Restructuring

solutions/ProjectEuler/024/desc.yml

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+title: What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
+url: http://projecteuler.net/problem=24
+
+desc: |
+  A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:
+  012   021   102   120   201   210
+  What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
+
+solution: Use factoring
+solutions:
+  solve.php:
+    desc: Basic Solution
+    language: php

solutions/ProjectEuler/024/solve.php

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+<?php
+define('NUM_PERMUTATION',1000000);
+define('DIGITS',9);
+$target = NUM_PERMUTATION - 1;
+
+$digits = range(0, 9);
+$permus = array(1 => 1);
+for ($i = 2; $i <= 9; $i++) {
+        $permus[$i] = $permus[$i - 1] * $i;
+}
+$permus = array_reverse($permus);
+$values = array();
+
+foreach ($permus as $n) {
+        $values[] = floor($target / $n);
+        $target = $target%$n;
+}
+
+$result = "";
+foreach ($values as $val) {
+        $result .= $digits[$val];
+        unset($digits[$val]);
+        sort($digits);
+}
+$result .= $digits[0];
+echo $result;