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Formatted question description: https://leetcode.ca/all/1372.html

1372. Longest ZigZag Path in a Binary Tree (Medium)

Given a binary tree root, a ZigZag path for a binary tree is defined as follow:

  • Choose any node in the binary tree and a direction (right or left).
  • If the current direction is right then move to the right child of the current node otherwise move to the left child.
  • Change the direction from right to left or right to left.
  • Repeat the second and third step until you can't move in the tree.

Zigzag length is defined as the number of nodes visited - 1. (A single node has a length of 0).

Return the longest ZigZag path contained in that tree.

 

Example 1:

Input: root = [1,null,1,1,1,null,null,1,1,null,1,null,null,null,1,null,1]
Output: 3
Explanation: Longest ZigZag path in blue nodes (right -> left -> right).

Example 2:

Input: root = [1,1,1,null,1,null,null,1,1,null,1]
Output: 4
Explanation: Longest ZigZag path in blue nodes (left -> right -> left -> right).

Example 3:

Input: root = [1]
Output: 0

 

Constraints:

  • Each tree has at most 50000 nodes..
  • Each node's value is between [1, 100].

Related Topics:
Dynamic Programming, Tree

Solution 1.

  • /**
     * Definition for a binary tree node.
     * public class TreeNode {
     *     int val;
     *     TreeNode left;
     *     TreeNode right;
     *     TreeNode(int x) { val = x; }
     * }
     */
    class Solution {
        public int longestZigZag(TreeNode root) {
            Map<TreeNode, int[]> map = new HashMap<TreeNode, int[]>();
            map.put(root, new int[]{0, 0});
            int maxLength = 0;
            Queue<TreeNode> queue = new LinkedList<TreeNode>();
            queue.offer(root);
            while (!queue.isEmpty()) {
                TreeNode node = queue.poll();
                int[] lengths = map.get(node);
                TreeNode left = node.left, right = node.right;
                if (left != null) {
                    int[] leftLengths = new int[2];
                    leftLengths[0] = lengths[1] + 1;
                    maxLength = Math.max(maxLength, leftLengths[0]);
                    map.put(left, leftLengths);
                    queue.offer(left);
                }
                if (right != null) {
                    int[] rightLengths = new int[2];
                    rightLengths[1] = lengths[0] + 1;
                    maxLength = Math.max(maxLength, rightLengths[1]);
                    map.put(right, rightLengths);
                    queue.offer(right);
                }
            }
            return maxLength;
        }
    }
    
    ############
    
    /**
     * Definition for a binary tree node.
     * public class TreeNode {
     *     int val;
     *     TreeNode left;
     *     TreeNode right;
     *     TreeNode() {}
     *     TreeNode(int val) { this.val = val; }
     *     TreeNode(int val, TreeNode left, TreeNode right) {
     *         this.val = val;
     *         this.left = left;
     *         this.right = right;
     *     }
     * }
     */
    class Solution {
        private int ans;
    
        public int longestZigZag(TreeNode root) {
            dfs(root, 0, 0);
            return ans;
        }
    
        private void dfs(TreeNode root, int l, int r) {
            if (root == null) {
                return;
            }
            ans = Math.max(ans, Math.max(l, r));
            dfs(root.left, r + 1, 0);
            dfs(root.right, 0, l + 1);
        }
    }
    
  • // OJ: https://leetcode.com/problems/longest-zigzag-path-in-a-binary-tree
    // Time: O(N)
    // Space: O(H)
    class Solution {
        int A = 0;
        pair<int, int> postorder(TreeNode* root)  {
            if (!root || (!root->left && !root->right)) return { 0, 0 };
            pair<int, int> ans;
            if (root->left) {
                auto left = postorder(root->left);
                ans.first = 1 + left.second;
            }
            if (root->right) {
                auto right = postorder(root->right);
                ans.second = 1 + right.first;
            }
            A = max({ A, ans.first, ans.second });
            return ans;
        }
    public:
        int longestZigZag(TreeNode* root) {
            postorder(root);
            return A;
        }
    };
    
  • # Definition for a binary tree node.
    # class TreeNode:
    #     def __init__(self, val=0, left=None, right=None):
    #         self.val = val
    #         self.left = left
    #         self.right = right
    class Solution:
        def longestZigZag(self, root: TreeNode) -> int:
            def dfs(root, l, r):
                if root is None:
                    return
                nonlocal ans
                ans = max(ans, l, r)
                dfs(root.left, r + 1, 0)
                dfs(root.right, 0, l + 1)
    
            ans = 0
            dfs(root, 0, 0)
            return ans
    
    
    
  • /**
     * Definition for a binary tree node.
     * type TreeNode struct {
     *     Val int
     *     Left *TreeNode
     *     Right *TreeNode
     * }
     */
    func longestZigZag(root *TreeNode) int {
    	ans := 0
    	var dfs func(root *TreeNode, l, r int)
    	dfs = func(root *TreeNode, l, r int) {
    		if root == nil {
    			return
    		}
    		ans = max(ans, max(l, r))
    		dfs(root.Left, r+1, 0)
    		dfs(root.Right, 0, l+1)
    	}
    	dfs(root, 0, 0)
    	return ans
    }
    
    func max(a, b int) int {
    	if a > b {
    		return a
    	}
    	return b
    }
    

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