Add min change problem

Author: mgechev

src/others/min-coins-change.js

@@ -0,0 +1,50 @@
+(function (exports) {
+  'use strict';
+
+  /**
+   * Returns the minimum number of coins from given set,
+   * which sum equals to given change. This is famous
+   * problem from the dymanic programming:
+   *   https://en.wikipedia.org/wiki/Change-making_problem
+   *
+   * @public
+   * @module others/minCoinsChange
+   *
+   * @example
+   *
+   * var minCoinsChange =
+   *  require('path-to-algorithms/src/others/min-coins-change')
+   *  .minCoinsChange;
+   * var coins = minCoinsChange([1, 2, 3], 5); // [ 2, 3 ]
+   *
+   * @param {Array} coins The sorted list of the coins used for the change.
+   * @param {Number} change The change, which should be returned.
+   * @return Array which contains the minimum coins from the given
+   *  list, required for the change.
+   */
+  function minCoinsChange(coins, change) {
+    var minChange = [[0]];
+    if (coins.indexOf(change) >= 0) {
+      return [change];
+    }
+    for (var i = 1; i <= change; i += 1) {
+      var current = null;
+      for (var j = 0; j < coins.length && coins[j] <= change; j += 1) {
+        for (var k = 0; k < minChange.length; k += 1) {
+          if (k + coins[j] === i &&
+             (!current || minChange[k].length + 1 < current.length)) {
+            minChange[i] = minChange[k].concat([coins[j]]);
+          }
+        }
+      }
+    }
+    var result = minChange[change];
+    if (!result) {
+      return undefined;
+    }
+    return result.slice(1);
+  }
+
+  exports.minCoinsChange = minCoinsChange;
+
+})(typeof window === 'undefined' ? module.exports : window);

test/others/min-coins-sum.spec.js

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+'use strict';
+
+var minCoinsChange =
+  require('../../src/others/min-coins-change.js').minCoinsChange;
+
+describe('Change making problem', function () {
+  it('should be defined', function () {
+    expect(minCoinsChange).toBeDefined();
+  });
+
+  it('should work for 0 change', function () {
+    expect(minCoinsChange([1, 2], 0)).toEqual([]);
+  });
+
+  it('should work for change equals to array element', function () {
+    expect(minCoinsChange([1, 2], 1)).toEqual([1]);
+  });
+
+  it('should return the minimum amount of coins', function () {
+    expect(minCoinsChange([1], 2)).toEqual([1, 1]);
+    expect(minCoinsChange([1, 2], 3)).toEqual([1, 2]);
+    // [2, 3, 2, 3] or [1, 3, 3, 3]
+    expect(minCoinsChange([1, 2, 3], 10).length).toEqual(4);
+  });
+
+  it('should return undefined for combination, which is not possible',
+    function () {
+      expect(minCoinsChange([1, 2, 3], 0.5)).not.toBeDefined();
+    });
+});