grid47 Exploring patterns and algorithms
Aug 17, 2024
5 min read
Solution to LeetCode 814: Binary Tree Pruning Problem
You are given the root of a binary tree. Your task is to remove all subtrees in the tree that do not contain at least one node with the value 1. A subtree is defined as the node and all its descendants. Return the modified tree.
Problem
Approach
Steps
Complexity
Input: You are given the root of a binary tree. The tree is represented as a series of node values in a binary tree structure.
Example: Input: root = [1,null,0,0,1]
Constraints:
• The number of nodes in the tree is between 1 and 200.
• Node values are either 0 or 1.
Output: Return the same binary tree where every subtree not containing a 1 has been removed. The returned tree should be in the same binary tree structure.
Example: Output: [1,null,0,null,1]
Constraints:
• The tree should be returned as a binary tree structure.
Goal: The goal is to prune the binary tree such that every subtree that does not contain a 1 is removed.
Steps:
• Traverse the tree in a post-order manner (visit left, right, then root).
• If a node's left and right subtrees do not contain any 1s, remove those subtrees.
• If the current node itself has a value of 0 and both subtrees are removed, prune the current node as well.
Goal: Ensure that the solution works for small trees with one node as well as for larger trees up to 200 nodes.
Steps:
• The binary tree has at least one node.
• The tree will not contain values other than 0 or 1.
Assumptions:
• The tree is valid and consists of integers either 0 or 1.
• Each node has at most two children.
• Input: Input: root = [1,null,0,0,1]
• Explanation: After pruning, the tree retains the root node with value 1, and only the right child containing a 1 remains. The left child is pruned because it does not contain any 1s.
Approach: The approach is to perform a post-order traversal on the tree. For each node, check its subtrees. If a subtree does not contain any 1s, it is pruned. This is achieved through recursion and modifying the left and right pointers of each node.
Observations:
• This problem is a typical tree traversal problem where pruning nodes is based on conditions.
• The pruning should happen in a bottom-up manner, meaning we should first prune the children before making decisions about the parent node.
Steps:
• Start with a recursive function to prune each node's left and right children.
• If both left and right children of a node do not contain a 1, set those children to null.
• Finally, if the current node itself has a value of 0 and its children are null, prune the current node by returning null.
Empty Inputs:
• A tree with only one node having a value of 0 should return null.
Large Inputs:
• The solution should efficiently handle trees with up to 200 nodes.
Special Values:
• Consider trees where all nodes have a value of 0 or where every node is a 1.
Constraints:
• Make sure the pruning does not break the tree structure for non-zero subtrees.
