Formatted question description: https://leetcode.ca/all/1339.html

1339. Maximum Product of Splitted Binary Tree (Medium)

Given a binary tree root. Split the binary tree into two subtrees by removing 1 edge such that the product of the sums of the subtrees are maximized.

Since the answer may be too large, return it modulo 10^9 + 7.

 

Example 1:

Input: root = [1,2,3,4,5,6]
Output: 110
Explanation: Remove the red edge and get 2 binary trees with sum 11 and 10. Their product is 110 (11*10)

Example 2:

Input: root = [1,null,2,3,4,null,null,5,6]
Output: 90
Explanation:  Remove the red edge and get 2 binary trees with sum 15 and 6.Their product is 90 (15*6)

Example 3:

Input: root = [2,3,9,10,7,8,6,5,4,11,1]
Output: 1025

Example 4:

Input: root = [1,1]
Output: 1

 

Constraints:

  • Each tree has at most 50000 nodes and at least 2 nodes.
  • Each node's value is between [1, 10000].

Related Topics:
Dynamic Programming, Tree

Solution 1.

// OJ: https://leetcode.com/problems/maximum-product-of-splitted-binary-tree/

// Time: O(N)
// Space: O(H)
class Solution {
    long long s = 0, mod = 1e9 + 7, ans = 0;
    int postorder(TreeNode *root) {
        if (!root) return 0;
        int sum = root->val + postorder(root->left) + postorder(root->right);
        if (s) ans = max(ans, sum * (s - sum));
        return sum;
    }
public:
    int maxProduct(TreeNode* root) {
        s = postorder(root);
        postorder(root);
        return ans % mod;
    }
};

Java

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int maxProduct(TreeNode root) {
        final int MODULO = 1000000007;
        List<TreeNode> nodesList = new ArrayList<TreeNode>();
        Map<TreeNode, TreeNode> childParentMap = new HashMap<TreeNode, TreeNode>();
        Queue<TreeNode> queue = new LinkedList<TreeNode>();
        queue.offer(root);
        while (!queue.isEmpty()) {
            TreeNode node = queue.poll();
            nodesList.add(node);
            TreeNode left = node.left, right = node.right;
            if (left != null) {
                childParentMap.put(left, node);
                queue.offer(left);
            }
            if (right != null) {
                childParentMap.put(right, node);
                queue.offer(right);
            }
        }
        for (int i = nodesList.size() - 1; i > 0; i--) {
            TreeNode node = nodesList.get(i);
            TreeNode parent = childParentMap.get(node);
            if (parent != null)
                parent.val += node.val;
        }
        long maxProduct = 0;
        for (int i = nodesList.size() - 1; i > 0; i--) {
            TreeNode node = nodesList.get(i);
            int value1 = node.val, value2 = root.val - node.val;
            long product = (long) value1 * (long) value2;
            maxProduct = Math.max(maxProduct, product);
        }
        int maxProductModulo = (int) (maxProduct % MODULO);
        return maxProductModulo;
    }
}

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