Leetcode 1457. Pseudo-Palindromic Paths in a Binary Tree (二叉树遍历题)

Pseudo-Palindromic Paths in a Binary Tree
Medium
Given a binary tree where node values are digits from 1 to 9. A path in the binary tree is said to be pseudo-palindromic if at least one permutation of the node values in the path is a palindrome.

Return the number of pseudo-palindromic paths going from the root node to leaf nodes.

Example 1:

Input: root = $2,3,1,3,1,null,1$

Output: 2

Explanation: The figure above represents the given binary tree. There are three paths going from the root node to leaf nodes: the red path $2,3,3$ , the green path $2,1,1$ , and the path $2,3,1$ . Among these paths only red path and green path are pseudo-palindromic paths since the red path $2,3,3$ can be rearranged in $3,2,3$ (palindrome) and the green path $2,1,1$ can be rearranged in $1,2,1$ (palindrome).

Example 2:

Input: root = $2,1,1,1,3,null,null,null,null,null,1$

Output: 1

Explanation: The figure above represents the given binary tree. There are three paths going from the root node to leaf nodes: the green path $2,1,1$ , the path $2,1,3,1$ , and the path $2,1$ . Among these paths only the green path is pseudo-palindromic since $2,1,1$ can be rearranged in $1,2,1$ (palindrome).

Example 3:

Input: root = $9$

Output: 1

Constraints:

The number of nodes in the tree is in the range $1, 105$ .

1 <= Node.val <= 9

解法1：

注意：这里的path是指从root到leaf。

怎么才能算pseudo-palindromic呢? 只要统计出1-9每个数字的个数，如果奇数个的个数<=1就算！

cpp 复制代码

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int pseudoPalindromicPaths (TreeNode* root) {
        pathNum.resize(10, 0);
        helper(root);
        return count;
    }
private:
    vector<int> pathNum;
    int count = 0;
    void helper(TreeNode *root) {
        if (!root) return;
        pathNum[root->val]++;
        if (!root->left && !root->right) {
            int oddNum = 0, evenNum = 0;
            for (int i = 1; i <= 9; i++) {
                if (pathNum[i] & 0x1) oddNum++;
                else evenNum++;
            }
            if (oddNum <= 1) {
                count++;
                //return;
            }
            pathNum[root->val]--; //记得这里也要--
            return;
        }
        helper(root->left);
        helper(root->right);
        pathNum[root->val]--;
        return;        
    }
};

解法2：思路跟上面差不多，但是用XOR。

注意:

bitwise的操作优先级都很低，要加括号。比如
(pathXor & (pathXor - 1)) == 0
pathXor ^= (0x1 << (root->val));
要用 pathXor ^= (0x1 << (root->val))，不能直接用pathXor ^= root->val。
否则如果有多个数的个数是奇数的话，pathXor看不出来。
用pathXor ^= (0x1 << (root->val))的话，1-9每个数字个数是奇数还是偶数就一目了然了。
int x。 x & (x-1)会抹掉最后一个1。那么如果x=0的话，是不是也成立呢? 是的，因为0&(-1)=0.
所以，如果pathXor有一个1，或者为全0，那么pathXor & (pathXor - 1)都是0。这个就可以作为有pseudo-palindromic的评判标准。

cpp 复制代码

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int pseudoPalindromicPaths (TreeNode* root) {
        helper(root);
        return count;
    }
private:
    int pathXor = 0;
    int count = 0;
    void helper(TreeNode *root) {
        if (!root) return;
        pathXor ^= (0x1 << (root->val));
        if (!root->left && !root->right) {
            if ((pathXor & (pathXor - 1)) == 0) count++;
            pathXor ^= (0x1 << (root->val));
            return;
        }
        helper(root->left);
        helper(root->right);
        pathXor ^= (0x1 << (root->val));
        return;        
    }
};