Add permutations and combinations.

Author: trekhleb

src/algorithms/string/combinations/README.md

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+# Combinations
+
+When the order doesn't matter, it is a **Combination**.
+
+When the order **does** matter it is a **Permutation**.
+
+**"My fruit salad is a combination of apples, grapes and bananas"**
+We don't care what order the fruits are in, they could also be 
+"bananas, grapes and apples" or "grapes, apples and bananas", 
+its the same fruit salad.
+
+## Combinations without repetitions
+
+## Combinations with repetitions
+
+## References
+
+[Math Is Fun](https://www.mathsisfun.com/combinatorics/combinations-permutations.html)

src/algorithms/string/permutations/__test__/permutateWithRepetitions.test.js

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+import permutateWithRepetition from '../permutateWithRepetitions';
+
+describe('permutateWithRepetition', () => {
+  it('should permutate string with repetition', () => {
+    const permutations0 = permutateWithRepetition('');
+    expect(permutations0).toEqual([]);
+
+    const permutations1 = permutateWithRepetition('A');
+    expect(permutations1).toEqual(['A']);
+
+    const permutations2 = permutateWithRepetition('AB');
+    expect(permutations2).toEqual([
+      'AA',
+      'AB',
+      'BA',
+      'BB',
+    ]);
+
+    const permutations3 = permutateWithRepetition('ABC');
+    expect(permutations3).toEqual([
+      'AAA',
+      'AAB',
+      'AAC',
+      'ABA',
+      'ABB',
+      'ABC',
+      'ACA',
+      'ACB',
+      'ACC',
+      'BAA',
+      'BAB',
+      'BAC',
+      'BBA',
+      'BBB',
+      'BBC',
+      'BCA',
+      'BCB',
+      'BCC',
+      'CAA',
+      'CAB',
+      'CAC',
+      'CBA',
+      'CBB',
+      'CBC',
+      'CCA',
+      'CCB',
+      'CCC',
+    ]);
+
+    const permutations4 = permutateWithRepetition('ABCD');
+    expect(permutations4.length).toBe(4 * 4 * 4 * 4);
+  });
+});

src/algorithms/string/permutations/permutateWithRepetitions.js

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+/**
+ * @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;
+}

src/algorithms/string/permutations/permutateWithoutRepetitions.js

@@ -1,3 +1,7 @@
+/**
+ * @param {string} str
+ * @return {string[]}
+ */
 export default function permutateWithoutRepetitions(str) {
   if (str.length === 0) {
     return [];