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1080. Insufficient Nodes in Root to Leaf Paths

Description

Given the root of a binary tree and an integer limit, delete all insufficient nodes in the tree simultaneously, and return the root of the resulting binary tree.

A node is insufficient if every root to leaf path intersecting this node has a sum strictly less than limit.

A leaf is a node with no children.

 

Example 1:

Input: root = [1,2,3,4,-99,-99,7,8,9,-99,-99,12,13,-99,14], limit = 1
Output: [1,2,3,4,null,null,7,8,9,null,14]

Example 2:

Input: root = [5,4,8,11,null,17,4,7,1,null,null,5,3], limit = 22
Output: [5,4,8,11,null,17,4,7,null,null,null,5]

Example 3:

Input: root = [1,2,-3,-5,null,4,null], limit = -1
Output: [1,null,-3,4]

 

Constraints:

  • The number of nodes in the tree is in the range [1, 5000].
  • -105 <= Node.val <= 105
  • -109 <= limit <= 109

Solutions

Solution 1

Thinking

Nodes that lie only on root-to-leaf paths summing to less than \(\textit{limit}\) must go. A path is decided at the leaf; a parent stays only if a child survives. \(n\le 5000\) allows one postorder.

Descending subtracts the current value from \(\textit{limit}\). A leaf is removed when the remainder is still positive. An internal node is removed only after both children become null.

The call returns the new subtree root, which may be empty.

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# 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 sufficientSubset(
        self, root: Optional[TreeNode], limit: int
    ) -> Optional[TreeNode]:
        if root is None:
            return None
        limit -= root.val
        if root.left is None and root.right is None:
            return None if limit > 0 else root
        root.left = self.sufficientSubset(root.left, limit)
        root.right = self.sufficientSubset(root.right, limit)
        return None if root.left is None and root.right is None else root

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/**
 * 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 {
    public TreeNode sufficientSubset(TreeNode root, int limit) {
        if (root == null) {
            return null;
        }
        limit -= root.val;
        if (root.left == null && root.right == null) {
            return limit > 0 ? null : root;
        }
        root.left = sufficientSubset(root.left, limit);
        root.right = sufficientSubset(root.right, limit);
        return root.left == null && root.right == null ? null : root;
    }
}

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/**
 * 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:
    TreeNode* sufficientSubset(TreeNode* root, int limit) {
        if (!root) {
            return nullptr;
        }
        limit -= root->val;
        if (!root->left && !root->right) {
            return limit > 0 ? nullptr : root;
        }
        root->left = sufficientSubset(root->left, limit);
        root->right = sufficientSubset(root->right, limit);
        return !root->left && !root->right ? nullptr : root;
    }
};

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/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func sufficientSubset(root *TreeNode, limit int) *TreeNode {
    if root == nil {
        return nil
    }

    limit -= root.Val
    if root.Left == nil && root.Right == nil {
        if limit > 0 {
            return nil
        }
        return root
    }

    root.Left = sufficientSubset(root.Left, limit)
    root.Right = sufficientSubset(root.Right, limit)

    if root.Left == nil && root.Right == nil {
        return nil
    }
    return root
}

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/**
 * Definition for a binary tree node.
 * class TreeNode {
 *     val: number
 *     left: TreeNode | null
 *     right: TreeNode | null
 *     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.left = (left===undefined ? null : left)
 *         this.right = (right===undefined ? null : right)
 *     }
 * }
 */

function sufficientSubset(root: TreeNode | null, limit: number): TreeNode | null {
    if (root === null) {
        return null;
    }
    limit -= root.val;
    if (root.left === null && root.right === null) {
        return limit > 0 ? null : root;
    }
    root.left = sufficientSubset(root.left, limit);
    root.right = sufficientSubset(root.right, limit);
    return root.left === null && root.right === null ? null : root;
}

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/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} limit
 * @return {TreeNode}
 */
var sufficientSubset = function (root, limit) {
    if (root === null) {
        return null;
    }
    limit -= root.val;
    if (root.left === null && root.right === null) {
        return limit > 0 ? null : root;
    }
    root.left = sufficientSubset(root.left, limit);
    root.right = sufficientSubset(root.right, limit);
    return root.left === null && root.right === null ? null : root;
};

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