Add a Divide and Conquer version of the MaxSubArray problem.

Author: trekhleb

Diff for: .npmrc

@@ -1 +1 @@
-engine-strict=false
+engine-strict=true

Diff for: .nvmrc

@@ -0,0 +1 @@
+v14

Diff for: README.md

@@ -207,6 +207,7 @@ algorithm is an abstraction higher than a computer program.
   * `B` [Best Time To Buy Sell Stocks](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - divide and conquer and one-pass examples
   * `A` [Permutations](src/algorithms/sets/permutations) (with and without repetitions)
   * `A` [Combinations](src/algorithms/sets/combinations) (with and without repetitions)
+  * `A` [Maximum Subarray](src/algorithms/sets/maximum-subarray)
 * **Dynamic Programming** - build up a solution using previously found sub-solutions
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game)
@@ -278,6 +279,8 @@ rm -rf ./node_modules
 npm i
 ```
 
+Also make sure that you're using a correct Node version (`>=14.16.0`). If you're using [nvm](https://github.com/nvm-sh/nvm) for Node version management you may run `nvm use` from the root folder of the project and the correct version will be picked up.
+
 **Playground**
 
 You may play with data-structures and algorithms in `./src/playground/playground.js` file and write

Diff for: src/algorithms/sets/maximum-subarray/README.md

@@ -1,7 +1,7 @@
 # Maximum subarray problem
 
-The maximum subarray problem is the task of finding the contiguous 
-subarray within a one-dimensional array, `a[1...n]`, of numbers 
+The maximum subarray problem is the task of finding the contiguous
+subarray within a one-dimensional array, `a[1...n]`, of numbers
 which has the largest sum, where,
 
 ![Maximum subarray](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8960f093107b71b21827e726e2bad8b023779b2)
@@ -10,11 +10,17 @@ which has the largest sum, where,
 
 ## Example
 
-The list usually contains both positive and negative numbers along 
-with `0`. For example, for the array of 
-values `−2, 1, −3, 4, −1, 2, 1, −5, 4` the contiguous subarray 
+The list usually contains both positive and negative numbers along
+with `0`. For example, for the array of
+values `−2, 1, −3, 4, −1, 2, 1, −5, 4` the contiguous subarray
 with the largest sum is `4, −1, 2, 1`, with sum `6`.
 
+## Solutions
+
+- Brute Force solution `O(n^2)`: [bfMaximumSubarray.js](./bfMaximumSubarray.js)
+- Divide and Conquer solution `O(n^2)`: [dcMaximumSubarraySum.js](./dcMaximumSubarraySum.js)
+- Dynamic Programming solution `O(n)`: [dpMaximumSubarray.js](./dpMaximumSubarray.js)
+
 ## References
 
 - [Wikipedia](https://en.wikipedia.org/wiki/Maximum_subarray_problem)

Diff for: src/algorithms/sets/maximum-subarray/__test__/bfMaximumSubarray.test.js

@@ -1,7 +1,7 @@
 import bfMaximumSubarray from '../bfMaximumSubarray';
 
 describe('bfMaximumSubarray', () => {
-  it('should find maximum subarray using brute force algorithm', () => {
+  it('should find maximum subarray using the brute force algorithm', () => {
     expect(bfMaximumSubarray([])).toEqual([]);
     expect(bfMaximumSubarray([0, 0])).toEqual([0]);
     expect(bfMaximumSubarray([0, 0, 1])).toEqual([0, 0, 1]);

Diff for: src/algorithms/sets/maximum-subarray/__test__/dcMaximumSubarraySum.test.js

@@ -0,0 +1,16 @@
+import dcMaximumSubarray from '../dcMaximumSubarraySum';
+
+describe('dcMaximumSubarraySum', () => {
+  it('should find maximum subarray sum using the divide and conquer algorithm', () => {
+    expect(dcMaximumSubarray([])).toEqual(-Infinity);
+    expect(dcMaximumSubarray([0, 0])).toEqual(0);
+    expect(dcMaximumSubarray([0, 0, 1])).toEqual(1);
+    expect(dcMaximumSubarray([0, 0, 1, 2])).toEqual(3);
+    expect(dcMaximumSubarray([0, 0, -1, 2])).toEqual(2);
+    expect(dcMaximumSubarray([-1, -2, -3, -4, -5])).toEqual(-1);
+    expect(dcMaximumSubarray([1, 2, 3, 2, 3, 4, 5])).toEqual(20);
+    expect(dcMaximumSubarray([-2, 1, -3, 4, -1, 2, 1, -5, 4])).toEqual(6);
+    expect(dcMaximumSubarray([-2, -3, 4, -1, -2, 1, 5, -3])).toEqual(7);
+    expect(dcMaximumSubarray([1, -3, 2, -5, 7, 6, -1, 4, 11, -23])).toEqual(27);
+  });
+});

Diff for: src/algorithms/sets/maximum-subarray/__test__/dpMaximumSubarray.test.js

@@ -1,7 +1,7 @@
 import dpMaximumSubarray from '../dpMaximumSubarray';
 
 describe('dpMaximumSubarray', () => {
-  it('should find maximum subarray using dynamic programming algorithm', () => {
+  it('should find maximum subarray using the dynamic programming algorithm', () => {
     expect(dpMaximumSubarray([])).toEqual([]);
     expect(dpMaximumSubarray([0, 0])).toEqual([0]);
     expect(dpMaximumSubarray([0, 0, 1])).toEqual([0, 0, 1]);

Diff for: src/algorithms/sets/maximum-subarray/dcMaximumSubarraySum.js

@@ -0,0 +1,33 @@
+/**
+ * Divide and Conquer solution.
+ * Complexity: O(n^2) in case if no memoization applied
+ *
+ * @param {Number[]} inputArray
+ * @return {Number[]}
+ */
+export default function dcMaximumSubarraySum(inputArray) {
+  /**
+   * We are going through the inputArray array and for each element we have two options:
+   * - to pick
+   * - not to pick
+   *
+   * Also keep in mind, that the maximum sub-array must be contiguous. It means if we picked
+   * the element, we need to continue picking the next elements or stop counting the max sum.
+   *
+   * @param {number} elementIndex - the index of the element we're deciding to pick or not
+   * @param {boolean} mustPick - to pick or not to pick the element
+   * @returns {number} - maximum subarray sum that we'll get
+   */
+  function solveRecursively(elementIndex, mustPick) {
+    if (elementIndex >= inputArray.length) {
+      return mustPick ? 0 : -Infinity;
+    }
+    return Math.max(
+      // Option #1: Pick the current element, and continue picking next one.
+      inputArray[elementIndex] + solveRecursively(elementIndex + 1, true),
+      // Option #2: Don't pick the current element.
+      mustPick ? 0 : solveRecursively(elementIndex + 1, false),
+    );
+  }
+  return solveRecursively(0, false);
+}