From 00e40a0eca2d086571df846a2a25053877e233e7 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Mon, 2 Apr 2018 12:27:20 +0300
Subject: [PATCH] Add power set algorithm.

---
 .eslintrc                                     |  3 ++
 README.md                                     |  1 +
 src/algorithms/math/power-set/README.md       |  5 ++++
 .../math/power-set/__test__/powerSet.test.js  | 24 ++++++++++++++++
 src/algorithms/math/power-set/powerSet.js     | 28 +++++++++++++++++++
 5 files changed, 61 insertions(+)
 create mode 100644 src/algorithms/math/power-set/README.md
 create mode 100644 src/algorithms/math/power-set/__test__/powerSet.test.js
 create mode 100644 src/algorithms/math/power-set/powerSet.js

diff --git a/.eslintrc b/.eslintrc
index 634529e0..3790cd52 100644
--- a/.eslintrc
+++ b/.eslintrc
@@ -4,5 +4,8 @@
   "plugins": ["jest"],
   "env": {
     "jest/globals": true
+  },
+  "rules": {
+    "no-bitwise": "off"
   }
 }
diff --git a/README.md b/README.md
index 63a02f2b..f5ffe8ad 100644
--- a/README.md
+++ b/README.md
@@ -16,6 +16,7 @@
 * Math
   * [Fibonacci Number](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fibonacci)
   * [Cartesian Product](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/cartesian-product)
+  * [Power Set](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/power-set)
 
 ## Running Tests
 
diff --git a/src/algorithms/math/power-set/README.md b/src/algorithms/math/power-set/README.md
new file mode 100644
index 00000000..0857e680
--- /dev/null
+++ b/src/algorithms/math/power-set/README.md
@@ -0,0 +1,5 @@
+# Power Set
+
+Power set of a set A is the set of all of the subsets of A.
+
+Eg. for `{x, y, z}`, the subsets are : `{{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}`
diff --git a/src/algorithms/math/power-set/__test__/powerSet.test.js b/src/algorithms/math/power-set/__test__/powerSet.test.js
new file mode 100644
index 00000000..26195081
--- /dev/null
+++ b/src/algorithms/math/power-set/__test__/powerSet.test.js
@@ -0,0 +1,24 @@
+import powerSet from '../powerSet';
+
+describe('powerSet', () => {
+  it('should calculate power set of given set', () => {
+    const powerSets1 = powerSet([1]);
+    const powerSets2 = powerSet([1, 2, 3]);
+
+    expect(powerSets1).toEqual([
+      [],
+      [1],
+    ]);
+
+    expect(powerSets2).toEqual([
+      [],
+      [1],
+      [2],
+      [1, 2],
+      [3],
+      [1, 3],
+      [2, 3],
+      [1, 2, 3],
+    ]);
+  });
+});
diff --git a/src/algorithms/math/power-set/powerSet.js b/src/algorithms/math/power-set/powerSet.js
new file mode 100644
index 00000000..8619f32e
--- /dev/null
+++ b/src/algorithms/math/power-set/powerSet.js
@@ -0,0 +1,28 @@
+export default function powerSet(originalSet) {
+  const subSets = [];
+
+  // We will have 2^n possible combinations (where n is a length of original set).
+  // It is because for every element of original set we will decide whether to include
+  // it or not (2 options for each set element).
+  const numberOfCombinations = 2 ** originalSet.length;
+
+  // Each number in binary representation in a range from 0 to 2^n does exactly what we need:
+  // it shoes by its bits (0 or 1) whether to include related element from the set or not.
+  // For example, for the set {1, 2, 3} the binary number of 010 would mean that we need to
+  // include only "2" to the current set.
+  for (let combinationIndex = 0; combinationIndex < numberOfCombinations; combinationIndex += 1) {
+    const subSet = [];
+
+    for (let setElementIndex = 0; setElementIndex < originalSet.length; setElementIndex += 1) {
+      // Decide whether we need to include current element into the subset or not.
+      if (combinationIndex & (1 << setElementIndex)) {
+        subSet.push(originalSet[setElementIndex]);
+      }
+    }
+
+    // Add current subset to the list of all subsets.
+    subSets.push(subSet);
+  }
+
+  return subSets;
+}