webDevInterviewQuestions/algorithm/03-data-structure.md

# 数据结构与算法

## 1. 链表

> **场景**：操作历史记录（浏览器前进后退）、LRU 缓存淘汰、撤销重做功能、音乐播放列表。
> **解决**：频繁插入/删除场景下数组性能差的问题，O(1) 插入删除。

### 反转链表

```js
function reverseList(head) {
  let prev = null, curr = head;
  while (curr) {
    const next = curr.next;
    curr.next = prev;
    prev = curr;
    curr = next;
  }
  return prev;
}
```

### 环形链表判断

```js
function hasCycle(head) {
  let slow = head, fast = head;
  while (fast?.next) {
    slow = slow.next;
    fast = fast.next.next;
    if (slow === fast) return true;
  }
  return false;
}
```

### 合并有序链表

```js
function mergeTwoLists(l1, l2) {
  const dummy = { next: null };
  let curr = dummy;
  while (l1 && l2) {
    if (l1.val <= l2.val) {
      curr.next = l1;
      l1 = l1.next;
    } else {
      curr.next = l2;
      l2 = l2.next;
    }
    curr = curr.next;
  }
  curr.next = l1 || l2;
  return dummy.next;
}
```

---

## 2. 二叉树

> **场景**：DOM 树遍历、文件目录结构、组织架构图、表达式解析、前端路由匹配。
> **解决**：层级数据的存储与高效查找，遍历、搜索与路径问题。

### 遍历（前中后序）

```js
// 前序：根-左-右
const preorder = (root, res = []) => {
  if (!root) return res;
  res.push(root.val);
  preorder(root.left, res);
  preorder(root.right, res);
  return res;
};

// 中序：左-根-右
const inorder = (root, res = []) => {
  if (!root) return res;
  inorder(root.left, res);
  res.push(root.val);
  inorder(root.right, res);
  return res;
};

// 后序：左-右-根
const postorder = (root, res = []) => {
  if (!root) return res;
  postorder(root.left, res);
  postorder(root.right, res);
  res.push(root.val);
  return res;
};
```

### 求最大深度

```js
const maxDepth = root => {
  if (!root) return 0;
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
};
```

### 路径和

```js
function hasPathSum(root, targetSum) {
  if (!root) return false;
  if (!root.left && !root.right) return targetSum === root.val;
  return hasPathSum(root.left, targetSum - root.val) 
      || hasPathSum(root.right, targetSum - root.val);
}
```

---

## 3. 栈与队列

> **场景**：栈用于括号匹配、撤销操作、函数调用栈；队列用于任务调度、消息队列、BFS 广度优先搜索。
> **解决**：先进后出/先进先出的数据操作顺序控制。

### 用栈实现队列

```js
class MyQueue {
  constructor() {
    this.inStack = [];
    this.outStack = [];
  }
  
  push(x) { this.inStack.push(x); }
  
  pop() {
    if (!this.outStack.length) {
      while (this.inStack.length) this.outStack.push(this.inStack.pop());
    }
    return this.outStack.pop();
  }
  
  peek() {
    if (!this.outStack.length) {
      while (this.inStack.length) this.outStack.push(this.inStack.pop());
    }
    return this.outStack[this.outStack.length - 1];
  }
  
  empty() { return !this.inStack.length && !this.outStack.length; }
}
```

### 有效的括号

```js
function isValid(s) {
  const map = { ')': '(', ']': '[', '}': '{' };
  const stack = [];
  for (const c of s) {
    if (map[c]) {
      if (stack.pop() !== map[c]) return false;
    } else {
      stack.push(c);
    }
  }
  return !stack.length;
}
```

---

## 4. 哈希表

> **场景**：快速查找（用户ID查询）、统计词频、数据去重、分组操作。
> **解决**：O(1) 时间复杂度的键值对存储和查找，避免线性遍历。

### 两数之和

```js
function twoSum(nums, target) {
  const map = new Map();
  for (let i = 0; i < nums.length; i++) {
    const diff = target - nums[i];
    if (map.has(diff)) return [map.get(diff), i];
    map.set(nums[i], i);
  }
  return [];
}
```

### 字母异位词分组

```js
function groupAnagrams(strs) {
  const map = new Map();
  for (const s of strs) {
    const key = [...s].sort().join('');
    map.set(key, (map.get(key) || []).concat(s));
  }
  return [...map.values()];
}
```

---

## 5. 排序算法

> **场景**：商品价格/销量排序、排行榜、数据可视化预处理。
> **解决**：无序数据有序化，理解分治思想（快排、归并）是算法基础。

### 快速排序

```js
function quickSort(arr) {
  if (arr.length <= 1) return arr;
  const pivot = arr[Math.floor(arr.length / 2)];
  const left = arr.filter(x => x < pivot);
  const middle = arr.filter(x => x === pivot);
  const right = arr.filter(x => x > pivot);
  return [...quickSort(left), ...middle, ...quickSort(right)];
}
```

### 归并排序

```js
function mergeSort(arr) {
  if (arr.length <= 1) return arr;
  const mid = Math.floor(arr.length / 2);
  const left = mergeSort(arr.slice(0, mid));
  const right = mergeSort(arr.slice(mid));
  return merge(left, right);
}

function merge(left, right) {
  const result = [];
  let i = 0, j = 0;
  while (i < left.length && j < right.length) {
    result.push(left[i] < right[j] ? left[i++] : right[j++]);
  }
  return result.concat(left.slice(i), right.slice(j));
}
```

---

## 6. 二分查找

> **场景**：有序列表快速定位（分页跳转）、版本号查找、IP 地址归属地查询、猜数字游戏。
> **解决**：在有序数据中 O(log n) 时间复杂度快速查找，比线性查找效率高很多。

### 基础二分查找

```js
function binarySearch(arr, target) {
  let left = 0, right = arr.length - 1;
  while (left <= right) {
    const mid = Math.floor((left + right) / 2);
    if (arr[mid] === target) return mid;
    arr[mid] < target ? (left = mid + 1) : (right = mid - 1);
  }
  return -1;
}
```

### 旋转数组查找

```js
function searchRotated(nums, target) {
  let left = 0, right = nums.length - 1;
  while (left <= right) {
    const mid = Math.floor((left + right) / 2);
    if (nums[mid] === target) return mid;
    
    // 左半边有序
    if (nums[left] <= nums[mid]) {
      if (target >= nums[left] && target < nums[mid]) right = mid - 1;
      else left = mid + 1;
    } else {
      // 右半边有序
      if (target > nums[mid] && target <= nums[right]) left = mid + 1;
      else right = mid - 1;
    }
  }
  return -1;
}
```