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| 1 | +# 1457. Pseudo-Palindromic Paths in a Binary Tree |
| 2 | + |
| 3 | +- Difficulty: Medium. |
| 4 | +- Related Topics: Bit Manipulation, Tree, Depth-First Search, Breadth-First Search, Binary Tree. |
| 5 | +- Similar Questions: . |
| 6 | + |
| 7 | +## Problem |
| 8 | + |
| 9 | +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. |
| 10 | + |
| 11 | +**Return the number of **pseudo-palindromic** paths going from the root node to leaf nodes.** |
| 12 | + |
| 13 | + |
| 14 | +Example 1: |
| 15 | + |
| 16 | + |
| 17 | + |
| 18 | + |
| 19 | + |
| 20 | +``` |
| 21 | +Input: root = [2,3,1,3,1,null,1] |
| 22 | +Output: 2 |
| 23 | +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). |
| 24 | +``` |
| 25 | + |
| 26 | +Example 2: |
| 27 | + |
| 28 | + |
| 29 | + |
| 30 | + |
| 31 | + |
| 32 | +``` |
| 33 | +Input: root = [2,1,1,1,3,null,null,null,null,null,1] |
| 34 | +Output: 1 |
| 35 | +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). |
| 36 | +``` |
| 37 | + |
| 38 | +Example 3: |
| 39 | + |
| 40 | +``` |
| 41 | +Input: root = [9] |
| 42 | +Output: 1 |
| 43 | +``` |
| 44 | + |
| 45 | + |
| 46 | +**Constraints:** |
| 47 | + |
| 48 | + |
| 49 | + |
| 50 | +- The number of nodes in the tree is in the range `[1, 105]`. |
| 51 | + |
| 52 | +- `1 <= Node.val <= 9` |
| 53 | + |
| 54 | + |
| 55 | + |
| 56 | +## Solution |
| 57 | + |
| 58 | +```javascript |
| 59 | +/** |
| 60 | + * Definition for a binary tree node. |
| 61 | + * function TreeNode(val, left, right) { |
| 62 | + * this.val = (val===undefined ? 0 : val) |
| 63 | + * this.left = (left===undefined ? null : left) |
| 64 | + * this.right = (right===undefined ? null : right) |
| 65 | + * } |
| 66 | + */ |
| 67 | +/** |
| 68 | + * @param {TreeNode} root |
| 69 | + * @return {number} |
| 70 | + */ |
| 71 | +var pseudoPalindromicPaths = function(root) { |
| 72 | + return dfs(root, Array(10).fill(0), 0); |
| 73 | +}; |
| 74 | + |
| 75 | +var dfs = function(node, map, numOfOdd) { |
| 76 | + if (!node) return 0; |
| 77 | + if (map[node.val] % 2) { |
| 78 | + numOfOdd -= 1; |
| 79 | + } else { |
| 80 | + numOfOdd += 1; |
| 81 | + } |
| 82 | + if (!node.left && !node.right) { |
| 83 | + return numOfOdd <= 1 ? 1 : 0; |
| 84 | + } |
| 85 | + map[node.val] += 1; |
| 86 | + var res = dfs(node.left, map, numOfOdd) |
| 87 | + + dfs(node.right, map, numOfOdd); |
| 88 | + map[node.val] -= 1; |
| 89 | + return res; |
| 90 | +}; |
| 91 | +``` |
| 92 | + |
| 93 | +**Explain:** |
| 94 | + |
| 95 | +nope. |
| 96 | + |
| 97 | +**Complexity:** |
| 98 | + |
| 99 | +* Time complexity : O(n). |
| 100 | +* Space complexity : O(1). |
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