Jordan-Pólya numbers: Difference between revisions
Add Dart implementation
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(Add Dart implementation) |
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The 2800th Jordan-Polya number is: 439378587648000 = 14! * 7!
The 3800th Jordan-Polya number is: 7213895789838336 = 4!^8 * 2!^16
</pre>
=={{header|Dart}}==
{{trans|Java}}
<syntaxhighlight lang="Dart">
import "dart:collection";
import "dart:io";
void main() {
createJordanPolya();
final belowHundredMillion = jordanPolyaSet.lastWhere((element) => element <= 100000000, orElse: () => null);
List<int> jordanPolya = jordanPolyaSet.toList();
print("The first 50 Jordan-Polya numbers:");
for (int i = 0; i < 50; i++) {
// Right-align each number in a 5-character wide space
stdout.write(jordanPolya[i].toString().padLeft(5));
if (i % 10 == 9) {
print(""); // Newline every 10 numbers
}
}
print("");
print("The largest Jordan-Polya number less than 100 million: ${belowHundredMillion ?? 'Not found'}");
print("");
for (int i in [800, 1050, 1800, 2800, 3800]) {
var decomposition = decompositions[jordanPolya[i - 1]];
if (decomposition != null) {
print("The ${i}th Jordan-Polya number is: ${jordanPolya[i - 1]} = ${mapToString(decomposition)}");
}
}
}
SplayTreeSet<int> jordanPolyaSet = SplayTreeSet<int>();
Map<int, Map<int, int>> decompositions = {};
void createJordanPolya() {
jordanPolyaSet.add(1);
Set<int> nextSet = SplayTreeSet<int>();
decompositions[1] = {};
int factorial = 1;
for (int multiplier = 2; multiplier <= 20; multiplier++) {
factorial *= multiplier;
for (int number in jordanPolyaSet) {
int tempNumber = number;
while (tempNumber <= 9223372036854775807 ~/ factorial) {
int original = tempNumber;
tempNumber *= factorial;
nextSet.add(tempNumber);
var originalDecomposition = decompositions[original];
if (originalDecomposition != null) {
decompositions[tempNumber] = Map<int, int>.from(originalDecomposition)
..update(multiplier, (value) => value + 1, ifAbsent: () => 1);
}
}
}
jordanPolyaSet.addAll(nextSet);
nextSet.clear();
}
}
String mapToString(Map<int, int> map) {
String result = "";
map.forEach((key, value) {
result = "$key!${value == 1 ? '' : '^$value'} * $result";
});
return result.isEmpty ? result : result.substring(0, result.length - 3);
}
</syntaxhighlight>
{{out}}
<pre>
The first 50 Jordan-Polya numbers:
1 2 4 6 8 12 16 24 32 36
48 64 72 96 120 128 144 192 216 240
256 288 384 432 480 512 576 720 768 864
960 1024 1152 1296 1440 1536 1728 1920 2048 2304
2592 2880 3072 3456 3840 4096 4320 4608 5040 5184
The largest Jordan-Polya number less than 100 million: 99532800
The 800th Jordan-Polya number is: 18345885696 = 4!^7 * 2!^2
The 1050th Jordan-Polya number is: 139345920000 = 8! * 5!^3 * 2!
The 1800th Jordan-Polya number is: 9784472371200 = 6!^2 * 4!^2 * 2!^15
The 2800th Jordan-Polya number is: 439378587648000 = 14! * 7!
The 3800th Jordan-Polya number is: 7213895789838336 = 4!^8 * 2!^16
</pre>
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