Add combinations.

Author: trekhleb

src/algorithms/string/combinations/__test__/combineWithRepetitions.test.js

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+import combineWithRepetitions from '../combineWithRepetitions';
+import factorial from '../../../math/factorial/factorial';
+
+describe('combineWithRepetitions', () => {
+  it('should combine string with repetitions', () => {
+    expect(combineWithRepetitions(['A'], 1)).toEqual([
+      ['A'],
+    ]);
+
+    expect(combineWithRepetitions(['A', 'B'], 1)).toEqual([
+      ['A'],
+      ['B'],
+    ]);
+
+    expect(combineWithRepetitions(['A', 'B'], 2)).toEqual([
+      ['A', 'A'],
+      ['A', 'B'],
+      ['B', 'B'],
+    ]);
+
+    expect(combineWithRepetitions(['A', 'B'], 3)).toEqual([
+      ['A', 'A', 'A'],
+      ['A', 'A', 'B'],
+      ['A', 'B', 'B'],
+      ['B', 'B', 'B'],
+    ]);
+
+    expect(combineWithRepetitions(['A', 'B', 'C'], 2)).toEqual([
+      ['A', 'A'],
+      ['A', 'B'],
+      ['A', 'C'],
+      ['B', 'B'],
+      ['B', 'C'],
+      ['C', 'C'],
+    ]);
+
+    expect(combineWithRepetitions(['A', 'B', 'C'], 3)).toEqual([
+      ['A', 'A', 'A'],
+      ['A', 'A', 'B'],
+      ['A', 'A', 'C'],
+      ['A', 'B', 'B'],
+      ['A', 'B', 'C'],
+      ['A', 'C', 'C'],
+      ['B', 'B', 'B'],
+      ['B', 'B', 'C'],
+      ['B', 'C', 'C'],
+      ['C', 'C', 'C'],
+    ]);
+
+    const combinationOptions = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'];
+    const combinationSlotsNumber = 4;
+    const combinations = combineWithRepetitions(combinationOptions, combinationSlotsNumber);
+    const n = combinationOptions.length;
+    const r = combinationSlotsNumber;
+    const expectedNumberOfCombinations = factorial((r + n) - 1) / (factorial(r) * factorial(n - 1));
+
+    expect(combinations.length).toBe(expectedNumberOfCombinations);
+  });
+});

src/algorithms/string/combinations/combineWithRepetitions.js

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+/**
+ * @param {*[]} combinationOptions
+ * @param {number} combinationLength
+ * @return {*[]}
+ */
+
+export default function combineWithRepetitions(combinationOptions, combinationLength) {
+  // If combination length equal to 0 then return empty combination.
+  if (combinationLength === 0) {
+    return [[]];
+  }
+
+  // If combination options are empty then return "no-combinations" array.
+  if (combinationOptions.length === 0) {
+    return [];
+  }
+
+  // Init combinations array.
+  const combos = [];
+
+  // Find all shorter combinations and attach head to each of those.
+  const headCombo = [combinationOptions[0]];
+  const shorterCombos = combineWithRepetitions(combinationOptions, combinationLength - 1);
+
+  for (let combinationIndex = 0; combinationIndex < shorterCombos.length; combinationIndex += 1) {
+    const combo = headCombo.concat(shorterCombos[combinationIndex]);
+    combos.push(combo);
+  }
+
+  // Let's shift head to the right and calculate all the rest combinations.
+  const combinationsWithoutHead = combineWithRepetitions(
+    combinationOptions.slice(1),
+    combinationLength,
+  );
+
+  // Join all combinations and return them.
+  return combos.concat(combinationsWithoutHead);
+}