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Longest Path with Same Values in a Binary Tree

  • Difficulty Level : Hard
  • Last Updated : 30 Jun, 2021

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

 

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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;
}

Java




// Java program to find the length of longest
// path with same values in a binary tree.
class GFG
{
static int ans;
 
/* A binary tree node has data, pointer to
left child and a pointer to right child */
static class Node
{
    int val;
    Node left, right;
};
 
/* Function to print the longest path
of same values */
static int length(Node node)
{
    if (node == null)
        return 0;
     
    // Recursive calls to check for subtrees
    int left = length(node.left);
    int right = length(node.right);
     
    // 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 != null &&
        node.left.val == node.val)
        Leftmax += left + 1;
     
    // If curr node and it's right child
    // has same value
    if (node.right != null &&
        node.right.val == node.val)
        Rightmax += right + 1;
         
    ans = Math.max(ans, Leftmax + Rightmax);
    return Math.max(Leftmax, Rightmax);
}
 
// Function to find length of
// longest same value path
static int longestSameValuePath(Node root)
{
    ans = 0;
    length(root);
    return ans;
}
 
/* Helper function that allocates a
new node with the given data and
null left and right pointers. */
static Node newNode(int data)
{
    Node temp = new Node();
    temp.val = data;
    temp.left = temp.right = null;
    return temp;
}
 
// Driver code
public static void main(String[] args)
{
     
    /* Let us cona 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);
    System.out.print(longestSameValuePath(root));
}
}
 
// This code is contributed by PrinciRaj1992

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 print the 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

C#




// C# program to find the length of longest
// path with same values in a binary tree.
using System;
 
class GFG
{
static int ans;
 
/* A binary tree node has data, pointer to
left child and a pointer to right child */
public class Node
{
    public int val;
    public Node left, right;
};
 
/* Function to print the longest path
of same values */
static int length(Node node)
{
    if (node == null)
        return 0;
     
    // Recursive calls to check for subtrees
    int left = length(node.left);
    int right = length(node.right);
     
    // 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 != null &&
        node.left.val == node.val)
        Leftmax += left + 1;
     
    // If curr node and it's right child
    // has same value
    if (node.right != null &&
        node.right.val == node.val)
        Rightmax += right + 1;
         
    ans = Math.Max(ans, Leftmax + Rightmax);
    return Math.Max(Leftmax, Rightmax);
}
 
// Function to find length of
// longest same value path
static int longestSameValuePath(Node root)
{
    ans = 0;
    length(root);
    return ans;
}
 
/* Helper function that allocates a
new node with the given data and
null left and right pointers. */
static Node newNode(int data)
{
    Node temp = new Node();
    temp.val = data;
    temp.left = temp.right = null;
    return temp;
}
 
// Driver code
public static void Main(String[] args)
{
     
    /* Let us cona 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);
    Console.Write(longestSameValuePath(root));
}
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
 
    // JavaScript program to find the length of longest
    // path with same values in a binary tree.
     
    let ans;
   
    /* A binary tree node has data, pointer to
    left child and a pointer to right child */
    class Node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.val = data;
        }
    }
 
    /* Function to print the longest path
    of same values */
    function length(node)
    {
        if (node == null)
            return 0;
 
        // Recursive calls to check for subtrees
        let left = length(node.left);
        let right = length(node.right);
 
        // Variables to store maximum lengths
        // in two directions
        let Leftmax = 0, Rightmax = 0;
 
        // If curr node and it's left child
        // has same value
        if (node.left != null &&
            node.left.val == node.val)
            Leftmax += left + 1;
 
        // If curr node and it's right child
        // has same value
        if (node.right != null &&
            node.right.val == node.val)
            Rightmax += right + 1;
 
        ans = Math.max(ans, Leftmax + Rightmax);
        return Math.max(Leftmax, Rightmax);
    }
 
    // Function to find length of
    // longest same value path
    function longestSameValuePath(root)
    {
        ans = 0;
        length(root);
        return ans;
    }
 
    /* Helper function that allocates a
    new node with the given data and
    null left and right pointers. */
    function newNode(data)
    {
        let temp = new Node(data);
        temp.val = data;
        temp.left = temp.right = null;
        return temp;
    }
     
    /* Let us cona Binary Tree
         4
        / \
        4 4
       / \ \
       4 9 5 */
    let 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);
    document.write(longestSameValuePath(root));
 
</script>

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.

 




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