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数据结构全解参考：数据结构 | 博客园-SRIGT

相关代码仓库查看：data-struct-js | Github-SR1GT

0x00 前置知识

（1）类

  1. 使用关键字 class 声明一个类

    class Person {
  
}

  2. JavaScript 的类中通过 constructor 使用构建函数

    class Person {
  constructor(name) {
    this.name = name;
  }
}

  3. 定义 Getter 与 Setter

    class Person {
  constructor(name) {
    this.name = name;
  }
  getName() {
    return this.name;
  }
  setName(name) {
    this.name = name;
  }
}

  4. 使用关键字 new 创建对象，并调用对象方法

    class Person {
  constructor(name) {
    this.name = name;
  }
  getName() {
    return this.name;
  }
  setName(name) {
    this.name = name;
  }
}

var person = new Person("SRIGT");
console.log(person.getName());		// "SRIGT"
person.setName("SR1GT");
console.log(person.getName());		// "SR1GT"

（2）指针

  • 以下代码仅实现值的传递，并未涉及指针

    var num1 = 1;
var num2 = num1;
console.log(num1, num2);	// 1 1
num1 = 2;
console.log(num1, num2);	// 2 1

  • 当声明的变量是对象时，实现指针的传递

    var num1 = { value: 1 };
var num2 = num1;
console.log(num1.value, num2.value);	// 1 1
num1.value = 2;
console.log(num1.value, num2.value);	// 2 2
    • var num2 = num1; 是将变量 num2 指向 num1，同时 num1 又指向对象 { value: 1 }

  • 当某个对象不被任何变量指向时，该对象不可访问，但依旧占用内存空间，此时 JavaScript 提供的垃圾回收机制很好的解决了这个问题

（3）递归

  • 递归是指在函数中调用自身

    function func() {
  if (condition === true) return;
  func();
}
    • 当没有合适条件停止递归，会造成堆栈溢出

  • 举例：阶乘

    function factorial(n) {
  if (n === 1) return 1;
  return n * factorial(n - 1);
}

console.log(factorial(4));		// 24

0x01 链表

（1）单链表

  1. 声明类并实现构造函数

    class Node {
  constructor(value) {
    this.value = value;
    this.next = null;
  }
}

class LinkedList {
  constructor(value) {
    this.head = new Node(value);
    this.tail = this.head;
    this.length = 1;
  }
}

var myLinkedList = new LinkedList(1);
console.log(myLinkedList);

  2. 在 LinkedList 类中，添加 push 方法，用于在尾部添加节点

    push(value) {
  const newNode = new Node(value);
  if (!this.head) {
    this.head = newNode;
    this.tail = this.head;
  } else {
    this.tail.next = newNode;
    this.tail = newNode;
  }
  this.length++;
  return this;
}

  3. 添加 pop 方法，用于删除尾部最后一个节点

    pop() {
  if (!this.head) return undefined;

  let prev = this.head;
  let temp = this.head;
  while (temp.next) {
    prev = temp;
    temp = temp.next;
  }
  this.tail = prev;
  this.tail.next = null;
  this.length--;

  if (this.length === 0) this.head = this.tail = null;
  return temp;
}

  4. 添加 unshift 和 shift 方法，分别用于在头部添加和删除第一个节点

    unshift(value) {
  const newNode = new Node(value);
  if (!this.head) {
    this.head = newNode;
    this.tail = this.head;
  } else {
    newNode.next = this.head;
    this.head = newNode;
  }
  this.length++;
  return this;
}

shift() {
  if (!this.head) return undefined;

  let temp = this.head;
  this.head = this.head.next;
  temp.next = null;
  this.length--;

  if (this.length === 0) this.tail = null;
  return temp;
}

  5. 添加 get 方法，用于获取特定索引位置的值

    get(index) {
  if (index === 0) return this.head;
  if (index < this.length * -1 || index >= this.length)
    throw new Error("Index out of bounds");
  if (index < 0) index = this.length + index;
  let temp = this.head;
  for (let i = 0; i < index; i++) temp = temp.next;
  return temp;
}

  6. 添加 set 方法，用于修改指定位置的值

    set(index, value) {
  let temp = this.get(index);
  if (!temp) return false;
  temp.value = value;
  return true;
}

  7. 添加 insert 方法，用于在指定位置添加新节点

    insert(index, value) {
  if (index === 0) return this.unshift(value);
  if (index === this.length) return this.push(value);
  if (index < 0 || index > this.length)
    throw new Error("Index out of bounds");

  let newNode = new Node(value);
  let prev = this.get(index - 1);
  newNode.next = prev.next;
  prev.next = newNode;
  this.length++;
  return this;
}

  8. 添加 remove 方法，用于删除指定位置的节点

    remove(index) {
  if (index === 0) return this.shift();
  if (index === this.length - 1) return this.pop();
  if (index < 0 || index >= this.length)
    throw new Error("Index out of bounds");

  let prev = this.get(index - 1);
  let temp = prev.next;
  prev.next = temp.next;
  temp.next = null;
  this.length--;
  return temp;
}

  9. 添加 reverse 方法，用于翻转链表

    reverse() {
  let temp = this.head;
  let next = temp.next,
    prev = null;

  [this.head, this.tail] = [this.tail, this.head];
  for (let i = 0; i < this.length; i++) {
    next = temp.next;
    temp.next = prev;
    prev = temp;
    temp = next;
  }
  return this;
}

  10. 添加 forEach 方法，用于遍历链表

    forEach(callback) {
  if (!this.head) return;
  let temp = this.head;
  while (temp) {
    callback(temp);
    temp = temp.next;
  }
}

（2）双向链表

  1. 声明类并实现构造函数

    class Node {
  constructor(value) {
    this.value = value;
    this.prev = null;
    this.next = null;
  }
}

class DoublyLinkedList {
  constructor(value) {
    this.head = new Node(value);
    this.tail = this.head;
    this.length = 1;
  }
}

var myDoublyLinkedList = new DoublyLinkedList(1);
console.log(myDoublyLinkedList);

  2. push 与 pop 方法

    push(value) {
  const newNode = new Node(value);
  if (!this.head) {
    this.head = newNode;
    this.tail = this.head;
  } else {
    newNode.prev = this.tail;
    this.tail.next = newNode;
    this.tail = newNode;
  }
  this.length++;
  return this;
}

pop() {
  if (!this.head) return undefined;

  let temp = this.tail;
  this.tail = this.tail.prev;
  this.tail.next = null;
  temp.prev = null;
  this.length--;

  if (this.length === 0) this.head = this.tail = null;
  return temp;
}

  3. unshift 与 shift 方法

    unshift(value) {
  const newNode = new Node(value);
  if (!this.head) {
    this.head = newNode;
    this.tail = this.head;
  } else {
    this.head.prev = newNode;
    newNode.next = this.head;
    this.head = newNode;
  }
  this.length++;
  return this;
}

shift() {
  if (!this.head) return undefined;

  let temp = this.head;
  this.head = this.head.next;
  this.head.prev = null;
  temp.next = null;
  this.length--;

  if (this.length === 0) this.tail = null;
  return temp;
}

  4. get 与 set 方法

    get(index) {
  if (index === 0) return this.head;
  if (index === this.length - 1 || index === -1) return this.tail;
  if (index < this.length * -1 || index >= this.length)
    throw new Error("Index out of bounds");

  // 优化方向: 折半查找

  if (index < 0) {
    let temp = this.tail;
    for (let i = this.length - 1; i > this.length + index; i--)
      temp = temp.prev;
    return temp;
  } else {
    let temp = this.head;
    for (let i = 0; i < index; i++) temp = temp.next;
    return temp;
  }
}

set(index, value) {
  let temp = this.get(index);
  temp.value = value;
  return temp;
}

  5. insert 与 remove 方法

    insert(index, value) {
  if (index === 0) return this.unshift(value);
  if (index === this.length) return this.push(value);
  if (index < 0 || index > this.length)
    throw new Error("Index out of bounds");

  let newNode = new Node(value);
  let prev = this.get(index - 1);

  newNode.next = prev.next;
  prev.next.prev = newNode;

  prev.next = newNode;
  newNode.prev = prev;

  this.length++;
  return this;
}

remove(index) {
  if (index === 0) return this.shift();
  if (index === this.length - 1) return this.pop();
  if (index < 0 || index >= this.length)
    throw new Error("Index out of bounds");

  let temp = this.get(index);

  temp.prev.next = temp.next;
  temp.next.prev = temp.prev;
  temp.prev = null;
  temp.next = null;
  this.length--;
  return temp;
}

（3）栈

  1. 声明类并实现构造函数

    class Node {
  constructor(value) {
    this.value = value;
    this.next = null;
  }
}

class Stack {
  constructor(value) {
    this.top = new Node(value);
    this.length = 1;
  }
}

var myStack = new Stack(1);
console.log(myStack);

  2. 压栈方法 push

    push(value) {
  const newNode = new Node(value);
  if (!this.top) this.top = newNode;
  else {
    newNode.next = this.top;
    this.top = newNode;
  }
  this.length++;
  return this;
}

  3. 出栈方法 pop

    pop() {
  if (!this.top) return undefined;
  let temp = this.top;
  this.top = this.top.next;
  temp.next = null;
  this.length--;
  if (this.length === 0) this.top = null;
  return temp;
}

（4）队列

  1. 声明类并实现构造函数

    class Node {
  constructor(value) {
    this.value = value;
    this.next = null;
  }
}

class Queue {
  constructor(value) {
    this.first = new Node(value);
    this.last = this.first;
    this.length = 1;
  }
}

var myQueue = new Queue(1);
console.log(myQueue);

  2. 入队方法 enQueue

    enQueue(value) {
  const newNode = new Node(value);
  if (!this.first) {
    this.first = newNode;
    this.last = this.first;
  } else {
    this.last.next = newNode;
    this.last = newNode;
  }
  this.length++;
  return this;
}

  3. 出队方法 deQueue

    deQueue() {
  if (!this.first) return undefined;
  let temp = this.first;
  this.first = this.first.next;
  temp.next = null;
  this.length--;
  if (this.length === 0) this.first = this.last = null;
  return temp;
}

0x02 树与表

（1）二叉搜索树

  1. 声明类并实现构造函数

    class Node {
  constructor(value) {
    this.value = value;
    this.left = null;
    this.right = null;
  }
}

class BinarySearchTree {
  constructor() {
    this.root = null;
  }
}

var myBST = new BinarySearchTree();
console.log(myBST);

  2. 添加 insert 方法，用于添加节点

    insert(value) {
  const newNode = new Node(value);
  if (!this.root) {
    this.root = newNode;
    return this;
  } 

  let temp = this.root;
  while (true) {
    if (temp.value === value) return undefined;
    else if (temp.value > value) {
      if (!temp.left) {
        temp.left = newNode;
        return this;
      }
      temp = temp.left;
    } else {
      if (!temp.right) {
        temp.right = newNode;
        return this;
      }
      temp = temp.right;
    }
  }
}

  3. 添加 contains 方法，用于判断节点是否存在

    contains(value) {
  if (!this.root) return false;

  let temp = this.root;
  while (true) {
    if (temp.value === value) return true;
    else if (temp.value > value) {
      if (!temp.left) return false;
      temp = temp.left;
    } else {
      if (!temp.right) return false;
      temp = temp.right;
    }
  }
}

  4. 添加 minValueNode 方法，获取最小节点值

    minValueNode() {
  let temp = this.root;
  while (temp.left) temp = temp.left;
  return temp;
}

（2）哈希表

  1. 声明类并实现构造函数

    class HashTable {
  constructor(size = 10) {
    this.dataMap = new Array(size);
  }

  _hash(key) {
    let hash = 0;
    for (let i in key)
      hash = (hash + key.charCodeAt(i) * 23) % this.dataMap.length;
    return hash;
  }
}

var myHashTable = new HashTable();
console.log(myHashTable);

  2. 添加 set 方法，用于添加新映射

    set(key, value) {
  const index = this._hash(key);
  if (!this.dataMap[index]) this.dataMap[index] = [];
  this.dataMap[index].push({ key: key, value: value });
  return this;
}

  3. 添加 get 方法，用于获取键值对应的值

    get(key) {
  const index = this._hash(key);
  if (this.dataMap[index])
    for (let item of this.dataMap[index]) if (item.key === key) return item.value;
  return undefined;
}

  4. 添加 keys 方法，用于获取全部键

    keys() {
  let allKeys = [];
  for (let item of this.dataMap)
    if (item) for (let kv of item) allKeys.push(kv.key);
  return allKeys;
}

0x03 图

采用邻接表实现

（1）无向图

  1. 声明类并实现构造函数

    class Graph {
  constructor() {
    this.adjacencyList = new Object();
  }
}

var myGraph = new Graph();
console.log(myGraph);

  2. 添加 addVertex 方法，用于新增顶点

    addVertex(vertex) {
  if (!this.adjacencyList[vertex]) {
    this.adjacencyList[vertex] = [];
    return this;
  }
  throw new Error("Vertex already exists");
}

  3. 添加 addEdge 方法，用于新增边

    addEdge(vertex1, vertex2) {
  if (this.adjacencyList[vertex1] && this.adjacencyList[vertex2]) {
    this.adjacencyList[vertex1].push(vertex2);
    this.adjacencyList[vertex2].push(vertex1);
    return this;
  }
  throw new Error("Vertex not found");
}

  4. 添加 removeEdge 方法，用于删除边

    removeEdge(vertex1, vertex2) {
  if (this.adjacencyList[vertex1] && this.adjacencyList[vertex2]) {
    this.adjacencyList[vertex1] = this.adjacencyList[vertex1].filter(
      (vertex) => vertex != vertex2
    );
    this.adjacencyList[vertex2] = this.adjacencyList[vertex2].filter(
      (vertex) => vertex != vertex1
    );
    return this;
  }
  throw new Error("Vertex not found");
}

  5. 添加 removeVertex 方法，用于删除顶点

    removeVertex(vertex) {
  if (this.adjacencyList[vertex]) {
    this.adjacencyList[vertex].forEach((item) => {
      this.removeEdge(vertex, item);
    });
    delete this.adjacencyList[vertex];
    return this;
  }
  throw new Error("Vertex not found");
}

（2）有向图

  1. 声明类并实现构造函数

    class Digraph {
  constructor() {
    this.adjacencyList = new Object();
  }
}

var myDigraph = new Digraph();
console.log(myDigraph);

  2. 添加 addVertex 方法，用于新增顶点

    addVertex(vertex) {
  if (!this.adjacencyList[vertex]) {
    this.adjacencyList[vertex] = [];
    return this;
  }
  throw new Error("Vertex already exists");
}

  3. 添加 addEdge 方法，用于新增有向边

    addEdge(vertexFrom, vertexTo) {
  if (this.adjacencyList[vertexFrom] && this.adjacencyList[vertexTo]) {
    this.adjacencyList[vertexFrom].push(vertexTo);
    return this;
  }
  throw new Error("Vertex not found");
}

  4. 添加 removeEdge 方法，用于删除边

    removeEdge(vertexFrom, vertexTo) {
  if (this.adjacencyList[vertexFrom] && this.adjacencyList[vertexTo]) {
    this.adjacencyList[vertexFrom] = this.adjacencyList[vertexFrom].filter(
      (vertex) => vertex != vertexTo
    );
    return this;
  }
  throw new Error("Vertex not found");
}

  5. 添加 removeVertex 方法，用于删除顶点

    removeVertex(vertex) {
  if (this.adjacencyList[vertex]) {
    Object.keys(this.adjacencyList).forEach((key) => {
      this.removeEdge(key, vertex);
    });
    delete this.adjacencyList[vertex];
    return this;
  }
  throw new Error("Vertex not found");
}

0x04 树遍历算法

构造树

class Node {
  constructor(value) {
    this.value = value;
    this.left = null;
    this.right = null;
  }
}

class Tree {
  constructor() {
    this.root = null;
  }

  insert(value) {
    const newNode = new Node(value);
    if (!this.root) {
      this.root = newNode;
      return this;
    }

    let temp = this.root;
    while (true) {
      if (temp.value === value) return undefined;
      else if (temp.value > value) {
        if (!temp.left) {
          temp.left = newNode;
          return this;
        }
        temp = temp.left;
      } else {
        if (!temp.right) {
          temp.right = newNode;
          return this;
        }
        temp = temp.right;
      }
    }
  }
}

本章的算法均作为类方法写在 Tree 类中

（1）广度优先搜索 BFS

  • 广度优先搜索（Breadth First Search）指对于一个二叉树进行层序遍历

    • 举例：有如下二叉树

      flowchart TB
20-->15 & 26
15-->4 & 19
26-->22 & 102
      Loading

      其 BFS 结果为

      flowchart LR
20-->15-->26-->4-->19-->22-->102
      Loading

  • 算法实现

    BFS() {
  let temp = this.root,
    queue = [],
    result = [];
  queue.push(temp);
  while (queue.length) {
    temp = queue.shift();
    result.push(temp.value);
    if (temp.left) queue.push(temp.left);
    if (temp.right) queue.push(temp.right);
  }
  return result;
}

    测试

    var myTree = new Tree();
myTree.insert(20);
myTree.insert(15);
myTree.insert(4);
myTree.insert(19);
myTree.insert(26);
myTree.insert(22);
myTree.insert(102);
console.log(myTree.BFS());

（2）深度优先搜索 DFS

  • 深度优先搜索（Depth First Search）指对于一个二叉树进行中序遍历（或前序遍历、后序遍历）

    • 举例：有如下二叉树

      flowchart TB
20-->15 & 26
15-->4 & 19
26-->22 & 102
      Loading

      其 DFS 结果为

      flowchart LR
4-->15-->19-->20-->22-->26-->102
      Loading

  • 算法实现

    DFS(order) {
  let result = [];
  const expression = [
    (node) => result.push(node.value),
    (node) => {
      if (node.left) traverse(node.left);
    },
    (node) => {
      if (node.right) traverse(node.right);
    },
  ];
  const traverse = (node) => {
    order.forEach((item) => {
      expression[item](node);
    });
  };
  traverse(this.root);
  return result;
}

    测试

    var myTree = new Tree();
myTree.insert(20);
myTree.insert(15);
myTree.insert(4);
myTree.insert(19);
myTree.insert(26);
myTree.insert(22);
myTree.insert(102);

const Order = Object.freeze({
  PRE: [0, 1, 2],
  IN: [1, 0, 2],
  POST: [1, 2, 0],
});
console.log(myTree.DFS(Order.PRE));
console.log(myTree.DFS(Order.IN));
console.log(myTree.DFS(Order.POST));

0x05 排序算法

（1）冒泡排序

从后出发，比较并交换，使最后一个值为最大值，进入下一个，重复上述操作

Array.prototype.bubbleSort = function () {
  for (let i = this.length - 1; i > 0; i--)
    for (let j = 0; j < i; j++)
      if (this[j] > this[j + 1])
        [this[j], this[j + 1]] = [this[j + 1], this[j]];
  return this;
};

console.log([4, 2, 3, 1, 5].bubbleSort());

（2）选择排序

（冒泡排序的逆向）从头出发，记录当前位置以后的最小值的索引，比较并交换，进入下一个，重复上述操作

Array.prototype.selectionSort = function () {
  let minIndex = this[0];
  for (let i = 0; i < this.length - 1; i++) {
    minIndex = i;
    for (let j = i + 1; j < this.length; j++)
      if (this[j] < this[minIndex]) minIndex = j;
    if (i !== minIndex) [this[i], this[minIndex]] = [this[minIndex], this[i]];
  }
  return this;
};

console.log([4, 2, 3, 1, 5].selectionSort());

（3）插入排序

从第二项出发，找到比当前值小的值，该小值以后的值后移一位，小值后面插入到当前值，进入下一个，重复此操作

Array.prototype.insertionSort = function () {
  let temp, j;
  for (let i = 1; i < this.length; i++) {
    (temp = this[i]), (j = i - 1);
    for (; this[j] > temp && j >= 0; j--) this[j + 1] = this[j];
    this[j + 1] = temp;
  }
  return this;
};

console.log([4, 2, 3, 1, 5].insertionSort());

（4）归并排序

将数组递归二分分组，直至每组只有两个数字，比较并交换后逐步归并各组至原数组大小

  1. 编写 merge 方法，用于按大小归并两个数组

    const merge = (array1, array2) => {
  let i = 0, j = 0, result = [];
  while (i < array1.length && j < array2.length)
    if (array1[i] < array2[j]) result.push(array1[i++]);
    else result.push(array2[j++]);
  while (i < array1.length) result.push(array1[i++]);
  while (j < array2.length) result.push(array2[j++]);
  return result;
};

  2. 结合合并方法，完成合并排序方法

    Array.prototype.mergeSort = function () {
  if (this.length <= 1) return this;

  const merge = (array1, array2) => {/*...*/};

  let mid = Math.floor(this.length / 2),
    left = this.slice(0, mid),
    right = this.slice(mid);
  return merge(left.mergeSort(), right.mergeSort());
};

console.log([4, 2, 3, 1, 5].mergeSort());

（5）快速排序

找到中心值，所有小于中心值的值放在中心值以左，其余的值放在中心值以右，递归此操作

  1. 编写 pivot 方法，用于获取数组中心值的索引

    const pivot = (pivotIndex, endIndex) => {
  let temp = pivotIndex;
  for (let i = pivotIndex + 1; i <= endIndex; i++)
    if (this[i] < this[pivotIndex])
      [this[temp], this[i]] = [this[i], this[++temp]];
  [this[pivotIndex], this[temp]] = [this[temp], this[pivotIndex]];
  return temp;
};

  2. 结合中心值索引获取方法，完成快速排序方法

    Array.prototype.quickSort = function (left = 0, right = this.length - 1) {
  const pivot = (pivotIndex, endIndex) => {/*...*/};

  if (left < right) {
    const pivotIndex = pivot(left, right);
    this.quickSort(left, pivotIndex - 1);
    this.quickSort(pivotIndex + 1, right);
  }
  return this;
};

console.log([4, 2, 3, 1, 5].quickSort());

（6）计数排序

在数组中记录每个数的出现次数，借助数组的有序性，完成原数组的排序

也可以不记录出现次数，而是分别组成数组后连接

Array.prototype.countingSort = function () {
  let counter = [];
  for (let item of this)
    if (counter[item]) counter[item].push(item);
    else counter[item] = [item];
  this.length = 0;
  for (let item of counter) if (item) Array.prototype.push.apply(this, item);
  return this;
};

console.log([4, 2, 3, 1, 5].countingSort());

（7）基数排序

（基于桶排序）将每个数分别按个位数排序后重组，再依次按十位数、百位数直至最高位，重复上述操作

  1. 编写 regroup 方法，用于按指定位排序所有数并重组

    const regroup = (array, digit = 1) => {
  let buckets = Array.from({ length: 10 }, () => []),
    flag = false,
    digitPow = Math.pow(10, digit - 1);
  for (let item of array) {
    if (!flag && item >= digitPow * 10) flag = true;
    buckets[Math.floor((item / digitPow) % 10)].push(item);
  }
  array = buckets.reduce((acc, curr) => acc.concat(curr), []);
  return flag ? regroup(array, digit + 1) : array;
};

  2. 结合排序重组方法，完成基数排序方法

    Array.prototype.radixSort = function (digit = 1) {
  if (this.length < 2) return this;

  const regroup = (array, digit = 1) => {/*...*/};

  return regroup(this);
};

console.log([4, 2, 3, 1, 5].radixSort());

0x06 查找算法

（1）顺序查找

（又称线性搜索）通过遍历数组一一对比搜索

Array.prototype.orderSearch = function (target) {
  for (let index in this) if (this[index] === target) return index;
  return -1;
};

console.log([0, 1, 2, 3, 4].orderSearch(2));

（2）二分查找

记录每个数的索引后将数组排序，通过二分法递归查找出目标数的索引

  1. 编写 divide 方法，用于二分

    const divide = (map, target, low = 0, high = this.length - 1) => {
  if (low > high) return -1;
  let mid = Math.floor((low + high) / 2);
  if (map[mid].value === target) return map[mid].index;
  else if (map[mid].value > target) return divide(map, target, low, mid - 1);
  else if (map[mid].value < target) return divide(map, target, mid + 1, high);
  else return -1;
};

  2. 结合二分方法，完成二分查找方法

    Array.prototype.binarySearch = function (target) {
  if (this.length === 0) return -1;

  const divide = (map, target, low = 0, high = this.length - 1) => {/*...*/};

  let map = new Array();
  this.map((value, index) => map.push({ value: value, index: index }));
  map.sort((a, b) => a.value - b.value);
  return divide(map, target);
};

console.log([1, 0, 2, 4, 3].binarySearch(2));

（3）内插查找

（基于二分查找）优化了 mid 的计算方法，使 mid 为范围中目标值的相对位置（如 30%），而非默认中间

  1. 修改 divide 方法

    const divide = (map, target, low = 0, high = this.length - 1) => {
  if (low > high || target < map[low].value || target > map[high].value)
    return -1;
  let mid =
    low +
    Math.floor(
      (
        (target - map[low].value) / (map[high].value - map[low].value)
      ) * (high - low)
    );

  if (map[mid].value === target) return map[mid].index;
  else if (map[mid].value > target) return divide(map, target, low, mid - 1);
  else if (map[mid].value < target) return divide(map, target, mid + 1, high);
  else return -1;
};

  2. 其他与二分查找相同

    Array.prototype.insertionSearch = function (target) {
  if (this.length === 0) return -1;

  const divide = (map, target, low = 0, high = this.length - 1) => {/*...*/};

  let map = new Array();
  this.map((value, index) => map.push({ value: value, index: index }));
  map.sort((a, b) => a.value - b.value);
  return divide(map, target);
};

console.log([1, 0, 2, 4, 3].insertionSearch(2));

0x07 其他算法

（1）随机算法

用于将数组打乱顺序，且通过处理位置前于当前数，使得不会处理已经经过随机的数

Array.prototype.shuffle = function () {
  for (let i = this.length - 1; i > 0; i--) {
    const randomIndex = Math.floor(Math.random() * (i + 1));
    [this[i], this[randomIndex]] = [this[randomIndex], this[i]];
  }
  return this;
};

console.log([1, 2, 3, 4, 5].shuffle());

（2）动态规划

实现动态规划的重要步骤：

  1. 定义状态
  2. 状态转移方程
  3. 初始化与边界条件

a. 背包问题

存在一个背包，能携带限定空间的物品，而每个物品有各自的空间与价值，如何实现有限空间携带的价值最大

  • 背包大小：10

  • 物品大小与价值：

    编号 大小 价值
    0 2 6
    1 2 3
    2 6 5
    3 5 4
    4 4 6

  • 动态规划表

    编号 大小 价值 0 1 2 3 4 5 6 7 8 9 10
    0 2 6 0 0 6(0) 6 6 6 6 6 6 6 6
    1 2 3 0 0 6 6 9(01) 9 9 9 9 9 9
    2 6 5 0 0 6 6 9 9 9 9 11(02) 11 14(012)
    3 5 4 0 0 6 6 9 9 9 10(03) 11 11 14
    4 4 6 0 0 6 6 9 9 12(04) 12 15(014) 15 15

  • 代码实现

    function knapsackDP(weights, values, total) {
  let dp = new Array(weights.length); // rows
  dp[-1] = new Array(total + 1).fill(0); // columns
  for (let row = 0; row < weights.length; row++) {
    dp[row] = new Array(total).fill(0);
    for (let col = 0; col <= total; col++) {
      if (col < weights[row]) dp[row][col] = dp[row - 1][col];
      else
        dp[row][col] = Math.max(
          dp[row - 1][col],
          dp[row - 1][col - weights[row]] + values[row]
        );
    }
  }
  return dp[weights.length - 1][total];
}

console.log(knapsackDP([2, 2, 6, 5, 4], [6, 3, 5, 4, 6], 10));

b. 最长公共子序列问题

在两个字符串中，找到出现顺序相同、可以不连续的字符串

  • 字符串：

    1. acbaed
    2. abcadf

  • 最长公共子序列：acad

  • 动态规划表

    a b c a d f
    0 0 0 0 0 0 0
    a 0 1 1 1 1 1 1
    c 0 1 1 2 2 2 2
    b 0 1 2 2 2 2 2
    a 0 1 2 2 3 3 3
    e 0 1 2 2 3 3 3
    d 0 1 2 2 3 4 4

  • 代码实现

    function LCS(string1, string2) {
  let dp = [new Array(string2.length + 1).fill(0)],
    result = "";
  for (let row = 1; row <= string1.length; row++) {
    dp[row] = [0];
    for (let col = 1; col <= string2.length; col++) {
      if (string1[row - 1] === string2[col - 1]) {
        dp[row][col] = dp[row - 1][col - 1] + 1;
        if (
          dp[row][col] > dp[row - 1][col] &&
          dp[row][col] > dp[row][col - 1] &&
          result.length === dp[row][col] - 1
        )
          result += string1[row - 1];
      } else dp[row][col] = Math.max(dp[row - 1][col], dp[row][col - 1]);
    }
  }
  return result;
}

console.log(LCS("acbaed", "abcadf"));

（3）贪心算法

  • 特点是求解时，仅选择局部最优解，而非从全局考虑

  • 举例：背包问题

    将每个物品按标准赋分，将分数降序排序，依次取最高分并放入背包

    function knapsackGreedy(weights, values, total) {
  let marks = [];
  for (let index = 0; index < weights.length; index++)
    marks.push({
      id: index,
      weight: weights[index],
      value: values[index],
      mark: values[index] / weights[index],
    });
  marks.sort((a, b) => b.mark - a.mark);

  let selections = [],
    valueTotal = 0;
  for (let item of marks) {
    if (item.weight <= total) {
      selections.push({
        id: item.id,
        weights: item.weight,
        values: item.value,
        rate: 1,
      });
      total -= item.weight;
      valueTotal += item.value;
    } else if (total > 0) {
      const rate = total / item.weight;
      selections.push({
        id: item.id,
        weights: item.weight * rate,
        values: item.value * rate,
        rate: rate,
      });
      valueTotal += item.value * rate;
      break;
    } else break;
  }
  return valueTotal;
}

console.log(knapsackGreedy([2, 2, 6, 5, 4], [6, 3, 5, 4, 6], 10));

（4）回溯算法

  • 本质上是试错，即遇到错误结果后，回溯到上一步，选择其他路径

  • 举例：给定一个字符串，判断在某个字符表中，能否通过相邻的字符拼接出这个字符串

    字符串：ABCCED

    字符表：

    A B C E
    S F C S
    A D E E

    1. 编写 find 方法，用于通过递归实现回溯查找目标路径

      const find = (row, col, index = 0) => {
  if (
    row >= board.length ||
    row < 0 ||
    col >= board[0].length ||
    col < 0 ||
    board[row][col] !== target[index]
  )
    return false;
  if (index === target.length - 1) return true;

  const temp = board[row][col];
  board[row][col] = null;
  const result =
    find(row + 1, col, index + 1) ||
    find(row - 1, col, index + 1) ||
    find(row, col + 1, index + 1) ||
    find(row, col - 1, index + 1);
  board[row][col] = temp;

  return result;
};

    2. 结合递归回溯查找方法，完成回溯算法

      function exist(board, target) {
  const find = (row, col, index = 0) => {/*...*/};

  for (let row = 0; row < board.length; row++)
    for (let col = 0; col < board[row].length; col++)
      if (find(row, col, 0)) return true;
  return false;
}

console.log(
  exist(
    [
      ["A", "B", "C", "E"],
      ["S", "F", "C", "S"],
      ["A", "D", "E", "E"],
    ],
    "ABCCED"
  )
);

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