdisplay()
else
helpdisplay()
end
elseif k < 0
k = -k
range = true
end
elseif pos == 3 || pos == 4 && comma
if arg == ","
comma = true
continue
elseif arg == "lucky"
continue
elseif arg == "evenLucky"
evenLucky = true
elseif compare(Hamming(), arg, "lucky") > 0.1 || compare(Hamming(), arg, "evenLucky") > 0.1
println("Did you misspell "\lucky\" or "\evenLucky\"?\n\n")
helpdisplay()
else
helpdisplay()
end
elseif arg == "lucky"
continue
elseif arg == "evenLucky"
evenLucky = true
else
println("Too many arguments.\n")
helpdisplay()
end
end
(j, k, evenLucky, range)
end
function runopts()
(j, k, evenLucky, range) = parsecommandline()
if j < 1 || (k != 0 && j >= k)
throw("Lucky number integer parameters out of range: $(typeof(j)), $j, $(typeof(k)), $k")
end
if range
println(luckyrange(j, k, evenLucky))
else
println(luckyindex(j, evenLucky, k))
end
end
runopts()
- Output:
> julia luckymath.jl 1 20 [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] > julia luckymath.jl 1 20 evenLucky [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] > julia luckymath.jl 6000 -6100 [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] > julia luckymath.jl 6000 -6100 evenLucky [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092] > julia luckymath.jl 10000 115591 > julia luckymath.jl 10000 evenLucky 111842
Kotlin
// version 1.1.51
typealias IAE = IllegalArgumentException
val luckyOdd = MutableList(100000) { it * 2 + 1 }
val luckyEven = MutableList(100000) { it * 2 + 2 }
fun filterLuckyOdd() {
var n = 2
while (n < luckyOdd.size) {
val m = luckyOdd[n - 1]
val end = (luckyOdd.size / m) * m - 1
for (j in end downTo m - 1 step m) luckyOdd.removeAt(j)
n++
}
}
fun filterLuckyEven() {
var n = 2
while (n < luckyEven.size) {
val m = luckyEven[n - 1]
val end = (luckyEven.size / m) * m - 1
for (j in end downTo m - 1 step m) luckyEven.removeAt(j)
n++
}
}
fun printSingle(j: Int, odd: Boolean) {
if (odd) {
if (j >= luckyOdd.size) throw IAE("Argument is too big")
println("Lucky number $j = ${luckyOdd[j - 1]}")
}
else {
if (j >= luckyEven.size) throw IAE("Argument is too big")
println("Lucky even number $j = ${luckyEven[j - 1]}")
}
}
fun printRange(j: Int, k: Int, odd: Boolean) {
if (odd) {
if (k >= luckyOdd.size) throw IAE("Argument is too big")
println("Lucky numbers $j to $k are:\n${luckyOdd.drop(j - 1).take(k - j + 1)}")
}
else {
if (k >= luckyEven.size) throw IAE("Argument is too big")
println("Lucky even numbers $j to $k are:\n${luckyEven.drop(j - 1).take(k - j + 1)}")
}
}
fun printBetween(j: Int, k: Int, odd: Boolean) {
val range = mutableListOf<Int>()
if (odd) {
val max = luckyOdd[luckyOdd.lastIndex]
if (j > max || k > max) {
throw IAE("At least one argument is too big")
}
for (num in luckyOdd) {
if (num < j) continue
if (num > k) break
range.add(num)
}
println("Lucky numbers between $j and $k are:\n$range")
}
else {
val max = luckyEven[luckyEven.lastIndex]
if (j > max || k > max) {
throw IAE("At least one argument is too big")
}
for (num in luckyEven) {
if (num < j) continue
if (num > k) break
range.add(num)
}
println("Lucky even numbers between $j and $k are:\n$range")
}
}
fun main(args: Array<String>) {
if (args.size !in 1..3) throw IAE("There must be between 1 and 3 command line arguments")
filterLuckyOdd()
filterLuckyEven()
val j = args[0].toIntOrNull()
if (j == null || j < 1) throw IAE("First argument must be a positive integer")
if (args.size == 1) { printSingle(j, true); return }
if (args.size == 2) {
val k = args[1].toIntOrNull()
if (k == null) throw IAE("Second argument must be an integer")
if (k >= 0) {
if (j > k) throw IAE("Second argument can't be less than first")
printRange(j, k, true)
}
else {
val l = -k
if (j > l) throw IAE("The second argument can't be less in absolute value than first")
printBetween(j, l, true)
}
return
}
var odd =
if (args[2].toLowerCase() == "lucky") true
else if (args[2].toLowerCase() == "evenlucky") false
else throw IAE("Third argument is invalid")
if (args[1] == ",") {
printSingle(j, odd)
return
}
val k = args[1].toIntOrNull()
if (k == null) throw IAE("Second argument must be an integer or a comma")
if (k >= 0) {
if (j > k) throw IAE("Second argument can't be less than first")
printRange(j, k, odd)
}
else {
val l = -k
if (j > l) throw IAE("The second argument can't be less in absolute value than first")
printBetween(j, l, odd)
}
}
- Output:
$ java -jar lucky.jar 1 20 Lucky numbers 1 to 20 are: [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] $ java -jar lucky.jar 1 20 evenLucky Lucky even numbers 1 to 20 are: [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] $ java -jar lucky.jar 6000 -6100 Lucky numbers between 6000 and 6100 are: [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] $ java -jar lucky.jar 6000 -6100 evenLucky Lucky even numbers between 6000 and 6100 are: [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092] $ java -jar lucky.jar 10000 , lucky Lucky number 10000 = 115591 $ java -jar lucky.jar 10000 , evenLucky Lucky even number 10000 = 111842
Mathematica /Wolfram Language
Save the following code in the file script.wls and execute the wolframscript from the command line:
ClearAll[GetLuckies, GetEvenLuckies]
GetLuckies[max_] := Module[{luckies, f, i},
luckies = Range[1, max, 2];
f[n_] := Block[{k = luckies[[n]]}, luckies = Delete[luckies, Table[{k}, {k, k, Length@luckies, k}]]];
i = 2;
While[i < Length[luckies],
f[i];
i++
];
luckies
]
GetEvenLuckies[max_] := Module[{lst, i, len},
lst = Range[2, max, 2];
i = 2;
While[i <= (len = Length@lst) && (k = lst[[i]]) <= len,
lst = Drop[lst, {k, len, k}];
i++
];
lst
]
GiveLucky[s_String] := GiveLucky[StringSplit[s, " "]]
GiveLucky[args_List] := Module[{argc = Length[args], j, k, type},
If[argc > 3,
Print["Too many arguments"]
,
If[argc == 0,
Print["Too few arguments"]
,
Switch[argc, 1,
j = Interpreter["Integer"][args[[1]]];
If[! FailureQ[j],
If[j > 0,
Print@GetLuckies[20 j][[j]]
,
Print["j should be positive"]
]
,
Print["one argument that is not an integer"]
]
, 2,
j = Interpreter["Integer"][args[[1]]];
k = Interpreter["Integer"][args[[2]]];
If[! FailureQ[j] \[And] ! FailureQ[k],
If[j > 0,
If[k > 0,
Print@GetLuckies[20 k][[j ;; k]]
,
Print@Select[GetLuckies[-k], GreaterEqualThan[j]]
]
,
Print["j should be positive"]
]
,
Print["one of the two arguments is not an integer\[Ellipsis]"]
]
, 3,
If[args[[2]] === ",",
j = Interpreter["Integer"][args[[1]]];
If[! FailureQ[j],
If[j > 0,
type = args[[3]];
If[MatchQ[type, "evenLucky" | "lucky"],
If[type === "evenLucky",
Print@GetEvenLuckies[20 j][[j]]
,
Print@GetLuckies[20 j][[j]]
]
,
Print["unknown type ", type]
]
,
Print["j should be positive"]
]
,
Print["j should be an integer"]
]
,
j = Interpreter["Integer"][args[[1]]];
k = Interpreter["Integer"][args[[2]]];
If[! FailureQ[j] \[And] ! FailureQ[k],
If[j > 0,
type = args[[3]];
If[k > 0,
If[MatchQ[type, "evenLucky" | "lucky"],
If[type === "evenLucky",
Print@GetEvenLuckies[20 k][[j ;; k]]
,
Print@GetLuckies[20 k][[j ;; k]]
]
,
Print["unknown type ", type]
]
,
If[MatchQ[type, "evenLucky" | "lucky"],
If[type === "evenLucky",
Print@Select[GetEvenLuckies[-k], GreaterEqualThan[j]]
,
Print@Select[GetLuckies[-k], GreaterEqualThan[j]]
]
,
Print["unknown type ", type]
]
]
,
Print["j should be positive"]
]
,
Print["one of the two arguments is not an integer\[Ellipsis]"]
]
]
]
]
]
]
GiveLucky[Last@$ScriptCommandLine]
- Output:
wolframscript -file script.wls -args "1 20 lucky" {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79} wolframscript -file script.wls -args "1 20 evenLucky" {2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76} wolframscript -file script.wls -args "6000 -6100" {6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093} wolframscript -file script.wls -args "6000 -6100 evenLucky" {6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092} wolframscript -file script.wls -args "10000 , lucky" 115591 wolframscript -file script.wls -args "10000 , evenLucky" 111842
Nim
For the generation of lucky numbers, we use the second Python algorithm, modified to return a sequence.
import os, strformat, strutils
type LuckyKind {.pure.} = enum Lucky = "lucky", EvenLucky = "evenlucky"
const NoValue = 0 # Indicates that no value have been specified.
####################################################################################################
# Lucky numbers generation.
func initLuckyNumbers(nelems: int; kind: LuckyKind): seq[int] =
## Initialize a list of lucky numbers.
result = newSeqOfCap[int](nelems)
for i in 0..<nelems:
var k = i
for j in countdown(result.high, 1):
k = k * result[j] div (result[j] - 1)
result.add 2 * k + 1 + ord(kind)
####################################################################################################
# Printing.
template name(kind: LuckyKind): string =
if kind == Lucky: "Lucky" else: "Even lucky"
proc printSingle(j: int; kind: LuckyKind) =
## Print the lucky number at a given index.
let luckySeq = initLuckyNumbers(j, kind)
echo &"{name(kind)} number at index {j} is {luckySeq[j - 1]}"
proc printRange(j, k: int; kind: LuckyKind) =
## print the luck numbers in a range of indexes.
let luckySeq = initLuckyNumbers(k, kind)
var list = &"{name(kind)} numbers at indexes {j} to {k} are: "
let start = list.len
for idx in (j - 1)..(k - 1):
list.addSep(", ", start)
list.add $luckySeq[idx]
echo list
proc printInRange(j, k: int; kind: LuckyKind) =
## Print the lucky numbers in a range of values.
let luckySeq = initLuckyNumbers(k, kind) # "k" is greater than needed.
var list = &"{name(kind)} numbers between {j} to {k} are: "
let start = list.len
for val in luckySeq:
if val > k: break
if val > j:
list.addSep(", ", start)
list.add $val
echo list
####################################################################################################
# Command line parsing.
proc parseCommandLine(): tuple[j, k: int; kind: LuckyKind] =
## Parse the command line.
# Internal exception to catch invalid argument value.
type InvalidArgumentError = object of ValueError
template raiseError(message, value = "") =
## Raise an InvalidArgumentError.
raise newException(InvalidArgumentError, message & value & '.')
result = (Novalue, Novalue, Lucky)
try:
if paramCount() notin 1..3: raiseError "Wrong number of arguments"
# First argument: "j" value.
let p1 = paramStr(1)
try:
result.j = parseInt(p1)
if result.j <= 0: raiseError "Expected a positive number, got: ", p1
except ValueError:
raiseError "Expected an integer, got: ", p1
# Second argument: "k" value or a comma.
if paramCount() > 1:
let p2 = paramStr(2)
if p2 == ",":
# Must be followed by the kind of lucky number.
if paramCount() != 3: raiseError "Missing kind argument"
else:
try:
result.k = parseInt(p2)
if result.k == 0: raiseError "Expected a non null number, got: ", p2
except ValueError:
raiseError "Expected an integer, got: ", p2
# Third argument: number kind.
if paramCount() == 3:
let p3 = paramStr(3)
try:
result.kind = parseEnum[LuckyKind](p3.toLowerAscii())
except ValueError:
raiseError "Wrong kind: ", p3
except InvalidArgumentError:
quit getCurrentExceptionMsg()
#———————————————————————————————————————————————————————————————————————————————————————————————————
# Main program.
let (j, k, kind) = parseCommandLine()
if k == NoValue:
# Print jth value.
printSingle(j, kind)
elif k > 0:
# Print jth to kth values.
printRange(j, k, kind)
else:
# Print values in range j..(-k).
printInRange(j, -k, kind)
- Output:
./lucky_numbers 1 20 Lucky numbers at indexes 1 to 20 are: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79 ./lucky_numbers 1 20 evenlucky Even lucky numbers at indexes 1 to 20 are: 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76 ./lucky_numbers 6000 -6100 Lucky numbers between 6000 to 6100 are: 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093 ./lucky_numbers 6000 -6100 evenlucky Even lucky numbers between 6000 to 6100 are: 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092 ./lucky_numbers 10000 , lucky Lucky number at index 10000 is 115591 ./lucky_numbers 10000 , evenlucky Even lucky number at index 10000 is 111842
Perl
The module Perl6::GatherTake
emulates the Raku gather/take syntax, and allows us to access values from what acts (mostly) like a lazy list.
use Perl6::GatherTake;
sub luck {
my($a,$b) = @_;
gather {
my $i = $b;
my(@taken,@rotor,$j);
take 0; # 0th index is a placeholder
push @taken, take $a;
while () {
for ($j = 0; $j < @rotor; $j++) {
--$rotor[$j] or last;
}
if ($j < @rotor) {
$rotor[$j] = $taken[$j+1];
}
else {
take $i;
push @taken, $i;
push @rotor, $i - @taken;
}
$i += 2;
}
}
}
# fiddle with user input
$j = shift || usage();
$k = shift || ',';
$l = shift || 'lucky';
usage() unless $k =~ /,|-?\d+/;
usage() unless $l =~ /^(even)?lucky$/i;
sub usage { print "Args must be: j [,|k|-k] [lucky|evenlucky]\n" and exit }
# seed the iterator
my $lucky = $l =~ /^l/i ? luck(1,3) : luck(2,4);
# access values from 'lazy' list
if ($k eq ',') {
print $lucky->[$j]
} elsif ($k > $j) {
print $lucky->[$_] . ' ' for $j..$k
} elsif ($k < 0) {
while () { last if abs($k) < $lucky->[$i++] } # must first extend the array
print join ' ', grep { $_ >= $j and $_ <= abs($k) } @$lucky
}
print "\n"
- Output:
$ ./lucky Args must be: j [,|k|-k] [lucky|evenlucky] $ ./lucky 20 , lucky 79 $ ./lucky 20 , evenlucky 76 $ ./lucky 1 20 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 $ ./lucky 1 20 evenlucky 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76 $ ./lucky 6000 -6100 6009 6019 6031 6049 6055 6061 6079 6093 $ ./lucky 6000 -6100 evenLucky 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092 $ ./lucky 10000 115591 $ ./lucky 10000 , EVENLUCKY 111842
Phix
with javascript_semantics constant luckyMax = 120000 sequence lucky procedure filterLucky() integer n = 2 while n<=length(lucky) do integer m = lucky[n], l = m-1 for k=m+1 to length(lucky) do if mod(k,m)!=0 then l += 1 lucky[l] = lucky[k] end if end for if l>=length(lucky) then exit end if lucky = lucky[1..l] n += 1 end while end procedure constant helptxt = """ argument(s) | what is displayed ======================================= j | jth lucky number j [,] lucky | jth lucky number j [,] evenLucky | jth even lucky number j k | jth through kth (inclusive) lucky numbers j k lucky | jth through kth (inclusive) lucky numbers j k evenLucky | jth through kth (inclusive) even lucky numbers j -k | all lucky numbers in the range j to k j -k lucky | all lucky numbers in the range j to k j -k evenLucky | all even lucky numbers in the range j to k """ procedure fatal(string msg) puts(1,msg) puts(1,helptxt) {} = wait_key() abort(0) end procedure procedure process(sequence cl) -- -- Allow eg "lucky j , evenLucky" to be == "lucky j evenLucky" -- if length(cl)=3 and cl[2]="," then cl[2..2] = {} end if integer j, k bool single = true, range = true, oddluck = true for i=1 to length(cl) do string cli = cl[i] if cli[1]<='9' then -- (includes '-') sequence d = scanf(cl[i],"%d") if length(d)!=1 then fatal("unrecognised "&cli) end if if i>2 then fatal("too many numbers") end if integer n = d[1][1] if i=1 then if n<1 then fatal("first argument must be a positive integer") end if j = n else single = false if n<0 then range = false n = -n end if if n<j then fatal("second argument cannot be less than first") end if k = n end if else integer l = find(cli,{"lucky","evenLucky"}) if l=0 then fatal("unrecognised "&cli) end if if i!=length(cl) then fatal(cli&" must be last parameter") end if oddluck = (l=1) end if end for lucky = tagset(luckyMax,2-oddluck,2) filterLucky() printf(1,"Output when args are %s\n",{join(cl)}) string evenstr = iff(oddluck?"":"even ") if single then if j>length(lucky) then fatal(sprintf("the argument, %d, is too big", j)) end if printf(1,"Lucky %snumber %d = %d\n",{evenstr,j, lucky[j]}) elsif range then if k>length(lucky) then fatal(sprintf("the argument, %d, is too big", k)) end if printf(1,"Lucky %snumbers %d to %d are: %v\n",{evenstr,j,k,lucky[j..k]}) else if j>lucky[$] then fatal("start of range is too big") elsif k>lucky[$] then fatal("end of range is too big") end if integer m = abs(binary_search(j,lucky)), n = binary_search(k,lucky) if n<0 then n = -n-1 end if printf(1,"Lucky %snumbers between %d and %d are: %v\n", {evenstr,j,k,lucky[m..n]}) end if end procedure procedure main() sequence cl = command_line() if length(cl)=2 then -- fatal("at least one argument must be supplied") -- (if preferred) sequence tests = {"1 20", "1 20 evenLucky", "20 lucky", "20 evenLucky", "6000 -6100", "6000 -6100 evenLucky", "10000 lucky", "10000 evenLucky"} -- (done this way to exercise the real command line handling...) if cl[1]=cl[2] then -- (compiled) cl = cl[1..1] elsif platform()=WINDOWS then -- (and interpreted) cl[1] = substitute(cl[1],"pw","p") -- (pw.exe -> p.exe) end if for i=1 to length(cl) do if find(' ',cl[i]) then cl[i] = sprintf("\"%s\"",{cl[i]}) end if end for for t=1 to length(tests) do if platform()=JS then -- (...except when we can't do that, of course) process(split(tests[t])) else string cmd = join(append(deep_copy(cl),tests[t])) -- printf(1,"running %s\n",{cmd}) {} = system_exec(cmd) end if end for puts(1, "tests complete\n") {} = wait_key() else cl = cl[3..$] -- ({1,2} are {interperter,source} or {exe,exe}) process(cl) end if end procedure main()
- Output:
You may need to run this from a [windows] console to get them all on the same screen, and use p.exe rather than pw.exe
Output when args are 1 20 Lucky numbers 1 to 20 are: {1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79} Output when args are 1 20 evenLucky Lucky even numbers 1 to 20 are: {2,4,6,10,12,18,20,22,26,34,36,42,44,50,52,54,58,68,70,76} Output when args are 20 lucky Lucky number 20 = 79 Output when args are 20 evenLucky Lucky even number 20 = 76 Output when args are 6000 -6100 Lucky numbers between 6000 and 6100 are: {6009,6019,6031,6049,6055,6061,6079,6093} Output when args are 6000 -6100 evenLucky Lucky even numbers between 6000 and 6100 are: {6018,6020,6022,6026,6036,6038,6050,6058,6074,6090,6092} Output when args are 10000 lucky Lucky number 10000 = 115591 Output when args are 10000 evenLucky Lucky even number 10000 = 111842 tests complete
PicoLisp
(off *Even)
(de nn (Lst N)
(seek
'((L)
(when (car L) (=0 (dec 'N))) )
Lst ) )
(de lucky (B)
(let Lst (range (if *Even 2 1) B 2)
(for A (cdr Lst)
(for (L (nn Lst A) L (nn (cdr L) A))
(set L) ) )
(filter bool Lst) ) )
(argv . *Argv) # without validations
(when (= "evenLucky" (last *Argv)) (on *Even))
(setq *Lst (lucky 7000))
(let (A (format (car *Argv)) B (format (cadr *Argv)))
(println
(if (lt0 B)
(filter '((N) (<= A N (abs B))) *Lst)
(head B (nth *Lst A)) ) ) )
- Output:
$ pil ./lucky.l 1 20 (1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79) $ pil ./lucky.l 1 20 evenLucky (2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76) $ pil ./lucky.l 6000 -6100 (6009 6019 6031 6049 6055 6061 6079 6093) $ pil ./lucky.l 6000 -6100 evenLucky (6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092)
Python
The generator
from __future__ import print_function
def lgen(even=False, nmax=1000000):
start = 2 if even else 1
n, lst = 1, list(range(start, nmax + 1, 2))
lenlst = len(lst)
yield lst[0]
while n < lenlst and lst[n] < lenlst:
yield lst[n]
n, lst = n + 1, [j for i,j in enumerate(lst, 1) if i % lst[n]]
lenlst = len(lst)
# drain
for i in lst[n:]:
yield i
The argument handler
from itertools import islice
import sys, re
class ArgumentError(Exception):
pass
def arghandler(argstring):
match_obj = re.match( r"""(?mx)
(?:
(?P<SINGLE>
(?: ^ (?P<SINGLEL> \d+ ) (?: | \s , \s lucky ) \s* $ )
|(?: ^ (?P<SINGLEE> \d+ ) (?: | \s , \s evenLucky ) \s* $ )
)
|(?P<KTH>
(?: ^ (?P<KTHL> \d+ \s \d+ ) (?: | \s lucky ) \s* $ )
|(?: ^ (?P<KTHE> \d+ \s \d+ ) (?: | \s evenLucky ) \s* $ )
)
|(?P<RANGE>
(?: ^ (?P<RANGEL> \d+ \s -\d+ ) (?: | \s lucky ) \s* $ )
|(?: ^ (?P<RANGEE> \d+ \s -\d+ ) (?: | \s evenLucky ) \s* $ )
)
)""", argstring)
if match_obj:
# Retrieve group(s) by name
SINGLEL = match_obj.group('SINGLEL')
SINGLEE = match_obj.group('SINGLEE')
KTHL = match_obj.group('KTHL')
KTHE = match_obj.group('KTHE')
RANGEL = match_obj.group('RANGEL')
RANGEE = match_obj.group('RANGEE')
if SINGLEL:
j = int(SINGLEL)
assert 0 < j < 10001, "Argument out of range"
print("Single %i'th lucky number:" % j, end=' ')
print( list(islice(lgen(), j-1, j))[0] )
elif SINGLEE:
j = int(SINGLEE)
assert 0 < j < 10001, "Argument out of range"
print("Single %i'th even lucky number:" % j, end=' ')
print( list(islice(lgen(even=True), j-1, j))[0] )
elif KTHL:
j, k = [int(num) for num in KTHL.split()]
assert 0 < j < 10001, "first argument out of range"
assert 0 < k < 10001 and k > j, "second argument out of range"
print("List of %i ... %i lucky numbers:" % (j, k), end=' ')
for n, luck in enumerate(lgen(), 1):
if n > k: break
if n >=j: print(luck, end = ', ')
print('')
elif KTHE:
j, k = [int(num) for num in KTHE.split()]
assert 0 < j < 10001, "first argument out of range"
assert 0 < k < 10001 and k > j, "second argument out of range"
print("List of %i ... %i even lucky numbers:" % (j, k), end=' ')
for n, luck in enumerate(lgen(even=True), 1):
if n > k: break
if n >=j: print(luck, end = ', ')
print('')
elif RANGEL:
j, k = [int(num) for num in RANGEL.split()]
assert 0 < j < 10001, "first argument out of range"
assert 0 < -k < 10001 and -k > j, "second argument out of range"
k = -k
print("List of lucky numbers in the range %i ... %i :" % (j, k), end=' ')
for n in lgen():
if n > k: break
if n >=j: print(n, end = ', ')
print('')
elif RANGEE:
j, k = [int(num) for num in RANGEE.split()]
assert 0 < j < 10001, "first argument out of range"
assert 0 < -k < 10001 and -k > j, "second argument out of range"
k = -k
print("List of even lucky numbers in the range %i ... %i :" % (j, k), end=' ')
for n in lgen(even=True):
if n > k: break
if n >=j: print(n, end = ', ')
print('')
else:
raise ArgumentError('''
Error Parsing Arguments!
Expected Arguments of the form (where j and k are integers):
j # Jth lucky number
j , lucky # Jth lucky number
j , evenLucky # Jth even lucky number
#
j k # Jth through Kth (inclusive) lucky numbers
j k lucky # Jth through Kth (inclusive) lucky numbers
j k evenLucky # Jth through Kth (inclusive) even lucky numbers
#
j -k # all lucky numbers in the range j --? |k|
j -k lucky # all lucky numbers in the range j --? |k|
j -k evenLucky # all even lucky numbers in the range j --? |k|
''')
if __name__ == '__main__':
arghandler(' '.join(sys.argv[1:]))
- Output:
# Output when arguments are: 1 20 lucky List of 1 ... 20 lucky numbers: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, # Output when arguments are: 1 20 evenLucky List of 1 ... 20 even lucky numbers: 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76, # Output when arguments are: 6000 -6100 lucky List of lucky numbers in the range 6000 ... 6100 : 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093, # Output when arguments are: 6000 -6100 evenLucky List of even lucky numbers in the range 6000 ... 6100 : 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092, # Output when arguments are: 10000 Single 10000'th lucky number: 115591 # Output when arguments are: 10000 , evenLucky Single 10000'th even lucky number: 111842
Python: streaming lazy generator
The following streaming version of function lgen returns odd or even lucky numbers until reaching system limits. Instead of creating a bounded table and deleting elements, it uses the insight that after each iteration the remaining numbers are shuffled left, modifying their indices in a regular way. Reversing this process tracks the k'th lucky number in the final list back to its position in the initial list of integers, and hence determines its value without any need to build the table. The only storage requirement is for the list of numbers found so far.
Based on the algorithm at https://oeis.org/A000959/a000959.txt.
from itertools import count
def lgen(even=False):
lucky = []
if not even:
yield 1
for k in count(1):
for l in reversed(lucky):
k = (k*l)//(l-1)
lucky.append(2*k+1 + even)
yield 2*k+1 + even
Raku
(formerly Perl 6)
sub luck(\a,\b) {
gather {
my @taken = take a;
my @rotor;
my $i = b;
loop {
loop (my $j = 0; $j < @rotor; $j++) {
--@rotor[$j] or last;
}
if $j < @rotor {
@rotor[$j] = @taken[$j+1];
}
else {
push @taken, take $i;
push @rotor, $i - @taken;
}
$i += 2;
}
}
}
constant @lucky = luck(1,3);
constant @evenlucky = luck(2,4);
subset Luck where m:i/^ 'even'? 'lucky' $/;
multi MAIN (Int $num where * > 0) {
say @lucky[$num-1];
}
multi MAIN (Int $num where * > 0, ',', Luck $howlucky = 'lucky') {
say @::(lc $howlucky)[$num-1];
}
multi MAIN (Int $first where * > 0, Int $last where * > 0, Luck $howlucky = 'lucky') {
say @::(lc $howlucky)[$first-1 .. $last - 1];
}
multi MAIN (Int $min where * > 0, Int $neg-max where * < 0, Luck $howlucky = 'lucky') {
say grep * >= $min, (@::(lc $howlucky) ...^ * > abs $neg-max);
}
- Output:
$ ./lucky Usage: ./lucky <num> ./lucky <num> , [<howlucky>] ./lucky <first> <last> [<howlucky>] ./lucky <min> <neg-max> [<howlucky>] $ ./lucky 20 , lucky 79 $ ./lucky 20 , evenlucky 76 $ ./lucky 1 20 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 $ ./lucky 1 20 evenlucky 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76 $ ./lucky 6000 -6100 6009 6019 6031 6049 6055 6061 6079 6093 $ ./lucky 6000 -6100 evenLucky 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092 $ ./lucky 10000 115591 $ ./lucky 10000 , EVENLUCKY 111842
REXX
This REXX version does extra error checking for the arguments.
/*REXX program displays lucky or evenLucky integers (numbers or a number range).*/
parse arg bot top func _ . /*obtain required & optional arguments.*/
if func=='' then func= 'lucky' /*Not specified? Then use the default.*/
s= left('s', bot\==top & top\==",") /*plural results (or maybe not plural).*/
say func 'number's":" bot top '───►' $lucky(bot, top, func, _)
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
$lucky: arg x,y,f,?; if y=='' | y=="," then y= x /*obtain some arguments; set Y.*/
#= 0; $=; ny= y<0 /*set variable NOY: value range*/
if f=='' then f= 'LUCKY'; lucky= (f=="LUCKY") /*assume LUCKY if omitted. */
if f\=='LUCKY' & f\=='EVENLUCKY' then return 'function not valid: ' f
if arg()>3 & ?\='' then return "too many arguments entered: " ?
if x='' then return "1st argument is missing."
if x<1 then return "1st argument isn't a positive integer: " x
if \datatype(x,'W') then return "1st argument isn't an integer: " x
if \datatype(y,'W') then return "2nd argument isn't an integer: " y
if x>ay then return "2nd argument is less than 1st arg."
ay=abs(y); yL=ay; if y>0 then yL= y*10 + y + y /*adjust the upper Y limit. */
/* [↓] build LUCKY | EVENLUCKY*/
do j=1 until j>=yL /*construct list pos. integers.*/
if j//2==(\lucky) then iterate /*EVENLUCKY? Use only even ints*/
if lucky then if (j+1)//6==0 then iterate /*prune if mod 6 ≡ zero.*/
else nop /*balance the IF-THEN logic.*/
else if j //8==0 then iterate /*prune next if mod 8 ≡ zero.*/
#= # + 1 /*bump the counter of numbers. */
$= $ j /*append integer to the $ list.*/
end /*j*/
q=0
do p=3 until q==''; q= word($, p) /*start to prune integer list.*/
if q># then leave /*if integer is too large, stop*/
do j=#%q*q by -q to q /*elide every Qth integer. */
$= delword($, j, 1) /*delete a particular number. */
#= # -1 /*decrease the integer count. */
end /*j*/ /*delete from the right side. */
end /*p*/
@.=
do k=1; parse var $ q $; if q=='' then leave; @.k= q
end /*k*/
@.0=k-1
do m=1 for # /*restrict the found integers. */
if (\ny & (m<x | m>ay)) | (ny & (@.m<x | @.m>ay)) then @.m=
end /*m*/ /* [↑] a list of #s or a range*/
_=
do b=1 for @.0; _= _ @.b /*construct a list of integers.*/
end /*b*/
return space(_) /*remove superfluous blanks. */
- output when using the input of: 1 20 lucky
lucky numbers: 1 20 ───► 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79
- output when using the input of: 1 20 evenlucky
evenLucky numbers: 1 20 ───► 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76
- output when using the input of: 6000 -6100 lucky
lucky numbers: 6000 -6100 ───► 6009 6019 6031 6049 6055 6061 6079 6093
- output when using the input of: 6000 -6100 evenLucky
evenLucky numbers: 6000 -6100 ───► 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092
- output when using the input of: 10000
lucky number: 10000 ───► 115591
- output when using the input of: 10000 , evenLucky
evenLucky number: 10000 ───► 111842
Ring
# Project : Lucky and even lucky numbers
lucky = list(50)
dellucky = []
for n = 1 to 50
lucky[n] = 2*n-1
next
see "the first 20 lucky numbers:" + nl
luckynumbers(lucky)
showarray(lucky)
see nl
lucky = list(50)
dellucky = []
for n = 1 to 50
lucky[n] = 2*n
next
see "the first 20 even lucky numbers:" + nl
luckynumbers(lucky)
showarray(lucky)
see nl
lucky = list(20000)
dellucky = []
for n = 1 to 10000
lucky[n] = 2*n-1
next
see "lucky numbers between 6,000 and 6,100:" + nl
luckynumbers2(lucky)
showarray2(lucky)
see nl
lucky = list(20000)
dellucky = []
for n = 1 to 10000
lucky[n] = 2*n
next
see "even lucky numbers between 6,000 and 6,100:" + nl
luckynumbers2(lucky)
showarray2(lucky)
see nl
func luckynumbers(lucky)
for n = 2 to len(lucky)
dellucky = []
for m = lucky[n] to len(lucky) step lucky[n]
add(dellucky, m)
next
for p = len(dellucky) to 1 step -1
del(lucky, dellucky[p])
next
next
func luckynumbers2(lucky)
for n = 2 to len(lucky)
dellucky = []
for m = lucky[n] to len(lucky) step lucky[n]
add(dellucky, m)
next
for p = len(dellucky) to 1 step -1
del(lucky, dellucky[p])
next
if lucky[n] >= 6100
exit
ok
next
func showarray(vect)
see "["
svect = ""
for n = 1 to 20
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
func showarray2(vect)
see "["
svect = ""
for n = 1 to len(vect)
if vect[n] >= 6000 and vect[n] <= 6100
svect = svect + vect[n] + ", "
ok
next
svect = left(svect, len(svect) - 2)
see svect
see "]" + nl
Output:
the first 20 lucky numbers: [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] the first 20 even lucky numbers: [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] lucky numbers between 6,000 and 6,100: [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] even lucky numbers between 6,000 and 6,100: [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092]
RPL
The program returns even lucky numbers when one of the 2 arguments is negative, which is more idiomatic.
RPL code | Comment |
---|---|
≪
1 CF DUP2 * 0 < ≪ 1 SF ≫ IFT
ABS SWAP ABS DUP2 ≤ ≪ #202h DOERR ≫ IFT
2 → b a n
≪ { } 1 1 FS? + b FOR j j + 2 STEP
DO
DUP n GET → m
≪ { } 1 3 PICK SIZE FOR j
OVER j DUP m + 2 - SUB + m STEP
≫ SWAP DROP 'n' INCR
UNTIL OVER SIZE > END
{ } 1 3 PICK SIZE FOR j
IF OVER j GET DUP a < THEN DROP ELSE + END
NEXT SWAP DROP
≫ ≫ 'LUCKY' STO
|
LUCKY ( a (-)b → { (even)lucky } )
Set flag 1 if a xor b is negative
abort if b ≤ a with an error message
n = 2
generate list of odd/even numbers according to flag 1
loop
m = nth number of the list
for j = 1 to size(list) step m
keep numbers from j to j+m-2
clean stack ; n++
until n > size(list)
for j = 1 to size(list)
keep jth number only if ≥ a
clean stack
return list
|
1 80 LUCKY 1 -80 LUCKY 6000 6100 LUCKY 6000 -6100 LUCKY
- Output:
4: { 1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 } 3: { 2 4 6 10 12 18 20 22 26 34 36 42 44 50 52 54 58 68 70 76 } 2: { 6009 6019 6031 6049 6055 6061 6079 6093 } 1: { 6018 6020 6022 6026 6036 6038 6050 6058 6074 6090 6092 }
A 6000-number sieve requiring more than 30 KB RAM, the last 2 demonstrations have been run on an emulator instead of a genuine calculator.
Ruby
def generator(even=false, nmax=1000000)
start = even ? 2 : 1
Enumerator.new do |y|
n = 1
ary = [0] + (start..nmax).step(2).to_a # adds [0] to revise the 0 beginnings.
y << ary[n]
while (m = ary[n+=1]) < ary.size
y << m
(m...ary.size).step(m){|i| ary[i]=nil}
ary.compact! # remove nil
end
# drain
ary[n..-1].each{|i| y << i}
raise StopIteration
end
end
def lucky(argv)
j, k = argv[0].to_i, argv[1].to_i
mode = /even/i=~argv[2] ? :'even lucky' : :lucky
seq = generator(mode == :'even lucky')
ord = ->(n){"#{n}#{(n%100).between?(11,19) ? 'th' : %w[th st nd rd th th th th th th][n%10]}"}
if k.zero?
puts "#{ord[j]} #{mode} number: #{seq.take(j).last}"
elsif 0 < k
puts "#{ord[j]} through #{ord[k]} (inclusive) #{mode} numbers",
" #{seq.take(k)[j-1..-1]}"
else
k = -k
ary = []
loop do
case num=seq.next
when 1...j
when j..k then ary << num
else break
end
end
puts "all #{mode} numbers in the range #{j}..#{k}",
" #{ary}"
end
end
if __FILE__ == $0
lucky(ARGV)
end
- Output:
C:\>ruby lucky.rb 1 20 1st through 20th (inclusive) lucky numbers [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] C:\>ruby lucky.rb 1 20 evenLucky 1st through 20th (inclusive) even lucky numbers [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] C:\>ruby lucky.rb 6000 -6100 Lucky all lucky numbers in the range 6000..6100 [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] C:\>ruby lucky.rb 6000 -6100 evenLucky all even lucky numbers in the range 6000..6100 [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092] C:\>ruby lucky.rb 10000 10000th lucky number: 115591 C:\>ruby lucky.rb 10000 , EVENLUCKY 10000th even lucky number: 111842
Swift
The lucky numbers sequence:
struct LuckyNumbers : Sequence, IteratorProtocol {
let even: Bool
let through: Int
private var drainI = 0
private var n = 0
private var lst: [Int]
init(even: Bool = false, through: Int = 1_000_000) {
self.even = even
self.through = through
self.lst = Array(stride(from: even ? 2 : 1, through: through, by: 2))
}
mutating func next() -> Int? {
guard n != 0 else {
defer { n += 1 }
return lst[0]
}
while n < lst.count && lst[n] < lst.count {
let retVal = lst[n]
lst = lst.enumerated().filter({ ($0.offset + 1) % lst[n] != 0 }).map({ $0.element })
n += 1
return retVal
}
if drainI == 0 {
lst = Array(lst.dropFirst(n))
}
while drainI < lst.count {
defer { drainI += 1 }
return lst[drainI]
}
return nil
}
}
The main file:
let args = Array(CommandLine.arguments.dropFirst())
guard let sj = args.first, let j = Int(sj), j > 0, j <= 10_000 else {
fatalError("Incorrect j")
}
func evenString(_ even: Bool) -> String {
return even ? "even" : ""
}
func jLuckyNumber(_ j: Int, even: Bool) {
print("The \(j)th \(evenString(even)) lucky number is \(Array(LuckyNumbers(even: even))[j-1..<j].first!)")
}
func luckyNumbersKth(j: Int, k: Int, even: Bool) {
print("List of \(j) ... \(k) \(evenString(even)) lucky numbers: ", terminator: "")
for (offset, luck) in LuckyNumbers(even: even).lazy.enumerated() {
guard offset + 1 <= k else { break }
if offset + 1 >= j {
print(luck, terminator: ", ")
}
}
print()
}
func luckyNumbersRange(j: Int, k: Int, even: Bool) {
print("List of \(evenString(even)) lucky numbers in the range \(j) ... \(-k): ", terminator: "")
for lucky in LuckyNumbers(even: even).lazy {
guard lucky <= -k else { break }
if lucky >= j {
print(lucky, terminator: ", ")
}
}
print()
}
switch args.count {
case 1:
jLuckyNumber(j, even: false)
case 2:
switch Int(args.last!) {
case let k? where k > 0 && k <= 10_000 && k > j:
luckyNumbersKth(j: j, k: k, even: false)
case let k? where k < 0 && -k > j:
luckyNumbersRange(j: j, k: k, even: false)
case _:
fatalError("Bad args")
}
case 3:
switch (Int(args[1]), args.last!) {
case (nil, "lucky"):
jLuckyNumber(j, even: false)
case (nil, "evenLucky"):
jLuckyNumber(j, even: true)
case let (k?, "lucky") where k > 0 && k <= 10_000 && k > j:
luckyNumbersKth(j: j, k: k, even: false)
case let (k?, "evenLucky") where k > 0 && k <= 10_000 && k > j:
luckyNumbersKth(j: j, k: k, even: true)
case let (k?, "lucky") where k < 0 && -k > j:
luckyNumbersRange(j: j, k: k, even: false)
case let (k?, "evenLucky") where k < 0 && -k > j:
luckyNumbersRange(j: j, k: k, even: true)
case _:
fatalError("Bad args")
}
case _:
fatalError()
}
- Output:
$ ./main 1 20 lucky List of 1 ... 20 lucky numbers: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, $ ./main 1 20 evenLucky List of 1 ... 20 even lucky numbers: 2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76, $ ./main 6000 -6100 lucky List of lucky numbers in the range 6000 ... 6100: 6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093, $ ./main 6000 -6100 evenLucky List of even lucky numbers in the range 6000 ... 6100: 6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092, $ ./main 10000 The 10000th lucky number is 115591 $ ./main 10000 , evenLucky The 10000th even lucky number is 111842
Tcl
#!/usr/bin/env tclsh8.6
package require Tcl 8.6
proc lgen {{even false} {nmax 200000}} {
coroutine lgen.[incr ::lgen] apply {{start nmax} {
set n 1
for {set i $start} {$i <= $nmax+1} {incr i 2} {lappend lst $i}
yield [info coroutine]
yield [lindex $lst 0]
while {$n < [llength $lst] && [lindex $lst $n] < [llength $lst]} {
yield [lindex $lst $n]
set lst [set i 0;lmap j $lst {
if {[incr i] % [lindex $lst $n]} {set j} else continue
}]
incr n
}
foreach i [lrange $lst $n end] {
yield $i
}
}} [expr {$even ? 2 : 1}] $nmax
}
proc collectIndices {generator from to} {
set result {}
for {set i 0} {$i <= $to} {incr i} {
set n [$generator]
if {$i >= $from} {lappend result $n}
}
rename $generator {}
return $result
}
proc collectValues {generator from to} {
set result {}
while 1 {
set n [$generator]
if {$n > $to} break
if {$n >= $from} {lappend result $n}
}
rename $generator {}
return $result
}
if {$argc<1||$argc>3} {
puts stderr "wrong # args: should be \"$argv0 from ?to? ?evenOdd?\""
exit 1
}
lassign $argv from to evenOdd
if {$argc < 3} {set evenOdd lucky}
if {$argc < 2} {set to ,}
if {![string is integer -strict $from] || $from < 1} {
puts stderr "\"from\" must be positive integer"
exit 1
} elseif {$to ne "," && (![string is integer -strict $to] || $to == 0)} {
puts stderr "\"to\" must be positive integer or comma"
exit 1
} elseif {[set evenOdd [string tolower $evenOdd]] ni {lucky evenlucky}} {
puts stderr "\"evenOdd\" must be \"lucky\" or \"evenLucky\""
exit 1
}
set l [lgen [expr {$evenOdd eq "evenlucky"}]]
set evenOdd [lindex {"lucky" "even lucky"} [expr {$evenOdd eq "evenlucky"}]]
if {$to eq ","} {
puts "$from'th $evenOdd number = [collectIndices $l [incr from -1] $from]"
} elseif {$to < 0} {
set to [expr {-$to}]
puts "all $evenOdd numbers from $from to $to: [join [collectValues $l $from $to] ,]"
} else {
puts "$from'th to $to'th $evenOdd numbers: [join [collectIndices $l [incr from -1] [incr to -1]] ,]"
}
- Output:
bash$ lucky.tcl 1 20 1'th to 20'th lucky numbers: 1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79 bash$ lucky.tcl 1 20 evenLucky 1'th to 20'th even lucky numbers: 2,4,6,10,12,18,20,22,26,34,36,42,44,50,52,54,58,68,70,76 bash$ lucky.tcl 6000 -6100 all lucky numbers from 6000 to 6100: 6009,6019,6031,6049,6055,6061,6079,6093 bash$ lucky.tcl 6000 -6100 evenLucky all even lucky numbers from 6000 to 6100: 6018,6020,6022,6026,6036,6038,6050,6058,6074,6090,6092 bash$ lucky.tcl 10000 10000'th lucky number = 115591 bash$ lucky.tcl 10000 , evenLucky 10000'th even lucky number = 111842
Wren
import "os" for Process
import "./iterate" for Stepped
import "./str" for Str
var luckyOdd = List.filled(1e5, 0)
var luckyEven = List.filled(1e5, 0)
var init = Fn.new {
for (i in 0...1e5) {
luckyOdd[i] = i*2 + 1
luckyEven[i] = i*2 + 2
}
}
var filterLuckyOdd = Fn.new {
var n = 2
while (n < luckyOdd.count) {
var m = luckyOdd[n-1]
var end = (luckyOdd.count/m).floor * m - 1
for (j in Stepped.descend(end..m-1, m)) luckyOdd.removeAt(j)
n = n + 1
}
}
var filterLuckyEven = Fn.new {
var n = 2
while (n < luckyEven.count) {
var m = luckyEven[n-1]
var end = (luckyEven.count/m).floor * m - 1
for (j in Stepped.descend(end..m-1, m)) luckyEven.removeAt(j)
n = n + 1
}
}
var printSingle = Fn.new { |j, odd|
if (odd) {
if (j >= luckyOdd.count) Fiber.abort("Argument is too big")
System.print("Lucky number %(j) = %(luckyOdd[j-1])")
} else {
if (j >= luckyEven.count) Fiber.abort("Argument is too big")
System.print("Lucky even number %(j) = %(luckyEven[j-1])")
}
}
var printRange = Fn.new { |j, k, odd|
if (odd) {
if (k >= luckyOdd.count) Fiber.abort("Argument is too big")
var rng = luckyOdd.skip(j-1).take(k-j+1).toList
System.print("Lucky numbers %(j) to %(k) are:\n %(rng)")
} else {
if (k >= luckyEven.count) Fiber.abort("Argument is too big")
var rng = luckyEven.skip(j-1).take(k-j+1).toList
System.print("Lucky even numbers %(j) to %(k) are:\n %(rng)")
}
}
var printBetween = Fn.new { |j, k, odd|
var rng = []
if (odd) {
var max = luckyOdd[-1]
if (j > max || k > max) {
Fiber.abort("At least one argument is too big")
}
for (num in luckyOdd) {
if (num >= j) {
if (num > k) break
rng.add(num)
}
}
System.print("Lucky numbers between %(j) and %(k) are:\n%(rng)")
} else {
var max = luckyEven[-1]
if (j > max || k > max) {
Fiber.abort("At least one argument is too big")
}
for (num in luckyEven) {
if (num >= j) {
if (num > k) break
rng.add(num)
}
}
System.print("Lucky even numbers between %(j) and %(k) are:\n%(rng)")
}
}
var args = Process.arguments
var argsSize = args.count
if (argsSize < 1 || argsSize > 3) Fiber.abort("There must be between 1 and 3 command line arguments")
init.call()
filterLuckyOdd.call()
filterLuckyEven.call()
var j = Num.fromString(args[0])
if (j.type != Num || !j.isInteger || j < 1) Fiber.abort("First argument must be a positive integer")
if (argsSize == 1) {
printSingle.call(j, true)
return
}
if (argsSize == 2) {
var k = Num.fromString(args[1])
if (k.type != Num || !k.isInteger) Fiber.abort("Second argument must be an integer")
if (k >= 0) {
if (j > k) Fiber.abort("Second argument can't be less than first")
printRange.call(j, k, true)
} else {
var l = -k
if (j > l) Fiber.abort("The second argument can't be less in absolute value than first")
printBetween.call(j, l, true)
}
return
}
args[2] = Str.lower(args[2])
var odd = (args[2] == "lucky") ? true :
(args[2] == "evenlucky") ? false : Fiber.abort("Third argument is invalid")
if (args[1] == ",") {
printSingle.call(j, odd)
return
}
var k = Num.fromString(args[1])
if (!((k.type == Num && k.isInteger) || (k.type == String && k == ","))) {
Fiber.abort("Second argument must be an integer or a comma")
}
if (k >= 0) {
if (j > k) Fiber.abort("Second argument can't be less than first")
printRange.call(j, k, odd)
} else {
var l = -k
if (j > l) Fiber.abort("The second argument can't be less in absolute value than first")
printBetween.call(j, l, odd)
}
- Output:
$ wren Lucky_and_even_lucky_numbers.wren 1 20 Lucky numbers 1 to 20 are: [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79] $ wren Lucky_and_even_lucky_numbers.wren 1 20 evenLucky Lucky even numbers 1 to 20 are: [2, 4, 6, 10, 12, 18, 20, 22, 26, 34, 36, 42, 44, 50, 52, 54, 58, 68, 70, 76] $ wren Lucky_and_even_lucky_numbers.wren 6000 -6100 Lucky numbers between 6000 and 6100 are: [6009, 6019, 6031, 6049, 6055, 6061, 6079, 6093] $ wren Lucky_and_even_lucky_numbers.wren 6000 -6100 evenLucky Lucky even numbers between 6000 and 6100 are: [6018, 6020, 6022, 6026, 6036, 6038, 6050, 6058, 6074, 6090, 6092] $ wren Lucky_and_even_lucky_numbers.wren 10000 , lucky Lucky number 10000 = 115591 $ wren Lucky_and_even_lucky_numbers.wren 10000 , evenLucky Lucky even number 10000 = 111842
zkl
The lucky number generator works by chaining filters to a even or odd infinite sequence. So it acts like a sieve as each starting number percolates through the filters. It also means there are lots and lots of filters, which doesn't scale well but works for the examples.
fcn lgen(a){
ns,idx:=[a..*,2],2;
vm.yield(ns.next());
while(1){
n:=ns.next();
vm.yield(n);
ns=ns.tweak(skipper.fp1(n,Ref(idx+=1))); // tack on another filter
}
}
fcn skipper(n,skp,cnt){ z:=cnt.inc(); if(z%skp==0) Void.Skip else n }
The command line is a bit funky (by Unix standards) so we just hard code it and use exceptions (such as trying to convert "foo" to int) to show the options.
cmdLineArgs,j,k,start:=vm.arglist,Void,Void,1;
try{
j=cmdLineArgs[0].toInt();
na:=cmdLineArgs.len();
if(na>1){
if(cmdLineArgs[1]==",")
start=cmdLineArgs[2][0].toLower()=="e" and 2 or 1;
else{
k=cmdLineArgs[1].toInt();
if(na>2)
start=cmdLineArgs[2][0].toLower()=="e" and 2 or 1;
}
}
}catch{
fcn options{
"args: j | j , [even]lucky | j k [even]lucky | j -k [even]lucky"
.println();
System.exit(1);
}()
}
luckies:=Utils.Generator(lgen,start);
try{
if(Void==k) luckies.drop(j-1).next().println();
else{
if(k>0) luckies.drop(j-1).walk(k-j+1).println();
else{ k=-k;
while((n:=luckies.next())<j){}
luckies.push(n);
luckies.pump(List,'wrap(n){ n<=k and n or Void.Stop }).println();
}
}
}catch(TheEnd){ options() }
- Output:
$ zkl lucky args: j | j , [even]lucky | j k [even]lucky | j -k [even]lucky $ zkl lucky 1 20 L(1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79) $ zkl lucky 1 20 evenLucky L(2,4,6,10,12,18,20,22,26,34,36,42,44,50,52,54,58,68,70,76) $ zkl lucky 6000 -6100 L(6009,6019,6031,6049,6055,6061,6079,6093) $ zkl lucky 6000 -6100 Even L(6018,6020,6022,6026,6036,6038,6050,6058,6074,6090,6092) $ zkl lucky 10000 115591 $ zkl lucky 10000 , evenLucky 111842 $ zkl lucky 6000 -5000 L() $ zkl lucky 4 2 args: j | j , [even]lucky | j k [even]lucky | j -k [even]lucky