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Longest consecutive sequence in Binary tree

Given a Binary Tree find the length of the longest path which comprises of nodes with consecutive values in increasing order. Every node is considered as a path of length 1.

Examples:

In below diagram binary tree with longest consecutive path(LCP) are shown :




We can solve above problem recursively. At each node we need information of its parent node, if current node has value one more than its parent node then it makes a consecutive path, at each node we will compare node’s value with its parent value and update the longest consecutive path accordingly.
For getting the value of parent node, we will pass the (node_value + 1) as an argument to the recursive method and compare the node value with this argument value, if satisfies, update the current length of consecutive path otherwise reinitialize current path length by 1.
Please see below code for better understanding :

C++

// C/C++ program to find longest consecutive
// sequence in 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 data;
    Node *left, *right;
};
  
// A utility function to create a node
Node* newNode(int data)
{
    Node* temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}
  
// Utility method to return length of longest
// consecutive sequence of tree
void longestConsecutiveUtil(Node* root, int curLength,
                              int expected, int& res)
{
    if (root == NULL)
        return;
  
    // if root data has one more than its parent
    // then increase current length
    if (root->data == expected)
        curLength++;
    else
        curLength = 1;
  
    //  update the maximum by current length
    res = max(res, curLength);
  
    // recursively call left and right subtree with
    // expected value 1 more than root data
    longestConsecutiveUtil(root->left, curLength,
                           root->data + 1, res);
    longestConsecutiveUtil(root->right, curLength,
                           root->data + 1, res);
}
  
// method returns length of longest consecutive
// sequence rooted at node root
int longestConsecutive(Node* root)
{
    if (root == NULL)
        return 0;
  
    int res = 0;
  
    //  call utility method with current length 0
    longestConsecutiveUtil(root, 0, root->data, res);
  
    return res;
}
  
//  Driver code to test above methods
int main()
{
    Node* root = newNode(6);
    root->right = newNode(9);
    root->right->left = newNode(7);
    root->right->right = newNode(10);
    root->right->right->right = newNode(11);
  
    printf("%d ", longestConsecutive(root));
    return 0;
}

Java

// Java program to find longest consecutive 
// sequence in binary tree
  
class Node
{
    int data;
    Node left, right;
  
    Node(int item)
    {
        data = item;
        left = right = null;
    }
}
  
class Result 
{
    int res = 0;
}
  
class BinaryTree
{
    Node root;
  
    // method returns length of longest consecutive 
    // sequence rooted at node root 
    int longestConsecutive(Node root)
    {
        if (root == null)
            return 0;
  
        Result res = new Result();
          
        // call utility method with current length 0 
        longestConsecutiveUtil(root, 0, root.data, res);
          
        return res.res;
    }
  
    // Utility method to return length of longest 
    // consecutive sequence of tree 
    private void longestConsecutiveUtil(Node root, int curlength, 
                                        int expected, Result res)
    {
        if (root == null)
            return;
  
        // if root data has one more than its parent 
        // then increase current length 
        if (root.data == expected)
            curlength++;
        else
            curlength = 1;
  
        // update the maximum by current length 
        res.res = Math.max(res.res, curlength);
  
        // recursively call left and right subtree with 
        // expected value 1 more than root data 
        longestConsecutiveUtil(root.left, curlength, root.data + 1, res);
        longestConsecutiveUtil(root.right, curlength, root.data + 1, res);
    }
  
    // Driver code
    public static void main(String args[]) 
    {
        BinaryTree tree = new BinaryTree();
  
        tree.root = new Node(6);
        tree.root.right = new Node(9);
        tree.root.right.left = new Node(7);
        tree.root.right.right = new Node(10);
        tree.root.right.right.right = new Node(11);
  
        System.out.println(tree.longestConsecutive(tree.root));
    }
}
  
// This code is contributed by shubham96301

Python3

# Python3 program to find longest consecutive 
# sequence in binary tree 
  
# A utility class to create a node 
class newNode:
    def __init__(self, data):
        self.data = data 
        self.left = self.right = None
  
# Utility method to return length of 
# longest consecutive sequence of tree 
def longestConsecutiveUtil(root, curLength, 
                           expected, res):
    if (root == None):
        return
  
    # if root data has one more than its 
    # parent then increase current length 
    if (root.data == expected): 
        curLength += 1
    else:
        curLength = 1
  
    # update the maximum by current length 
    res[0] = max(res[0], curLength)
  
    # recursively call left and right subtree 
    # with expected value 1 more than root data 
    longestConsecutiveUtil(root.left, curLength, 
                           root.data + 1, res) 
    longestConsecutiveUtil(root.right, curLength,
                           root.data + 1, res)
  
# method returns length of longest consecutive 
# sequence rooted at node root 
def longestConsecutive(root):
    if (root == None): 
        return 0
  
    res = [0]
  
    # call utility method with current length 0 
    longestConsecutiveUtil(root, 0, root.data, res) 
  
    return res[0]
  
# Driver Code
if __name__ == '__main__':
  
    root = newNode(6
    root.right = newNode(9
    root.right.left = newNode(7
    root.right.right = newNode(10
    root.right.right.right = newNode(11
  
    print(longestConsecutive(root))
  
# This code is contributed by PranchalK


Output:

3

Also discussed on below link:
Maximum Consecutive Increasing Path Length in Binary Tree

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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