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synced 2024-12-25 22:46:20 +08:00
Add combinations.
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@ -32,13 +32,13 @@
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* [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
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* [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/cartesian-product)
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* [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/power-set)
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* [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (trial division)
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* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/permutations) (with and without repetitions)
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* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/combinations) (with and without repetitions)
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* [Primality Test](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/primality-test) (trial division method)
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* [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the greatest common divisor (GCD)
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* [Least Common Multiple (LCM)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple)
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* [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
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* **String**
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* [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/permutations) (with and without repetitions)
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* [Combinations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/combinations) (with and without repetitions)
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* Minimum Edit distance (Levenshtein Distance)
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* Hamming
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* Huffman
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@ -1,5 +1,5 @@
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import combineWithRepetitions from '../combineWithRepetitions';
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import factorial from '../../../math/factorial/factorial';
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import factorial from '../../factorial/factorial';
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describe('combineWithRepetitions', () => {
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it('should combine string with repetitions', () => {
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@ -0,0 +1,60 @@
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import combineWithoutRepetitions from '../combineWithoutRepetitions';
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import factorial from '../../factorial/factorial';
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describe('combineWithoutRepetitions', () => {
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it('should combine string without repetitions', () => {
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expect(combineWithoutRepetitions(['A', 'B'], 3)).toEqual([]);
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expect(combineWithoutRepetitions(['A', 'B'], 1)).toEqual([
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['A'],
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['B'],
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]);
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expect(combineWithoutRepetitions(['A'], 1)).toEqual([
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['A'],
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]);
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expect(combineWithoutRepetitions(['A', 'B'], 2)).toEqual([
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['A', 'B'],
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]);
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expect(combineWithoutRepetitions(['A', 'B', 'C'], 2)).toEqual([
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['A', 'B'],
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['A', 'C'],
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['B', 'C'],
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]);
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expect(combineWithoutRepetitions(['A', 'B', 'C'], 3)).toEqual([
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['A', 'B', 'C'],
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]);
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expect(combineWithoutRepetitions(['A', 'B', 'C', 'D'], 3)).toEqual([
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['A', 'B', 'C'],
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['A', 'B', 'D'],
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['A', 'C', 'D'],
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['B', 'C', 'D'],
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]);
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expect(combineWithoutRepetitions(['A', 'B', 'C', 'D', 'E'], 3)).toEqual([
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['A', 'B', 'C'],
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['A', 'B', 'D'],
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['A', 'B', 'E'],
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['A', 'C', 'D'],
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['A', 'C', 'E'],
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['A', 'D', 'E'],
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['B', 'C', 'D'],
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['B', 'C', 'E'],
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['B', 'D', 'E'],
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['C', 'D', 'E'],
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]);
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const combinationOptions = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'];
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const combinationSlotsNumber = 4;
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const combinations = combineWithoutRepetitions(combinationOptions, combinationSlotsNumber);
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const n = combinationOptions.length;
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const r = combinationSlotsNumber;
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const expectedNumberOfCombinations = factorial(n) / (factorial(r) * factorial(n - r));
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expect(combinations.length).toBe(expectedNumberOfCombinations);
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});
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});
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@ -38,14 +38,14 @@
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*/
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/**
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* @param {string} combinationOptions
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* @param {*[]} combinationOptions
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* @param {number} combinationLength
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* @return {string[]}
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* @return {*[]}
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*/
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export default function combineWithoutRepetitions(combinationOptions, combinationLength) {
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// If combination length is just 1 then return combinationOptions.
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if (combinationLength === 1) {
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return Array.from(combinationOptions);
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return combinationOptions.map(option => [option]);
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}
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// Init combinations array.
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@ -53,12 +53,13 @@ export default function combineWithoutRepetitions(combinationOptions, combinatio
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for (let i = 0; i <= (combinationOptions.length - combinationLength); i += 1) {
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const smallerCombinations = combineWithoutRepetitions(
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combinationOptions.substr(i + 1),
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combinationOptions.slice(i + 1),
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combinationLength - 1,
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);
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for (let j = 0; j < smallerCombinations.length; j += 1) {
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combinations.push(combinationOptions[i] + smallerCombinations[j]);
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const combination = [combinationOptions[i]].concat(smallerCombinations[j]);
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combinations.push(combination);
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}
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}
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@ -0,0 +1,55 @@
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import permutateWithRepetitions from '../permutateWithRepetitions';
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describe('permutateWithRepetitions', () => {
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it('should permutate string with repetition', () => {
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const permutations0 = permutateWithRepetitions([]);
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expect(permutations0).toEqual([]);
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const permutations1 = permutateWithRepetitions(['A']);
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expect(permutations1).toEqual([
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['A'],
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]);
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const permutations2 = permutateWithRepetitions(['A', 'B']);
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expect(permutations2).toEqual([
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['A', 'A'],
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['A', 'B'],
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['B', 'A'],
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['B', 'B'],
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]);
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const permutations3 = permutateWithRepetitions(['A', 'B', 'C']);
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expect(permutations3).toEqual([
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['A', 'A', 'A'],
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['A', 'A', 'B'],
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['A', 'A', 'C'],
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['A', 'B', 'A'],
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['A', 'B', 'B'],
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['A', 'B', 'C'],
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['A', 'C', 'A'],
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['A', 'C', 'B'],
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['A', 'C', 'C'],
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['B', 'A', 'A'],
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['B', 'A', 'B'],
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['B', 'A', 'C'],
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['B', 'B', 'A'],
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['B', 'B', 'B'],
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['B', 'B', 'C'],
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['B', 'C', 'A'],
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['B', 'C', 'B'],
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['B', 'C', 'C'],
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['C', 'A', 'A'],
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['C', 'A', 'B'],
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['C', 'A', 'C'],
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['C', 'B', 'A'],
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['C', 'B', 'B'],
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['C', 'B', 'C'],
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['C', 'C', 'A'],
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['C', 'C', 'B'],
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['C', 'C', 'C'],
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]);
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const permutations4 = permutateWithRepetitions(['A', 'B', 'C', 'D']);
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expect(permutations4.length).toBe(4 * 4 * 4 * 4);
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});
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});
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@ -0,0 +1,71 @@
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import permutateWithoutRepetitions from '../permutateWithoutRepetitions';
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import factorial from '../../factorial/factorial';
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describe('permutateWithoutRepetitions', () => {
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it('should permutate string', () => {
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const permutations0 = permutateWithoutRepetitions([]);
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expect(permutations0).toEqual([]);
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const permutations1 = permutateWithoutRepetitions(['A']);
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expect(permutations1).toEqual([
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['A'],
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]);
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const permutations2 = permutateWithoutRepetitions(['A', 'B']);
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expect(permutations2.length).toBe(2);
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expect(permutations2).toEqual([
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['B', 'A'],
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['A', 'B'],
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]);
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const permutations6 = permutateWithoutRepetitions(['A', 'A']);
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expect(permutations6.length).toBe(2);
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expect(permutations6).toEqual([
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['A', 'A'],
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['A', 'A'],
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]);
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const permutations3 = permutateWithoutRepetitions(['A', 'B', 'C']);
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expect(permutations3.length).toBe(factorial(3));
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expect(permutations3).toEqual([
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['C', 'B', 'A'],
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['B', 'C', 'A'],
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['B', 'A', 'C'],
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['C', 'A', 'B'],
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['A', 'C', 'B'],
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['A', 'B', 'C'],
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]);
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const permutations4 = permutateWithoutRepetitions(['A', 'B', 'C', 'D']);
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expect(permutations4.length).toBe(factorial(4));
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expect(permutations4).toEqual([
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['D', 'C', 'B', 'A'],
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['C', 'D', 'B', 'A'],
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['C', 'B', 'D', 'A'],
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['C', 'B', 'A', 'D'],
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['D', 'B', 'C', 'A'],
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['B', 'D', 'C', 'A'],
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['B', 'C', 'D', 'A'],
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['B', 'C', 'A', 'D'],
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['D', 'B', 'A', 'C'],
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['B', 'D', 'A', 'C'],
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['B', 'A', 'D', 'C'],
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['B', 'A', 'C', 'D'],
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['D', 'C', 'A', 'B'],
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['C', 'D', 'A', 'B'],
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['C', 'A', 'D', 'B'],
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['C', 'A', 'B', 'D'],
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['D', 'A', 'C', 'B'],
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['A', 'D', 'C', 'B'],
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['A', 'C', 'D', 'B'],
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['A', 'C', 'B', 'D'],
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['D', 'A', 'B', 'C'],
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['A', 'D', 'B', 'C'],
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['A', 'B', 'D', 'C'],
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['A', 'B', 'C', 'D'],
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]);
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const permutations5 = permutateWithoutRepetitions(['A', 'B', 'C', 'D', 'E', 'F']);
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expect(permutations5.length).toBe(factorial(6));
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});
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});
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42
src/algorithms/math/permutations/permutateWithRepetitions.js
Normal file
42
src/algorithms/math/permutations/permutateWithRepetitions.js
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@ -0,0 +1,42 @@
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/**
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* @param {*[]} permutationOptions
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* @return {*[]}
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*/
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export default function permutateWithRepetitions(permutationOptions) {
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// There is no permutations for empty array.
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if (!permutationOptions || permutationOptions.length === 0) {
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return [];
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}
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// There is only one permutation for the 1-element array.
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if (permutationOptions.length === 1) {
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return [permutationOptions];
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}
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// Let's create initial set of permutations.
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let previousPermutations = permutationOptions.map(option => [option]);
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let currentPermutations = [];
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let permutationSize = 1;
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// While the size of each permutation is less then or equal to options length...
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while (permutationSize < permutationOptions.length) {
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// Reset all current permutations.
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currentPermutations = [];
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for (let permIndex = 0; permIndex < previousPermutations.length; permIndex += 1) {
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for (let optionIndex = 0; optionIndex < permutationOptions.length; optionIndex += 1) {
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let currentPermutation = previousPermutations[permIndex];
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currentPermutation = currentPermutation.concat([permutationOptions[optionIndex]]);
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currentPermutations.push(currentPermutation);
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}
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}
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// Make current permutations to be the previous ones.
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previousPermutations = currentPermutations.slice(0);
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// Increase permutation size counter.
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permutationSize += 1;
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}
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return currentPermutations;
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}
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@ -0,0 +1,39 @@
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/**
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* @param {*[]} permutationOptions
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* @return {*[]}
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*/
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export default function permutateWithoutRepetitions(permutationOptions) {
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if (permutationOptions.length === 0) {
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return [];
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}
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if (permutationOptions.length === 1) {
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return [permutationOptions];
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}
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const permutations = [];
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// Get all permutations of length (n - 1).
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const previousOptions = permutationOptions.slice(0, permutationOptions.length - 1);
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const previousPermutations = permutateWithoutRepetitions(previousOptions);
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// Insert last option into every possible position of every previous permutation.
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const lastOption = permutationOptions.slice(permutationOptions.length - 1);
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for (
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let permutationIndex = 0;
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permutationIndex < previousPermutations.length;
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permutationIndex += 1
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) {
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const currentPermutation = previousPermutations[permutationIndex];
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// Insert last option into every possible position of currentPermutation.
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for (let positionIndex = 0; positionIndex <= currentPermutation.length; positionIndex += 1) {
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const permutationPrefix = currentPermutation.slice(0, positionIndex);
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const permutationSuffix = currentPermutation.slice(positionIndex);
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permutations.push(permutationPrefix.concat(lastOption, permutationSuffix));
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}
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}
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return permutations;
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}
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@ -1,40 +0,0 @@
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import combineWithoutRepetitions from '../combineWithoutRepetitions';
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import factorial from '../../../math/factorial/factorial';
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describe('combineWithoutRepetitions', () => {
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it('should combine string without repetitions', () => {
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expect(combineWithoutRepetitions('AB', 3)).toEqual([]);
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expect(combineWithoutRepetitions('AB', 1)).toEqual(['A', 'B']);
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expect(combineWithoutRepetitions('A', 1)).toEqual(['A']);
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expect(combineWithoutRepetitions('AB', 2)).toEqual(['AB']);
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expect(combineWithoutRepetitions('ABC', 2)).toEqual(['AB', 'AC', 'BC']);
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expect(combineWithoutRepetitions('ABC', 3)).toEqual(['ABC']);
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expect(combineWithoutRepetitions('ABCD', 3)).toEqual([
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'ABC',
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'ABD',
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'ACD',
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'BCD',
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]);
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expect(combineWithoutRepetitions('ABCDE', 3)).toEqual([
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'ABC',
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'ABD',
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'ABE',
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'ACD',
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'ACE',
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'ADE',
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'BCD',
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'BCE',
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'BDE',
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'CDE',
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]);
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const combinationOptions = 'ABCDEFGH';
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const combinationSlotsNumber = 4;
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const combinations = combineWithoutRepetitions(combinationOptions, combinationSlotsNumber);
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const n = combinationOptions.length;
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const r = combinationSlotsNumber;
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const expectedNumberOfCombinations = factorial(n) / (factorial(r) * factorial(n - r));
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expect(combinations.length).toBe(expectedNumberOfCombinations);
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});
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});
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@ -1,53 +0,0 @@
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import permutateWithRepetition from '../permutateWithRepetitions';
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describe('permutateWithRepetition', () => {
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it('should permutate string with repetition', () => {
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const permutations0 = permutateWithRepetition('');
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expect(permutations0).toEqual([]);
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const permutations1 = permutateWithRepetition('A');
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expect(permutations1).toEqual(['A']);
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const permutations2 = permutateWithRepetition('AB');
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expect(permutations2).toEqual([
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'AA',
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'AB',
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'BA',
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'BB',
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]);
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const permutations3 = permutateWithRepetition('ABC');
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expect(permutations3).toEqual([
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'AAA',
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'AAB',
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'AAC',
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'ABA',
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'ABB',
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'ABC',
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'ACA',
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'ACB',
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'ACC',
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'BAA',
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'BAB',
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'BAC',
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'BBA',
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'BBB',
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'BBC',
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'BCA',
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'BCB',
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'BCC',
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'CAA',
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'CAB',
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'CAC',
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'CBA',
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'CBB',
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'CBC',
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'CCA',
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'CCB',
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'CCC',
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]);
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const permutations4 = permutateWithRepetition('ABCD');
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expect(permutations4.length).toBe(4 * 4 * 4 * 4);
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});
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});
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@ -1,69 +0,0 @@
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import permutateWithoutRepetitions from '../permutateWithoutRepetitions';
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import factorial from '../../../math/factorial/factorial';
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describe('permutateString', () => {
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it('should permutate string', () => {
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const permutations0 = permutateWithoutRepetitions('');
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expect(permutations0).toEqual([]);
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const permutations1 = permutateWithoutRepetitions('A');
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expect(permutations1).toEqual(['A']);
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const permutations2 = permutateWithoutRepetitions('AB');
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expect(permutations2.length).toBe(2);
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expect(permutations2).toEqual([
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'BA',
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'AB',
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]);
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const permutations6 = permutateWithoutRepetitions('AA');
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expect(permutations6.length).toBe(2);
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expect(permutations6).toEqual([
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'AA',
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'AA',
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]);
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const permutations3 = permutateWithoutRepetitions('ABC');
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expect(permutations3.length).toBe(factorial(3));
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expect(permutations3).toEqual([
|
||||
'CBA',
|
||||
'BCA',
|
||||
'BAC',
|
||||
'CAB',
|
||||
'ACB',
|
||||
'ABC',
|
||||
]);
|
||||
|
||||
const permutations4 = permutateWithoutRepetitions('ABCD');
|
||||
expect(permutations4.length).toBe(factorial(4));
|
||||
expect(permutations4).toEqual([
|
||||
'DCBA',
|
||||
'CDBA',
|
||||
'CBDA',
|
||||
'CBAD',
|
||||
'DBCA',
|
||||
'BDCA',
|
||||
'BCDA',
|
||||
'BCAD',
|
||||
'DBAC',
|
||||
'BDAC',
|
||||
'BADC',
|
||||
'BACD',
|
||||
'DCAB',
|
||||
'CDAB',
|
||||
'CADB',
|
||||
'CABD',
|
||||
'DACB',
|
||||
'ADCB',
|
||||
'ACDB',
|
||||
'ACBD',
|
||||
'DABC',
|
||||
'ADBC',
|
||||
'ABDC',
|
||||
'ABCD',
|
||||
]);
|
||||
|
||||
const permutations5 = permutateWithoutRepetitions('ABCDEF');
|
||||
expect(permutations5.length).toBe(factorial(6));
|
||||
});
|
||||
});
|
@ -1,41 +0,0 @@
|
||||
/**
|
||||
* @param {string} str
|
||||
* @return {string[]}
|
||||
*/
|
||||
export default function permutateWithRepetition(str) {
|
||||
// There is no permutations for empty string.
|
||||
if (!str || str.length === 0) {
|
||||
return [];
|
||||
}
|
||||
|
||||
// There is only one permutation for the 1-character string.
|
||||
if (str.length === 1) {
|
||||
return [str];
|
||||
}
|
||||
|
||||
// Let's create initial set of permutations.
|
||||
let previousPermutations = Array.from(str);
|
||||
let currentPermutations = [];
|
||||
let permutationSize = 1;
|
||||
|
||||
// While the size of each permutation is less then or equal to string length...
|
||||
while (permutationSize < str.length) {
|
||||
// Reset all current permutations.
|
||||
currentPermutations = [];
|
||||
|
||||
for (let pemIndex = 0; pemIndex < previousPermutations.length; pemIndex += 1) {
|
||||
for (let charIndex = 0; charIndex < str.length; charIndex += 1) {
|
||||
const currentPermutation = previousPermutations[pemIndex] + str[charIndex];
|
||||
currentPermutations.push(currentPermutation);
|
||||
}
|
||||
}
|
||||
|
||||
// Make current permutations to be the previous ones.
|
||||
previousPermutations = currentPermutations.slice(0);
|
||||
|
||||
// Increase permutation size counter.
|
||||
permutationSize += 1;
|
||||
}
|
||||
|
||||
return currentPermutations;
|
||||
}
|
@ -1,39 +0,0 @@
|
||||
/**
|
||||
* @param {string} str
|
||||
* @return {string[]}
|
||||
*/
|
||||
export default function permutateWithoutRepetitions(str) {
|
||||
if (str.length === 0) {
|
||||
return [];
|
||||
}
|
||||
|
||||
if (str.length === 1) {
|
||||
return [str];
|
||||
}
|
||||
|
||||
const permutations = [];
|
||||
|
||||
// Get all permutations of string of length (n - 1).
|
||||
const previousString = str.substring(0, str.length - 1);
|
||||
const previousPermutations = permutateWithoutRepetitions(previousString);
|
||||
|
||||
// Insert last character into every possible position of every previous permutation.
|
||||
const lastCharacter = str.substring(str.length - 1);
|
||||
|
||||
for (
|
||||
let permutationIndex = 0;
|
||||
permutationIndex < previousPermutations.length;
|
||||
permutationIndex += 1
|
||||
) {
|
||||
const currentPermutation = previousPermutations[permutationIndex];
|
||||
|
||||
// Insert strLastCharacter into every possible position of currentPermutation.
|
||||
for (let positionIndex = 0; positionIndex <= currentPermutation.length; positionIndex += 1) {
|
||||
const permutationPrefix = currentPermutation.substr(0, positionIndex);
|
||||
const permutationSuffix = currentPermutation.substr(positionIndex);
|
||||
permutations.push(permutationPrefix + lastCharacter + permutationSuffix);
|
||||
}
|
||||
}
|
||||
|
||||
return permutations;
|
||||
}
|
Loading…
Reference in New Issue
Block a user