feat(games-hanoi): implement towers of hanoi & references to Prolog solution

Author: uldissturms

README.md

@@ -39,6 +39,9 @@ More information about hashign on [wikipedia](https://en.wikipedia.org/wiki/Hash
   * ./interview-io/word-break.test.js
   * ./interview-io/shortest-continuous-subarray.test.js
 
+### Games
+  * ./games/tower-of-hanoi.test.js
+
 ### Sources
   * https://leetcode.com
   * http://www.crackingthecodinginterview.com

games/tower-of-hanoi.test.js

@@ -0,0 +1,115 @@
+/*
+ * Game - https://www.mathsisfun.com/games/towerofhanoi.html
+ * Prolog - https://www.cpp.edu/~jrfisher/www/prolog_tutorial/2_3.html
+ * Prolog (github) - https://github.com/dvberkel/prolog-hanoi
+ */
+
+import test from 'ava'
+import { clone, id } from '../helpers'
+
+let count = 0
+
+const countMoves = (t) => {
+  count += 1
+}
+
+test.beforeEach(t => {
+  count = 0
+})
+
+test('tower of hanoi - 1', t => {
+  t.deepEqual(
+    solve([
+      clone([1]), [], [] ],
+      countMoves
+    ),
+    [ [], [], clone([1]) ]
+  )
+  t.is(count, 1)
+})
+
+test('tower of hanoi - 2', t => {
+  t.deepEqual(
+    solve(
+      [ clone([1, 2]), [], [] ],
+      countMoves
+    ),
+    [ [], [], clone([1, 2]) ]
+  )
+  t.is(count, 3)
+})
+
+test('tower of hanoi - 3', t => {
+  const towerOf3 = [1, 2, 3]
+  t.deepEqual(
+    solve(
+      [ clone(towerOf3), [], [] ],
+      countMoves
+    ),
+    [ [], [], clone(towerOf3) ]
+  )
+  t.is(count, 7)
+})
+
+test('tower of hanoi - 5', t => {
+  const towerOf5 = [1, 2, 3, 4, 5]
+  t.deepEqual(
+    solve(
+      [ clone(towerOf5), [], [] ],
+      countMoves
+    ),
+    [ [], [], clone(towerOf5) ]
+  )
+  t.is(count, 31)
+})
+
+const left = (tower) => tower[0]
+const center = (tower) => tower[1]
+const right = (tower) => tower[2]
+
+const solve = (tower, onMove = id) => {
+  const [first] = tower
+  const levels = first.length
+  move(levels - 1, left, right, center, tower, onMove)
+  return tower
+}
+
+/* manual solution
+
+ * one (moves: 1)
+ * [1], [], []
+ *
+ * [], [], [1]
+ *
+ * two (moves: 3)
+ * [1, 2], [], []
+
+ * [2], [1], []
+ * [], [1], [2]
+ * [], [], [1, 2]
+
+ * three (moves: 7)
+ * [1, 2, 3], [], []
+
+ * [2, 3], [], [1]
+ * [3], [2], [1]
+ * [3], [1, 2], []
+ * [], [1, 2], [3]
+ * [1], [2], [3]
+ * [1], [], [2, 3]
+ * [], [], [1, 2, 3]
+
+*/
+
+const move = (index, left, right, center, tower, onMove) => {
+  if (index === 0) {
+    const item = left(tower).pop()
+    right(tower).push(item)
+    onMove()
+    return
+  }
+
+  move(index - 1, left, center, right, tower, onMove)
+  move(0, left, right, center, tower, onMove)
+  move(index - 1, center, right, left, tower, onMove)
+}