algorithm(recursion): add backtracking and hanoi tower

careteenL · careteenL · commit efdf62538afe · 2019-07-24T16:33:11.000+08:00
diff --git a/assets/alg-backtracking-1.jpg b/assets/alg-backtracking-1.jpg
diff --git a/assets/alg-backtracking-2.jpg b/assets/alg-backtracking-2.jpg
diff --git a/assets/alg-backtracking-3.jpg b/assets/alg-backtracking-3.jpg
diff --git a/assets/alg-backtracking-4.jpg b/assets/alg-backtracking-4.jpg
diff --git a/docs/README.Study.md b/docs/README.Study.md
@@ -11,11 +11,22 @@
     - [排序算法介绍](#排序算法介绍)
     - [基于比较的排序算法](#基于比较的排序算法)
     - [快速排序](#快速排序)
-- [合并排序的优化](#合并排序的优化)
-- [计数排序](#计数排序)
-- [基数排序](#基数排序)
-- [桶排序](#桶排序)
-- [外部排序](#外部排序)
+    - [合并排序的优化](#合并排序的优化)
+    - [计数排序](#计数排序)
+    - [基数排序](#基数排序)
+    - [桶排序](#桶排序)
+    - [外部排序](#外部排序)
+- [递归](#递归)
+    - [递归的基本概念](#递归的基本概念)
+        - [汉诺塔](#汉诺塔)
+    - [用递归绘制图形](#用递归绘制图形)
+    - [递归和穷举问题](#递归和穷举问题)
+        - [子集](#子集)
+        - [全排列](#全排列)
+    - [组合问题](#组合问题)
+    - [递归空间优化](#递归空间优化)
+    - [回溯算法](#回溯算法)
+
 
 ## 时间复杂度和空间复杂度
 
diff --git a/src/algorithm/README.md b/src/algorithm/README.md
@@ -0,0 +1 @@
+# 常见算法
diff --git a/src/algorithm/recursion/README.md b/src/algorithm/recursion/README.md
@@ -0,0 +1,7 @@
+# 递归
+
+## 传送门
+
+- [求一个数组的子集](./subsets.js)
+- [回溯算法](./backtracking.md)
+  - 老鼠逃出迷宫
diff --git a/src/algorithm/recursion/backtracking.js b/src/algorithm/recursion/backtracking.js
@@ -0,0 +1,45 @@
+/**
+ * @desc 回溯算法 - 老鼠逃出迷宫
+ * @param {Array<Array>} maze 二维数组的矩阵迷宫 
+ *              0表示没有走过的路 1表示墙体 2表示出口
+ * @param {Array<Number>} pos 当前位置
+ * @param {Array<Array>} path 路径
+ * @param {Array<Number>} transverse 记录走过的地方
+ * @return {Array<Array>} path 走出迷宫的路径
+ */
+export function rat_in_maze (
+  maze, pos = [0, 0], path = [[...pos]], transverse = []
+) {
+  const [x, y] = pos
+  if (maze[x][y] === 2) { // 结束条件
+    return path
+  }
+  // 记录走过的位置
+  transverse[x * maze.length + y] = 1
+  // 寻找可能的方向路径
+  const choices = [
+    [x + 1, y], [x - 1, y], // 向右 左
+    [x, y + 1], [x, y - 1] // 向上 下
+  ].filter(([nextX, nextY]) => {
+    return nextX >=0 && nextY >= 0 // 上 左 边界
+      && nextX < maze.length && nextY < maze[0].length // 右 下 边界
+      && maze[nextX][nextY] !== 1 // 非墙体
+      && !transverse[nextX * maze.length + nextY] // 非已经走过的格子
+  })
+  // 对每个选择 继续递归 寻找路径
+  for (const [nextX, nextY] of choices) {
+    const p = rat_in_maze(maze, [nextX, nextY], path.concat([[nextX, nextY]]), transverse)
+    if (p) return p
+  }
+}
+
+// TODO remove Test
+const maze = [ // 构建迷宫
+  [0, 1, 0, 0, 0, 0],
+  [0, 1, 0, 1, 1, 0],
+  [0, 0, 0, 1, 0, 1],
+  [1, 1, 0, 0, 0, 1],
+  [0, 0, 0, 1, 1, 1],
+  [2, 1, 0, 0, 0, 0]
+]
+console.log(rat_in_maze(maze))
diff --git a/src/algorithm/recursion/backtracking.md b/src/algorithm/recursion/backtracking.md
@@ -0,0 +1,14 @@
+# 回溯算法
+
+## 目录
+
+- [老鼠逃出迷宫](#老鼠逃出迷宫)
+
+## 老鼠逃出迷宫
+
+![alg-backtracking-1](../../../assets/alg-backtracking-1.jpg)
+![alg-backtracking-2](../../../assets/alg-backtracking-2.jpg)
+![alg-backtracking-3](../../../assets/alg-backtracking-3.jpg)
+![alg-backtracking-4](../../../assets/alg-backtracking-4.jpg)
+
+- [详细实现及测试用例](./backtracking.js)
diff --git a/src/algorithm/recursion/subsets.js b/src/algorithm/recursion/subsets.js
@@ -0,0 +1,31 @@
+/**
+ * @desc 求一个数组的子集
+ */
+export function * subsetsGen (array) {
+  for (let i = 0; i < 1 << array.length; i++) {
+    let ret = []
+    for (let k = 0; k < array.length; k++) {
+      const take = i & (1 << k)
+      take && ret.push(array[k])
+    }
+    yield ret.join('')
+  }
+}
+
+export function subsets (array) {
+  let outRet = []
+  for (let i = 0; i < 1 << array.length; i++) {
+    let ret = []
+    for (let k = 0; k < array.length; k++) {
+      const take = i & (1 << k)
+      take && ret.push(array[k])
+    }
+    outRet.push(ret.join(''))
+  }
+  return outRet
+}
+
+// TODO remove Test
+const array = ['a', 'b', 'c', 'd']
+console.log([...subsetsGen(array)])
+console.log(subsets(array))
diff --git a/src/algorithm/sort/bucket-sort-easy.js b/src/algorithm/sort/bucket-sort-easy.js
@@ -3,21 +3,25 @@
  * @param {Array} array 
  * @param {Number} bucketSize [default:5]
  * @return {Array}
- */ 
-import { insertionSort } from './insertion-sort'
+ */
+import {
+  insertionSort
+} from './insertion-sort'
 export function bucketSortEasy(array, bucketNum = 5, bucketSize = 10) {
-    const buckets = Array.from({ length: bucketNum }, _ => [])
-    // 放入桶中
-    for (let i = 0; i < array.length; i++) {
-        const index = ~~(array / bucketSize)
-        buckets[index].push(array[i])
-    }
-    // 排序每只桶
-    for (let i = 0; i < buckets.length; i++) {
-        insertionSort(buckets[i])
-    }
-    // 取出数据
-    return [].concat(...buckets)
+  const buckets = Array.from({
+    length: bucketNum
+  }, () => [])
+  // 放入桶中
+  for (let i = 0; i < array.length; i++) {
+    const index = ~~(array / bucketSize)
+    buckets[index].push(array[i])
+  }
+  // 排序每只桶
+  for (let i = 0; i < buckets.length; i++) {
+    insertionSort(buckets[i])
+  }
+  // 取出数据
+  return [].concat(...buckets)
 }
 
 // TODO remove Test
diff --git a/src/algorithm/sort/radix-sort-easy.js b/src/algorithm/sort/radix-sort-easy.js
@@ -5,7 +5,7 @@
  */
 export function radixSortEasy(array) {
   const max = Math.max(...array)
-  const buckets = Array.from({ length: 10 }, _ => [])
+  const buckets = Array.from({ length: 10 }, () => [])
   // 有效位数
   let m = 1
   while (m < max) {
diff --git a/src/algorithm/uncategorized/README.md b/src/algorithm/uncategorized/README.md
@@ -0,0 +1,5 @@
+## 未分类算法
+
+### Catalog
+
+- [汉诺塔](./hanoi-tower.md)
diff --git a/src/algorithm/uncategorized/hanoi-tower.js b/src/algorithm/uncategorized/hanoi-tower.js
@@ -0,0 +1,3 @@
+/**
+ * @desc 汉诺塔
+ */
diff --git a/src/algorithm/uncategorized/hanoi-tower.md b/src/algorithm/uncategorized/hanoi-tower.md
@@ -0,0 +1,40 @@
+## 汉诺塔 - Hanoi Tower
+
+### Catalog
+
+- [What](#what)
+- [How](#how)
+- [API](#api)
+- [Usage](#usage)
+- [Where](#where)
+
+### What
+
+to be replaced
+
+### How
+
+[详细实现](./hanoi-tower.js)
+
+### API
+
+#### to be replaced
+
+| desc | param | mean | type | return |
+| :---: | :---: | :--: | :--: | :--: |
+| - | - | - | - | - |
+
+...
+
+### Usage
+
+```js
+
+```
+
+### Where
+
+to be replaced
+
+- 更多使用场景...
+
