算法基础之二叉树

本文主要包括树相关的算法，二叉树结点基本结构如下

function TreeNode(x) {
  this.val = x;
  this.left = null;
  this.right = null;
}

本文还会继续更新。

二叉树的深度

function depth(pRoot){
    if(!pRoot){
        return 0;
    }

    var depth = 0;
    var currDepth = 0;
    dfs(pRoot);
    return depth;

    function dfs(node){
        if(!node){
            depth = depth > currDepth ? depth : currDepth;
            return;
        }
        currDepth++;
        dfs(node.left);
        dfs(node.right);
        currDepth--;
    }
}

二叉树的前序遍历

function preOrder(root){
  if(!root)
    return [];
  var result = [];
  _preOrder(root);
  return result;

  function _preOrder(node){
    result.push(node.val);
    node.left && _preOrder(node.left);
    node.right && _preOrder(node.right);
  }
}

二叉树的中序遍历

function inOrder(root){
  if(!root)
    return [];
  var result = [];
  _inOrder(root);
  return result;

  function _inOrder(node){
    node.left && _inOrder(node.left);
    result.push(node.val);
    node.right && _inOrder(node.right);
  }
}

二叉树的后序遍历

function postOrder(root){
  if(!root)
    return [];
  var result = [];
  _postOrder(root);
  return result;

  function _postOrder(node){
    node.left && _postOrder(node.left);
    node.right && _postOrder(node.right);
    result.push(node.val);
  }
}

二叉树的层序遍历

/* function TreeNode(x) {
    this.val = x;
    this.left = null;
    this.right = null;
} */
function printFromTopToBottom(root){
    if (!root) {
        return [];
    }
    var queue = [];
    queue.push(root);
    var result = [];

    while (queue.length) {
        var temp = queue.shift();
        result.push(temp.val);
        if (temp.left) {
            queue.push(temp.left);
        }
        if (temp.right) {
            queue.push(temp.right);
        }
    }
    return result;
}

根据层序遍历建立二叉树

//层序的空节点使用 null
function Tree(arr, node, num){   //也可以通过 new 调用
  if(!arr || arr.length === 0){
      return new TreeNode(null);
  }
  num = num || 1;
  node = node || new TreeNode(arr[num - 1]);

  var curr = node;
  if(num * 2 - 1 < arr.length && arr[num * 2 - 1] != null){
    curr.left = new TreeNode(arr[num * 2 - 1]);
    Tree(arr, curr.left, num * 2);
  }
  if(num * 2 < arr.length && arr[num * 2] != null){
    curr.right = new TreeNode(arr[num * 2]);
    Tree(arr, curr.right, num * 2 + 1);
  }
  return node;
}

根据中序遍历和前序遍历重建二叉树

function reBuildTree_pi(pre, vin){
    if(pre.length == 0 || vin.length == 0 || pre.length !== vin.length){
        return null;
    };
    var index = vin.indexOf(pre[0]);
    var left = vin.slice(0,index);
    var right = vin.slice(index+1);
    var node = new TreeNode(vin[index]);
    node.left = reBuildTree_pi(pre.slice(1,index+1),left);
    node.right = reBuildTree_pi(pre.slice(index+1),right);
    return node;
}

根据中序遍历和后序遍历重建二叉树

function reBuildTree_ip(vin, post){
    if(post.length == 0 || vin.length == 0 || vin.length !== post.length){
        return null;
    };
    var index = vin.indexOf(post.pop());
    var left = vin.slice(0,index);
    var right = vin.slice(index+1);
    var node = new TreeNode(vin[index]);
    node.left = reBuildTree_ip(left, post.slice(0,index));
    node.right = reBuildTree_ip(right, post.slice(index));
    return node;
}

求二叉树的最远节点距离

function maxDistance(root){     //root 二叉树根节点；
  if(root === null) return 0;
  var max = 0;
  _maxDistance(root, max);
  return max;    //函数返回最大值

  function _maxDistance(curr){   //curr: 当前节点；max: 最大值；
    if(curr === null) return 0;
    var leftDepth = curr.left ? _maxDistance(curr.left) : 0;
    var rightDepth = curr.right ? _maxDistance(curr.right) : 0;
    if(leftDepth + rightDepth > max) max = leftDepth + rightDepth;
    return leftDepth > rightDepth ? leftDepth + 1 : rightDepth + 1;
  }
}

二叉树的镜像

function mirror(root){
    if(!root){
        return null;
    }
    var temp = root.left;
    root.left = root.right;
    root.right = temp;
    if(root.left){
        Mirror(root.left);
    }
    if(root.right){
        Mirror(root.right);
    }
}

二叉搜索树转双向链表

将左子树构成双向链表，返回的是左子树的尾结点，将其连接到root的左边；
将右子树构成双向链表，将其追加到root结点之后，并返回尾结点；
向左遍历返回的链表至头结点处，即为所求双向链表的首结点。

function convert(pRootOfTree){
    if(!pRootOfTree) {
        return null;
    }
    var lastNode = null;
    lastNode = ConvertNode(pRootOfTree);
    var head = lastNode;
    while(head && head.left) {
        head = head.left;
    }
    return head;

    function ConvertNode(node){
        if(!node){
            return;
        }
        if(node.left) {
            lastNode = ConvertNode(node.left);
        }
        node.left = lastNode;
        if(lastNode){
            lastNode.right = node;
        }
        lastNode = node;
        if(node.right){
            lastNode = ConvertNode(node.right);
        }
        return lastNode;
    }
}

判断是否平衡二叉树

function isBalancedTree(pRoot){
    if(!pRoot){
        return true;
    }

    var left = TreeDepth(pRoot.left);
    var right = TreeDepth(pRoot.right);
    var diff = left - right;

    if(diff > 1 || diff < -1)
        return false;

    return IsBalanced_Solution(pRoot.left) && IsBalanced_Solution(pRoot.right);

    function TreeDepth(pRoot){
        if(!pRoot){
            return 0;
        }

        var depth = 0;
        var currDepth = 0;
        dfs(pRoot);
        return depth;

        function dfs(node){
            if(!node){
                depth = depth > currDepth ? depth : currDepth;
                return;
            }
            currDepth++;
            dfs(node.left);
            dfs(node.right);
            currDepth--;
        }
    }
}

判断是否对称二叉树

function isSymmetrical(pRoot){
    if(!pRoot){
      return true;
    }
    return symmetrical(pRoot, pRoot);

    function symmetrical(node1,node2){
        if(!node1 && !node2)
            return true;
        if(!node1 || !node2)
            return false;
        if(node1.val != node2.val)
            return false;
        return symmetrical(node1.left, node2.right) && symmetrical(node1.right, node2.left);
    }
}

判断是否完全二叉树

function isPrefectTree(root){
  if(!root)
    return true;
  var que = [];
  que.push(root);
  var curr;
  while(curr = que.shift()){
    que.push(curr.left);
    que.push(curr.right);
  }
  while (que.length > 0){
    if (que.pop())
      return false;
  }
  return true;
}

判断是否满二叉树

function isFullTree(root){
  if(!root)
    return true;
  var que = [];
  que.push(root);
  var curr;
  var nodeNum = 0;

  while(curr = que.shift()){
    que.push(curr.left);
    que.push(curr.right);
    nodeNum++;
  }
  while (que.length > 0){
    if (que.pop())
      return false;
  }

  return (nodeNum & (nodeNum + 1)) === 0;
}

堆操作

function Heap(isMaxHeap) {
    isMaxHeap = isMaxHeap || true; // 默认大根堆
    this.list = [];
    this.flag = isMaxHeap;
  }
  Heap.prototype = {
    constuctor: Heap,

    // 获取堆大小
    get length() {
      return this.list.length;
    },

    // 查看堆顶元素
    peek: function () {
      if (this.list.length === 0) return;
      return this.list[0];
    },
    // 添加一个元素
    add: function (val) {
      this.list.push(val);
      var i = this.list.length - 1,
        index, parent, cur;
      while (i > 0) {
        index = (i - 1) / 2;
        parent = this.list[index];
        cur = this.list[i];
        if (this.flag === true && parent < cur) {
          this._swap(index, i);
        } else if (this.flag === false && parent > cur) {
          this._swap(index, i);
        }
        i = index;
      }
    },

    _swap: function (i, j) {
      var temp = this.list[i];
      this.list[i] = this.list[j];
      this.list[j] = temp;
    },

    // 打印堆
    show: function () {
      return this.list.join();
    },

    // 取出对顶元素
    pop: function () {
      if (this.list.length === 0) return;
      var res = this.list[0];
      this.list[0] = this.list[this.list.length - 1];
      this.list.pop();
      var len = this.list.length - 1,
        i = 0;
      var left, right;
      while (i < len) {
        left = (i << 1) + 1;
        right = (i << 1) + 2;
        var maxIndex = i;
        if (this.flag == true) {
          if (left < len && this.list[left] > this.list[maxIndex]) maxIndex = left;
          if (right < len && this.list[right] > this.list[maxIndex]) maxIndex = right;
        } else {
          if (left < len && this.list[left] < this.list[maxIndex]) maxIndex = left;
          if (right < len && this.list[right] < this.list[maxIndex]) maxIndex = right;
        }
        if (maxIndex !== i) {
          this._swap(maxIndex, i);
          i = maxIndex;
        } else break;
      }
      return res;
    }
  };