[LeetCode] 549. Binary Tree Longest Consecutive Sequence II 二叉树最长连续序列之 II

Given a binary tree, you need to find the length of Longest Consecutive Path in Binary Tree.

Especially, this path can be either increasing or decreasing. For example, [1,2,3,4] and [4,3,2,1] are both considered valid, but the path [1,2,4,3] is not valid. On the other hand, the path can be in the child-Parent-child order, where not necessarily be parent-child order.

Example 1:

Input:
        1
       / 
      2   3
Output: 2
Explanation: The longest consecutive path is [1, 2] or [2, 1].

Example 2:

Input:
        2
       / 
      1   3
Output: 3
Explanation: The longest consecutive path is [1, 2, 3] or [3, 2, 1].

Note: All the values of tree nodes are in the range of [-1e7, 1e7].

128. Longest Consecutive Sequence 的拓展，还是找最长的连续序列，这一题里可以是升序也可以是降序，而且不必从父结点到子结点，可以子父子节点。

解法：递归。

对于以root为根的树来说，符合条件的path可以分为两类：一类是不经过root的，一类是经过root的。不经过root的可以直接通过对其左子树和右子树的递归调用获得。经过root的有两种：一种是在其左子树上由下到上连续递增到root之后，在其右子树上由上到下连续递增；一种是在其左子树上由下到上连续递减到root之后，在其右子树上由上到下继续连续递减。我们取所有可能类型的path的最长长度即可。

Compared with 298. Binary Tree Longest Consecutive Sequence, this question includes more different conditions since it allows for:

1. both increasing and decreasing order from a follows the parent-child path.
2. child-parent-child path.

Hence this question actually contains 2 subproblems to solve:

1. what is the longest increasing consecutive parent-child path sequence given a root node?
2. what is the longest decreasing consecutive parent-child path sequence given a root node?

Based on the above 2 sub-solution, we know that the longest consecutive sequence for a given root is longest_increasing_sequence + longest_decreasing_sequence from this root. We can simply add up this 2 value because the longest increasing consecutive sequence and longest decreasing consecutive sequence is guaranteed to showed up in different child path (otherwise there will be a contradiction--a child's value cannot be greater than and less than the root's value at the same time).

If the root's value's value is not consecutive with a child's value, then the length of current sequence is simply 1.

Time complexity: O(n) where n is the number of nodes in the tree.

Space complexity: O(logn) on average for the recursion stack since this is a binary tree.

Java:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    int max = 0;
    public int longestConsecutive(TreeNode root) {
        getLongestConsecutive(root);
        return max;
    }
    
    private int[] getLongestConsecutive(TreeNode root) {
        // returns [longest_decreasing_length_from_root, longest_increasing_length_from_root]
        if (root == null) return new int[]{0, 0};
        int[] left = getLongestConsecutive(root.left);
        int[] right = getLongestConsecutive(root.right);
        int dcr = 1, icr = 1;
        if (root.left != null) {
            if (root.left.val == root.val + 1) {
                icr = left[1] + 1;
            }
            if (root.left.val == root.val - 1) {
                dcr = left[0] + 1;
            }
        }
        if (root.right != null) {
            if (root.right.val == root.val + 1) {
                icr = Math.max(icr, right[1] + 1);
            } if (root.right.val == root.val - 1) {
                dcr = Math.max(dcr, right[0] + 1);
            }
        }
        max = Math.max(max, dcr + icr - 1);
        return new int[]{dcr, icr};
    }
}　　

Python:

# Time:  O(n)
# Space: O(h)
class Solution(object):
    def longestConsecutive(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        def longestConsecutiveHelper(root):
            if not root:
                return 0, 0
            left_len = longestConsecutiveHelper(root.left)
            right_len = longestConsecutiveHelper(root.right)
            cur_inc_len, cur_dec_len = 1, 1
            if root.left:
                if root.left.val == root.val + 1:
                    cur_inc_len = max(cur_inc_len, left_len[0] + 1)
                elif root.left.val == root.val - 1:
                    cur_dec_len = max(cur_dec_len, left_len[1] + 1)
            if root.right:
                if root.right.val == root.val + 1:
                    cur_inc_len = max(cur_inc_len, right_len[0] + 1)
                elif root.right.val == root.val - 1:
                    cur_dec_len = max(cur_dec_len, right_len[1] + 1)
            self.max_len = max(self.max_len, cur_dec_len + cur_inc_len - 1)
            return cur_inc_len, cur_dec_len

        self.max_len = 0
        longestConsecutiveHelper(root)
        return self.max_len

Python: 一次遍历 

class Solution(object):
    def solve(self, root):
        inc = dec = 0
        for child in (root.left, root.right):
            if not child: continue
            cinc, cdec = self.solve(child)
            if child.val == root.val - 1:
                dec = max(dec, cdec)
            elif child.val == root.val + 1:
                inc = max(inc, cinc)
        self.ans = max(self.ans, inc + dec + 1)
        return inc + 1, dec + 1
    
    def longestConsecutive(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.ans = 0
        if root: self.solve(root)
        return self.ans

Python: 递归 + 遍历二叉树, Time: O(n^2)

class Solution(object):
    def maxLength(self, root, val, delta):
        lchild, rchild = root.left, root.right
        lsize = rsize = 0
        if lchild and lchild.val == val + delta:
            lsize = self.maxLength(lchild, val + delta, delta)
        if rchild and rchild.val == val + delta:
            rsize = self.maxLength(rchild, val + delta, delta)
        return 1 + max(lsize, rsize)
    
    def longestConsecutive(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        if not root: return 0
        lchild, rchild = root.left, root.right
        lsize = rsize = 0
        clen = 1
        if lchild and abs(lchild.val - root.val) == 1:
            lsize = self.maxLength(lchild, lchild.val, lchild.val - root.val)
        if rchild and abs(rchild.val - root.val) == 1:
            rsize = self.maxLength(rchild, rchild.val, rchild.val - root.val)
        if lchild and rchild and lchild.val != rchild.val:
            clen += lsize + rsize
        else:
            clen += max(lsize, rsize)
        llen = self.longestConsecutive(lchild)
        rlen = self.longestConsecutive(rchild)
        return max(clen, llen, rlen)

C++:

// Time:  O(n)
// Space: O(h)

/**
 * 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:
    int longestConsecutive(TreeNode* root) {
        int max_len = 0;
        longestConsecutiveHelper(root, &max_len);
        return max_len;
    }

    pair<int, int> longestConsecutiveHelper(TreeNode *root, int *max_len) {
        if (!root) {
            return {0, 0};
        }
        const pair<int, int> left_len = longestConsecutiveHelper(root->left, max_len);
        const pair<int, int> right_len = longestConsecutiveHelper(root->right, max_len);

        int cur_inc_len = 1, cur_dec_len = 1;
        if (root->left) {
            if (root->left->val == root->val + 1) {
                cur_inc_len = max(cur_inc_len, left_len.first + 1);
            } else if (root->left->val == root->val - 1){
                cur_dec_len = max(cur_dec_len, left_len.second + 1);
            }
        }
        if (root->right) {
            if (root->right->val == root->val + 1) {
                cur_inc_len = max(cur_inc_len, right_len.first + 1);
            } else if (root->right->val == root->val - 1) {
                cur_dec_len = max(cur_dec_len, right_len.second + 1);
            }
        }
        *max_len = max(*max_len, cur_dec_len + cur_inc_len - 1);
        return {cur_inc_len, cur_dec_len};
    }
};

C++:

class Solution {
public:
    int longestConsecutive(TreeNode* root) {
        int res = 0;
        helper(root, root, res);
        return res;
    }
    pair<int, int> helper(TreeNode* node, TreeNode* parent, int& res) {
        if (!node) return {0, 0};
        auto left = helper(node->left, node, res);
        auto right = helper(node->right, node, res);
        res = max(res, left.first + right.second + 1);
        res = max(res, left.second + right.first + 1);
        int inc = 0, dec = 0;
        if (node->val == parent->val + 1) {
            inc = max(left.first, right.first) + 1;
        } else if (node->val + 1 == parent->val) {
            dec = max(left.second, right.second) + 1;
        }
        return {inc, dec};
    }
};

C++:　　

class Solution {
public:
    int longestConsecutive(TreeNode* root) {
        if (!root) return 0;
        int res = helper(root, 1) + helper(root, -1) + 1;
        return max(res, max(longestConsecutive(root->left), longestConsecutive(root->right)));
    }
    int helper(TreeNode* node, int diff) {
        if (!node) return 0;
        int left = 0, right = 0;
        if (node->left && node->val - node->left->val == diff) {
            left = 1 + helper(node->left, diff);
        }
        if (node->right && node->val - node->right->val == diff) {
            right = 1 + helper(node->right, diff);
        }
        return max(left, right);
    }
};

　　

　　

类似题目：

[LeetCode] 298. Binary Tree Longest Consecutive Sequence 二叉树最长连续序列

[LeetCode] 128. Longest Consecutive Sequence 求最长连续序列

[LeetCode] 300. Longest Increasing Subsequence 最长递增子序列

[LintCode] 619 Binary Tree Longest Consecutive Sequence III 二叉树最长连续序列 III

　　

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