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C++实现LeetCode(110.平衡二叉树)

程序员文章站 2022-06-26 11:35:35
[leetcode] 110.balanced binary tree 平衡二叉树given a binary tree, determine if it is height-balanced.for...

[leetcode] 110.balanced binary tree 平衡二叉树

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 everynode 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.

求二叉树是否平衡,根据题目中的定义,高度平衡二叉树是每一个结点的两个子树的深度差不能超过1,那么我们肯定需要一个求各个点深度的函数,然后对每个节点的两个子树来比较深度差,时间复杂度为o(nlgn),代码如下:

解法一:

class solution {
public:
    bool isbalanced(treenode *root) {
        if (!root) return true;
        if (abs(getdepth(root->left) - getdepth(root->right)) > 1) return false;
        return isbalanced(root->left) && isbalanced(root->right);    
    }
    int getdepth(treenode *root) {
        if (!root) return 0;
        return 1 + max(getdepth(root->left), getdepth(root->right));
    }
};

上面那个方法正确但不是很高效,因为每一个点都会被上面的点计算深度时访问一次,我们可以进行优化。方法是如果我们发现子树不平衡,则不计算具体的深度,而是直接返回-1。那么优化后的方法为:对于每一个节点,我们通过checkdepth方法递归获得左右子树的深度,如果子树是平衡的,则返回真实的深度,若不平衡,直接返回-1,此方法时间复杂度o(n),空间复杂度o(h),参见代码如下:

解法二:

class solution {
public:    
    bool isbalanced(treenode *root) {
        if (checkdepth(root) == -1) return false;
        else return true;
    }
    int checkdepth(treenode *root) {
        if (!root) return 0;
        int left = checkdepth(root->left);
        if (left == -1) return -1;
        int right = checkdepth(root->right);
        if (right == -1) return -1;
        int diff = abs(left - right);
        if (diff > 1) return -1;
        else return 1 + max(left, right);
    }
};

类似题目:

maximum depth of binary tree

参考资料:

https://leetcode.com/problems/balanced-binary-tree/discuss/35691/the-bottom-up-o(n)-solution-would-be-better

https://leetcode.com/problems/balanced-binary-tree/discuss/35686/java-solution-based-on-height-check-left-and-right-node-in-every-recursion-to-avoid-further-useless-search

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