binary tree | 二叉树基本操作(2)最低公共祖先问题、平衡二叉树

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选择匿名的用户   2021-6-2 20:54   3094   0

一、

题目:

236. Lowest Common Ancestor of a Binary Tree

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Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Given the following binary tree: root = [3,5,1,6,2,0,8,null,null,7,4]

        _______3______
       /              \
    ___5__          ___1__
   /      \        /      \
   6      _2       0       8
         /  \
         7   4

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of of nodes 5 and 1 is 3.

Example 2:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself
according to the LCA definition.

Note:

  • All of the nodes' values will be unique.
  • p and q are different and both values will exist in the binary tree.

解答:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        //递归法,根据root某一侧子树能不能找到p或者q 来判断
        if(!root || root == p || root == q)//若是root为空,或者等于左右中一个,返回
            return root;    
        TreeNode* lc = lowestCommonAncestor(root->left, p, q);//在root->left左子树找p,q 若找到,返回二者中任意一个
        TreeNode* rc = lowestCommonAncestor(root->right, p, q);
        
        if(lc && rc)//若是root两侧子树都找到了p,q二者之一,则root 就是lca
            return root;
        if(!lc)//若果左边子树lc没有找到二者之一,那么rc是lca
            return rc;
        if(!rc)//若果右边子树rc没又找到二者之一,则lc是lca
            return lc;
        
        
           
    }
    
};

二、

题目:

110. Balanced Binary Tree

Given a binary tree, determine if it is height-balanced.

For this problem, a height-balanced binary tree is defined as:

a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

Example 1:

Given the following tree [3,9,20,null,null,15,7]:

    3
   / \
  9  20
    /  \
   15   7

Return true.

Example 2:

Given the following tree [1,2,2,3,3,null,null,4,4]:

       1
      / \
     2   2
    / \
   3   3
  / \
 4   4

Return false.

解答:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool isBalanced(TreeNode* root) {
        if(!root)
            return Flag;
       depthOfTree(root);
        return Flag;
    }
    //开始时候,求深度和判断语句分别进行了两次递归,这样可以进行一次递归就可以
    int depthOfTree(TreeNode* root)
    {
        if(!root)
            return 0;
        int leftDepth = depthOfTree(root->left);
        int rightDepth = depthOfTree(root->right);
        //多加的一部分判断,合二次递归为一
        if(abs(leftDepth - rightDepth) > 1)
        {
            Flag = false;
        }
        
        return 1 + max(leftDepth, rightDepth);
    }
    private:
    bool Flag = true;
        
};

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