# Longest Path with Same Values in a Binary Tree

Given a binary tree, find the length of the longest path where each node in the path has the same value. This path may or may not pass through the root. The length of path between two nodes is represented by the number of edges between them.

Examples:

Input : 2 / \ 7 2 / \ \ 1 1 2 Output : 2 Input : 4 / \ 4 4 / \ \ 4 9 5 Output : 3

The idea is to recursively traverse given binary tree. We can think of any path (of nodes with the same values) in up to two directions(left and right) from it’s root. Then, for each node, we want to know what is the longest possible length extending in the left and the longest possible length extending in the right directions. The longest length that extends from the node will be 1 + length(node->left) if node->left exists, and has the same value as node. Similarly for the node->right case.

While we are computing lengths, each candidate answer will be the sum of the lengths in both directions from that node. We keep updating these answers and return the maximum one.

## C++

`// C++ program to find the length of longest ` `// path with same values in a binary tree. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `/* A binary tree node has data, pointer to ` `left child and a pointer to right child */` `struct` `Node { ` ` ` `int` `val; ` ` ` `struct` `Node *left, *right; ` `}; ` ` ` `/* Function to print the longest path ` ` ` `of same values */` `int` `length(Node *node, ` `int` `*ans) { ` ` ` `if` `(!node) ` ` ` `return` `0; ` ` ` ` ` `// Recursive calls to check for subtrees ` ` ` `int` `left = length(node->left, ans); ` ` ` `int` `right = length(node->right, ans); ` ` ` ` ` `// Variables to store maximum lengths in two directions ` ` ` `int` `Leftmax = 0, Rightmax = 0; ` ` ` ` ` `// If curr node and it's left child has same value ` ` ` `if` `(node->left && node->left->val == node->val) ` ` ` `Leftmax += left + 1; ` ` ` ` ` `// If curr node and it's right child has same value ` ` ` `if` `(node->right && node->right->val == node->val) ` ` ` `Rightmax += right + 1; ` ` ` ` ` `*ans = max(*ans, Leftmax + Rightmax); ` ` ` `return` `max(Leftmax, Rightmax); ` `} ` ` ` `/* Driver function to find length of ` ` ` `longest same value path*/` `int` `longestSameValuePath(Node *root) { ` ` ` `int` `ans = 0; ` ` ` `length(root, &ans); ` ` ` `return` `ans; ` `} ` ` ` `/* Helper function that allocates a ` `new node with the given data and ` `NULL left and right pointers. */` `Node *newNode(` `int` `data) { ` ` ` `Node *temp = ` `new` `Node; ` ` ` `temp->val = data; ` ` ` `temp->left = temp->right = NULL; ` ` ` `return` `temp; ` `} ` ` ` `// Driver code ` `int` `main() { ` ` ` `/* Let us construct a Binary Tree ` ` ` `4 ` ` ` `/ \ ` ` ` `4 4 ` ` ` `/ \ \ ` ` ` `4 9 5 */` ` ` ` ` `Node *root = NULL; ` ` ` `root = newNode(4); ` ` ` `root->left = newNode(4); ` ` ` `root->right = newNode(4); ` ` ` `root->left->left = newNode(4); ` ` ` `root->left->right = newNode(9); ` ` ` `root->right->right = newNode(5); ` ` ` `cout << longestSameValuePath(root); ` ` ` `return` `0; ` `} ` |

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## Python3

# Python3 program to find the length of longest

# path with same values in a binary tree.

# Helper function that allocates a

# new node with the given data and

# None left and right pointers.

class newNode:

def __init__(self, data):

self.val = data

self.left = self.right = None

# Function to prthe longest path

# of same values

def length(node, ans):

if (not node):

return 0

# Recursive calls to check for subtrees

left = length(node.left, ans)

right = length(node.right, ans)

# Variables to store maximum lengths

# in two directions

Leftmax = 0

Rightmax = 0

# If curr node and it’s left child has same value

if (node.left and node.left.val == node.val):

Leftmax += left + 1

# If curr node and it’s right child has same value

if (node.right and node.right.val == node.val):

Rightmax += right + 1

ans[0] = max(ans[0], Leftmax + Rightmax)

return max(Leftmax, Rightmax)

# Driver function to find length of

# longest same value path

def longestSameValuePath(root):

ans = [0]

length(root, ans)

return ans[0]

# Driver code

if __name__ == ‘__main__’:

# Let us construct a Binary Tree

# 4

# / \

# 4 4

# / \ \

# 4 9 5

root = None

root = newNode(4)

root.left = newNode(4)

root.right = newNode(4)

root.left.left = newNode(4)

root.left.right = newNode(9)

root.right.right = newNode(5)

print(longestSameValuePath(root))

# This code is contributed by PranchalK

**Output:**

3

**Complexity Analysis:**

- Time complexity : O(n), where n is the number of nodes in tree as every node is processed once.
- Auxiliary Space : O(h), where h is the height of tree as recursion can go upto depth h.

## Recommended Posts:

- Tree Traversals (Inorder, Preorder and Postorder)
- Find the node with minimum value in a Binary Search Tree
- Write a program to Calculate Size of a tree | Recursion
- Write a Program to Find the Maximum Depth or Height of a Tree
- Write a program to Delete a Tree
- If you are given two traversal sequences, can you construct the binary tree?
- Convert a Binary Tree into its Mirror Tree
- Given a binary tree, print out all of its root-to-leaf paths one per line.
- Lowest Common Ancestor in a Binary Search Tree.
- The Great Tree-List Recursion Problem.
- Check sum of Covered and Uncovered nodes of Binary Tree
- Level Order Tree Traversal
- Program to count leaf nodes in a binary tree
- A program to check if a binary tree is BST or not
- Check for Children Sum Property in a Binary Tree

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