Project Euler 024

Project-Euler/Problem024.js

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+/**
+ * Problem 24 - Lexicographic Permutations
+ *
+ * @see {@link https://projecteuler.net/problem=24}
+ *
+ * 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?
+*/
+
+export function lexicographicPermutations () {
+  const factorial = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
+  const digits = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+  let millionthCounter = 999999
+  let result = ''
+
+  for (let i = digits.length - 1; i >= 0; i--) {
+    const permutation = (millionthCounter / factorial[i]) | 0
+
+    millionthCounter %= factorial[i]
+    result += digits[permutation]
+
+    digits.splice(permutation, 1)
+  }
+
+  return result
+}

Project-Euler/test/Problem024.test.js

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+import { lexicographicPermutations } from '../Problem024.js'
+
+describe('checking Lexicographic Permutations', () => {
+  // Project Euler Lexicographic Permutations
+  test('Test Lexicographic Permutations', () => {
+    expect(lexicographicPermutations()).toBe('2783915460')
+  })
+})