Four is the number of letters in the ...

From Rosetta Code
Four is the number of letters in the ... is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The     Four is ...     sequence is based on the counting of the number of letters in the words of the (never─ending) sentence:

  Four is the number of letters in the first word of this sentence, two in the second,
  three in the third, six in the fourth, two in the fifth, seven in the sixth, ··· 


Definitions and directives
  •   English is to be used in spelling numbers.
  •   Letters   are defined as the upper─ and lowercase letters in the Latin alphabet   (A──►Z   and   a──►z).
  •   Commas are not counted,   nor are hyphens (dashes or minus signs).
  •   twenty─three   has eleven letters.
  •   twenty─three   is considered one word   (which is hyphenated).
  •   The American version of numbers will be used here in this task   (as opposed to the British version).
         2,000,000,000   is two billion,   not   two milliard.


Task
  •   Write a driver (invoking routine) and a function (subroutine/routine···) that returns the sequence (for any positive integer) of the number of letters in the first   N   words in the never─ending sentence.   For instance, the portion of the never─ending sentence shown above (2nd sentence of this task), the sequence would be:
         4  2  3  6  2  7
  •   Only construct as much as is needed for the never─ending sentence.
  •   Write a driver (invoking routine) to show the number of letters in the   Nth   word,   as well as   showing the   Nth   word itself.
  •   After each test case, show the total number of characters   (including blanks, commas, and punctuation)   of the sentence that was constructed.
  •   Show all output here.


Test cases
 Display the first  201  numbers in the sequence   (and the total number of characters in the sentence).
 Display the number of letters  (and the word itself)  of the       1,000th  word.
 Display the number of letters  (and the word itself)  of the      10,000th  word.
 Display the number of letters  (and the word itself)  of the     100,000th  word.
 Display the number of letters  (and the word itself)  of the   1,000,000th  word.
 Display the number of letters  (and the word itself)  of the  10,000,000th  word  (optional).


Related tasks



Kotlin[edit]

This pulls in (slightly adjusted) code from related tasks to convert numbers to text or ordinals.

// version 1.1.4-3
 
val names = mapOf(
1 to "one",
2 to "two",
3 to "three",
4 to "four",
5 to "five",
6 to "six",
7 to "seven",
8 to "eight",
9 to "nine",
10 to "ten",
11 to "eleven",
12 to "twelve",
13 to "thirteen",
14 to "fourteen",
15 to "fifteen",
16 to "sixteen",
17 to "seventeen",
18 to "eighteen",
19 to "nineteen",
20 to "twenty",
30 to "thirty",
40 to "forty",
50 to "fifty",
60 to "sixty",
70 to "seventy",
80 to "eighty",
90 to "ninety"
)
 
val bigNames = mapOf(
1_000L to "thousand",
1_000_000L to "million",
1_000_000_000L to "billion",
1_000_000_000_000L to "trillion",
1_000_000_000_000_000L to "quadrillion",
1_000_000_000_000_000_000L to "quintillion"
)
 
val irregOrdinals = mapOf(
"one" to "first",
"two" to "second",
"three" to "third",
"five" to "fifth",
"eight" to "eighth",
"nine" to "ninth",
"twelve" to "twelfth"
)
 
fun String.toOrdinal(): String {
if (this == "zero") return "zeroth" // or alternatively 'zeroeth'
val splits = this.split(' ', '-')
val last = splits[splits.lastIndex]
return if (irregOrdinals.containsKey(last)) this.dropLast(last.length) + irregOrdinals[last]!!
else if (last.endsWith("y")) this.dropLast(1) + "ieth"
else this + "th"
}
 
fun numToText(n: Long, uk: Boolean = false): String {
if (n == 0L) return "zero"
val neg = n < 0L
val maxNeg = n == Long.MIN_VALUE
var nn = if (maxNeg) -(n + 1) else if (neg) -n else n
val digits3 = IntArray(7)
for (i in 0..6) { // split number into groups of 3 digits from the right
digits3[i] = (nn % 1000).toInt()
nn /= 1000
}
 
fun threeDigitsToText(number: Int) : String {
val sb = StringBuilder()
if (number == 0) return ""
val hundreds = number / 100
val remainder = number % 100
if (hundreds > 0) {
sb.append(names[hundreds], " hundred")
if (remainder > 0) sb.append(if (uk) " and " else " ")
}
if (remainder > 0) {
val tens = remainder / 10
val units = remainder % 10
if (tens > 1) {
sb.append(names[tens * 10])
if (units > 0) sb.append("-", names[units])
}
else sb.append(names[remainder])
}
return sb.toString()
}
 
val strings = Array(7) { threeDigitsToText(digits3[it]) }
var text = strings[0]
var andNeeded = uk && digits3[0] in 1..99
var big = 1000L
for (i in 1..6) {
if (digits3[i] > 0) {
var text2 = strings[i] + " " + bigNames[big]
if (text.isNotEmpty()) {
text2 += if (andNeeded) " and " else " " // no commas inserted in this version
andNeeded = false
}
else andNeeded = uk && digits3[i] in 1..99
text = text2 + text
}
big *= 1000
}
if (maxNeg) text = text.dropLast(5) + "eight"
if (neg) text = "minus " + text
return text
}
 
val opening = "Four is the number of letters in the first word of this sentence,".split(' ')
 
val String.adjustedLength get() = this.replace(",", "").replace("-", "").length // no ',' or '-'
 
fun getWords(n: Int): List<String> {
val words = mutableListOf<String>()
words.addAll(opening)
if (n > opening.size) {
var k = 2
while (true) {
val len = words[k - 1].adjustedLength
val text = numToText(len.toLong())
val splits = text.split(' ')
words.addAll(splits)
words.add("in")
words.add("the")
val text2 = numToText(k.toLong()).toOrdinal() + "," // add trailing comma
val splits2 = text2.split(' ')
words.addAll(splits2)
if (words.size >= n) break
k++
}
}
return words
}
 
fun getLengths(n: Int): Pair<List<Int>, Int> {
val words = getWords(n)
val lengths = words.take(n).map { it.adjustedLength }
val sentenceLength = words.sumBy { it.length } + words.size - 1 // includes hyphens, commas & spaces
return Pair(lengths, sentenceLength)
}
 
fun getLastWord(n: Int): Triple<String, Int, Int> {
val words = getWords(n)
val nthWord = words[n - 1]
val nthWordLength = nthWord.adjustedLength
val sentenceLength = words.sumBy { it.length } + words.size - 1 // includes hyphens, commas & spaces
return Triple(nthWord, nthWordLength, sentenceLength)
}
 
fun main(args: Array<String>) {
var n = 201
println("The lengths of the first $n words are:\n")
val (list, sentenceLength) = getLengths(n)
for (i in 0 until n) {
if (i % 25 == 0) {
if (i > 0) println()
print("${"%3d".format(i + 1)}: ")
}
print("%3d".format(list[i]))
}
println("\n\nLength of sentence = $sentenceLength\n")
n = 1_000
do {
var (word, wLen, sLen) = getLastWord(n)
if (word.endsWith(",")) word = word.dropLast(1) // strip off any trailing comma
println("The length of word $n [$word] is $wLen")
println("Length of sentence = $sLen\n")
n *= 10
}
while (n <= 10_000_000)
}
Output:
The lengths of the first 201 words are:

  1:   4  2  3  6  2  7  2  3  5  4  2  4  8  3  2  3  6  5  2  3  5  3  2  3  6
 26:   3  2  3  5  5  2  3  5  3  2  3  7  5  2  3  6  4  2  3  5  4  2  3  5  3
 51:   2  3  8  4  2  3  7  5  2  3 10  5  2  3 10  3  2  3  9  5  2  3  9  3  2
 76:   3 11  4  2  3 10  3  2  3 10  5  2  3  9  4  2  3 11  5  2  3 12  3  2  3
101:  11  5  2  3 12  3  2  3 11  5  2  3 11  3  2  3 13  5  2  3 12  4  2  3 11
126:   4  2  3  9  3  2  3 11  5  2  3 12  4  2  3 11  5  2  3 12  3  2  3 11  5
151:   2  3 11  5  2  3 13  4  2  3 12  3  2  3 11  5  2  3  8  3  2  3 10  4  2
176:   3 11  3  2  3 10  5  2  3 11  4  2  3 10  4  2  3 10  3  2  3 12  5  2  3
201:  11

Length of sentence = 1203

The length of word 1000 [in] is 2
Length of sentence = 6279

The length of word 10000 [in] is 2
Length of sentence = 64140

The length of word 100000 [one] is 3
Length of sentence = 659474

The length of word 1000000 [the] is 3
Length of sentence = 7113621

The length of word 10000000 [thousand] is 8
Length of sentence = 70995756

Perl 6[edit]

Works with: Rakudo version 2017.09

Uses the Lingua::EN::Numbers::Cardinal module to generate both cardinal and ordinal numbers. This module places commas in number words between 3-orders-of-magnitude clusters. E.G. 12345678.&ordinal becomes: twelve million, three hundred forty-five thousand, six hundred seventy-eighth. Uses a custom 'no-commas' routine to filter them out for accurate character counts. Generates the 'sentence' lazily so only the words needed are ever calculated and reified.

use Lingua::EN::Numbers::Cardinal;
 
my $index = 1;
my @sentence = flat 'Four is the number of letters in the first word of this sentence, '.words,
{ @sentence[$index++].&alpha.&cardinal, 'in', 'the', |($index.&ordinal.&no-commas~',').words } ... * ;
 
sub alpha ( $str ) { $str.subst(/\W/, '', :g).chars }
sub no-commas ( $str ) { $str.subst(',', '', :g) }
sub count ( $index ) { @sentence[^$index].join(' ').chars ~ " characters in the sentence, up to and including this word.\n" }
 
say 'First 201 word lengths in the sequence:';
put ' ', map { @sentence[$_].&alpha.fmt("%2d") ~ (((1+$_) %% 25) ?? "\n" !! '') }, ^201;
say 201.&count;
 
for 1e3, 1e4, 1e5, 1e6, 1e7 {
say "{.&ordinal.tc} word, '{@sentence[$_ - 1]}', has {@sentence[$_ - 1].&alpha} characters. ", .&count
}
Output:
First 201 word lengths in the sequence:
  4  2  3  6  2  7  2  3  5  4  2  4  8  3  2  3  6  5  2  3  5  3  2  3  6
  3  2  3  5  5  2  3  5  3  2  3  7  5  2  3  6  4  2  3  5  4  2  3  5  3
  2  3  8  4  2  3  7  5  2  3 10  5  2  3 10  3  2  3  9  5  2  3  9  3  2
  3 11  4  2  3 10  3  2  3 10  5  2  3  9  4  2  3 11  5  2  3 12  3  2  3
 11  5  2  3 12  3  2  3 11  5  2  3 11  3  2  3 13  5  2  3 12  4  2  3 11
  4  2  3  9  3  2  3 11  5  2  3 12  4  2  3 11  5  2  3 12  3  2  3 11  5
  2  3 11  5  2  3 13  4  2  3 12  3  2  3 11  5  2  3  8  3  2  3 10  4  2
  3 11  3  2  3 10  5  2  3 11  4  2  3 10  4  2  3 10  3  2  3 12  5  2  3
 11
1203 characters in the sentence, up to and including this word.

One thousandth word, 'in', has 2 characters. 6249 characters in the sentence, up to and including this word.

Ten thousandth word, 'in', has 2 characters. 64097 characters in the sentence, up to and including this word.

One hundred thousandth word, 'one', has 3 characters. 659455 characters in the sentence, up to and including this word.

One millionth word, 'the', has 3 characters. 7113560 characters in the sentence, up to and including this word.

Ten millionth word, 'thousand', has 8 characters. 70995729 characters in the sentence, up to and including this word.

REXX[edit]

/*REXX pgm finds/shows the number of letters in the  Nth  word in a constructed sentence*/
@= 'Four is the number of letters in the first word of this sentence,' /*···*/
/* [↑] the start of a long sentence. */
parse arg N M /*obtain optional argument from the CL.*/
if N='' | N="," then N= 201 /*Not specified? Then use the default.*/
if M='' | M="," then M=1000 10000 100000 1000000 /* " " " " " " */
@abcU= 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' /*define the uppercase Latin alphabet. */
!.=.; #.=.; q=1; w=length(N) /* [↓] define some helpful low values.*/
call tell N
if N<0 then say y ' is the length of word ' a " ["word(@, a)"]"
say /* [↑] N negative? Just show 1 number*/
say 'length of sentence= ' length(@) /*display the length of the @ sentence.*/
 
if M\=='' then do k=1 for words(M) while M\=0 /*maybe handle counts (if specified). */
x=word(M, k) /*obtain the Kth word of the M list. */
call tell -x /*invoke subroutine (with negative arg)*/
say
say y ' is the length of word ' x " ["word(@, x)"]"
say 'length of sentence= ' length(@) /*display length of @ sentence.*/
end /*k*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
wordLen: arg ?; return length(?) - length( space( translate(?, , @abcU), 0) )
/*──────────────────────────────────────────────────────────────────────────────────────*/
tell: parse arg z,,$; idx=1; a=abs(z); group=25 /*show 25 numbers per line.*/
/*Q is the last number spelt by $SPELL#*/
do j=1 for a /*traipse through all the numbers to N.*/
do 2 /*perform loop twice (well ··· maybe).*/
y=wordLen( word(@, j) ) /*get the Jth word from the sentence.*/
if y\==0 then leave /*Is the word spelt? Then we're done.*/
q=q + 1 /*bump the on─going (moving) # counter.*/
if #.q==. then #.q=$spell#(q 'Q ORD') /*need to spell A as an ordinal number?*/
_=wordLen( word(@, q) ) /*use the length of the ordinal number.*/
if !._==. then !._=$spell#(_ 'Q') /*Not spelled? Then go and spell it. */
@[email protected]  !._ 'in the' #.q"," /*append words to never─ending sentence*/
end /*2*/ /* [↑] Q ≡ Quiet ORD ≡ ORDinal */
 
$=$ || right(y, 3) /* [↓] append a justified # to a line.*/
if j//group==0 & z>0 then do; say right(idx, w)'►'$; idx=idx+group; $=; end
end /*j*/ /* [↑] show line if there's enough #s.*/
 
if $\=='' & z>0 then say right(idx, w)'►'$ /*display if there are residual numbers*/
return

The   $SPELL#.REX   routine can be found here   ───►   $SPELL#.REX.

output:
  1►  4  2  3  6  2  7  2  3  5  4  2  4  8  3  2  3  6  5  2  3  5  3  2  3  6
 26►  3  2  3  5  5  2  3  5  3  2  3  7  5  2  3  6  4  2  3  5  4  2  3  5  3
 51►  2  3  8  4  2  3  7  5  2  3 10  5  2  3 10  3  2  3  9  5  2  3  9  3  2
 76►  3 11  4  2  3 10  3  2  3 10  5  2  3  9  4  2  3 11  5  2  3 12  3  2  3
101► 11  5  2  3 12  3  2  3 11  5  2  3 11  3  2  3 13  5  2  3 12  4  2  3 11
126►  4  2  3  9  3  2  3 11  5  2  3 12  4  2  3 11  5  2  3 12  3  2  3 11  5
151►  2  3 11  5  2  3 13  4  2  3 12  3  2  3 11  5  2  3  8  3  2  3 10  4  2
176►  3 11  3  2  3 10  5  2  3 11  4  2  3 10  4  2  3 10  3  2  3 12  5  2  3
201► 11

length of sentence=  1203

2  is the length of word  1000   [in]
length of sentence=  6279

2  is the length of word  10000   [in]
length of sentence=  64140

3  is the length of word  100000   [one]
length of sentence=  659474

3  is the length of word  1000000   [the]
length of sentence=  7113621

zkl[edit]

Uses the nth function from Spelling_of_ordinal_numbers#zkl

   // Built the sentence in little chucks but only save the last one
// Save the word counts
fcn fourIsThe(text,numWords){
const rmc="-,";
seq:=(text - rmc).split().apply("len").copy(); // (4,2,3,6...)
szs:=Data(numWords + 100,Int).howza(0).extend(seq); // bytes
cnt,lastWords := seq.len(),"";
total:=seed.len() - 1; // don't count trailing space
 
foreach idx in ([1..]){
sz:=szs[idx];
a,b := nth(sz,False),nth(idx+1); // "two","three hundred sixty-seventh"
lastWords="%s in the %s, ".fmt(a,b);
ws:=lastWords.counts(" ")[1]; // "five in the forty-ninth " --> 4
cnt+=ws; total+=lastWords.len();
lastWords.split().pump(szs.append,'-(rmc),"len");
if(cnt>=numWords){
if(cnt>numWords){
z,n:=lastWords.len(),z-2;
do(cnt - numWords){ n=lastWords.rfind(" ",n) - 1; }
lastWords=lastWords[0,n+1]; total-=(z - n);
}
break;
}
}
return(lastWords.strip(),szs,total);
}
fcn lastWord(sentence){ sentence[sentence.rfind(" ")+1,*] }
var seed="Four is the number of letters in the first word of this sentence, ";
sentence,szs,total := fourIsThe(seed,201);
print(" 1:");
foreach n,x in ([1..201].zip(szs)){
print("%3d".fmt(x));
if(0 == n%25) print("\n%3d:".fmt(n+1));
}
println("\nLength of above sentence: ",total);
Output:
  1:  4  2  3  6  2  7  2  3  5  4  2  4  8  3  2  3  6  5  2  3  5  3  2  3  6
 26:  3  2  3  5  5  2  3  5  3  2  3  7  5  2  3  6  4  2  3  5  4  2  3  5  3
 51:  2  3  8  4  2  3  7  5  2  3 10  5  2  3 10  3  2  3  9  5  2  3  9  3  2
 76:  3 11  4  2  3 10  3  2  3 10  5  2  3  9  4  2  3 11  5  2  3 12  3  2  3
101: 11  5  2  3 12  3  2  3 11  5  2  3 11  3  2  3 13  5  2  3 12  4  2  3 11
126:  4  2  3  9  3  2  3 11  5  2  3 12  4  2  3 11  5  2  3 12  3  2  3 11  5
151:  2  3 11  5  2  3 13  4  2  3 12  3  2  3 11  5  2  3  8  3  2  3 10  4  2
176:  3 11  3  2  3 10  5  2  3 11  4  2  3 10  4  2  3 10  3  2  3 12  5  2  3
201: 11
Length of above sentence: 1203
n:=1000; do(5){
sentence,x,total := fourIsThe(seed,n);
word:=lastWord(sentence);
println("%,d words: \"%s\" [%d]. Length=%,d"
.fmt(n,word,word.len(),total));
n*=10;
}
Output:
1,000 words: "in" [2]. Length=6,247
10,000 words: "in" [2]. Length=64,095
100,000 words: "one" [3]. Length=659,453
1,000,000 words: "the" [3]. Length=7,140,558
10,000,000 words: "thousand" [8]. Length=71,250,727