Given three vertices U, V and R of a binary tree, the task is to check whether R lies in the path between U and V. If it is not present in the path then print No otherwise print Yes.
Input: U = 4, V = 6, R = 2
Path 4 -> 2 -> 1 -> 3 -> 6 contains 2
Input: U = 4, V = 6, R = 5
Path 4 -> 2 -> 1 -> 3 -> 6 does not contain 5
Approach: The idea is to use Lowest Common Ancestor of two nodes. There are following cases for R to exist in the path between U and V:
- R is the lowest common ancestor of U and V.
- R is in the left subtree of the lowest common ancestor of U and V and is above V.
- R is in the right subtree of the lowest common ancestor of U and V and is above U.
To know more about the lowest commom ancestor, read the post here.
Below is the implementation of the above approach:
Time Complexity: O(NlogN) for pre-processing and logN for finding the lowest common ancestor.
- Sum of nodes on the longest path from root to leaf node
- Implementing a BST where every node stores the maximum number of nodes in the path till any leaf
- Minimum and maximum node that lies in the path connecting two nodes in a Binary Tree
- Queries to check if the path between two nodes in a tree is a palindrome
- Check if two nodes are in same subtree of the root node
- Sum of all odd nodes in the path connecting two given nodes
- Kth largest node among all directly connected nodes to the given node in an undirected graph
- Remove all nodes which don't lie in any path with sum>= k
- XOR of path between any two nodes in a Binary Tree
- Print path between any two nodes in a Binary Tree
- Print path between any two nodes in a Binary Tree | Set 2
- Print the path common to the two paths from the root to the two given nodes
- Root to leaf path with maximum distinct nodes
- Print path from root to all nodes in a Complete Binary Tree
- Shortest path between two nodes in array like representation of binary tree
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Improved By : princiraj1992