Maximum Consecutive Increasing Path Length 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: 

       10
      /    \     
     /      \
    11        9    
   / \        /\
  /   \      /  \
13    12    13   8
Maximum Consecutive Path Length is 3 (10, 11, 12)
Note: 10, 9 ,8 is NOT considered since
the nodes should be in increasing order.

        5
          /  \
         /    \
        8      11
        /        \
       /          \
       9      10   
      /              /
     /             /
    6           15
Maximum Consecutive Path Length is 2 (8, 9).

Every node in the Binary Tree can either become part of the path which is starting from one of its parent node or a new path can start from this node itself. The key is to recursively find the path length for the left and right sub tree and then return the maximum. Some cases need to be considered while traversing the tree which are discussed below.

• prev : stores the value of the parent node. Initialize prev with one less than value of root node so that the path starting at root can be of length at least 1. 
• len : Stores the path length which ends at the parent of currently visited node.

Case 1: Value of Current Node is prev +1 
In this case increase the path length by 1, and then recursively find the path length for the left and the right sub tree then return the maximum between two lengths.

Case 2: Value of Current Node is NOT prev+1 
A new path can start from this node, so recursively find the path length for the left and the right sub tree. The path which ends at the parent node of current node might be greater than the path which starts from this node.So take the maximum of the path which starts from this node and which ends at previous node.

Below is the implementation of above idea.

C++

// C++ Program to find Maximum Consecutive
// Path Length in a Binary Tree
#include <bits/stdc++.h>
using namespace std;

// To represent a node of a Binary Tree
struct Node
{
    Node *left, *right;
    int val;
};

// Create a new Node and return its address
Node *newNode(int val)
{
    Node *temp = new Node();
    temp->val = val;
    temp->left = temp->right = NULL;
    return temp;
}

// Returns the maximum consecutive Path Length
int maxPathLenUtil(Node *root, int prev_val, int prev_len)
{
    if (!root)
        return prev_len;

    // Get the value of Current Node
    // The value of the current node will be
    // prev Node for its left and right children
    int cur_val = root->val;

    // If current node has to be a part of the
    // consecutive path then it should be 1 greater
    // than the value of the previous node
    if (cur_val == prev_val+1)
    {

        // a) Find the length of the Left Path
        // b) Find the length of the Right Path
        // Return the maximum of Left path and Right path
        return max(maxPathLenUtil(root->left, cur_val, prev_len+1),
                   maxPathLenUtil(root->right, cur_val, prev_len+1));
    }

    // Find length of the maximum path under subtree rooted with this
    // node (The path may or may not include this node)
    int newPathLen = max(maxPathLenUtil(root->left, cur_val, 1),
                         maxPathLenUtil(root->right, cur_val, 1));

    // Take the maximum previous path and path under subtree rooted
    // with this node.
    return  max(prev_len, newPathLen);
}

// A wrapper over maxPathLenUtil().
int maxConsecutivePathLength(Node *root)
{
    // Return 0 if root is NULL
    if (root == NULL)
        return 0;

    // Else compute Maximum Consecutive Increasing Path
    // Length using maxPathLenUtil.
    return maxPathLenUtil(root, root->val-1, 0);
}

//Driver program to test above function
int main()
{
    Node *root = newNode(10);
    root->left = newNode(11);
    root->right = newNode(9);
    root->left->left = newNode(13);
    root->left->right = newNode(12);
    root->right->left = newNode(13);
    root->right->right = newNode(8);

    cout << "Maximum Consecutive Increasing Path Length is "
         << maxConsecutivePathLength(root);

    return 0;
}

Java

// Java Program to find Maximum Consecutive
// Path Length in a Binary Tree
import java.util.*;
class GfG {

// To represent a node of a Binary Tree
static class Node
{
    Node left, right;
    int val;
}

// Create a new Node and return its address
static Node newNode(int val)
{
    Node temp = new Node();
    temp.val = val;
    temp.left = null;
    temp.right = null;
    return temp;
}

// Returns the maximum consecutive Path Length
static int maxPathLenUtil(Node root, int prev_val, int prev_len)
{
    if (root == null)
        return prev_len;

    // Get the value of Current Node
    // The value of the current node will be
    // prev Node for its left and right children
    int cur_val = root.val;

    // If current node has to be a part of the
    // consecutive path then it should be 1 greater
    // than the value of the previous node
    if (cur_val == prev_val+1)
    {

        // a) Find the length of the Left Path
        // b) Find the length of the Right Path
        // Return the maximum of Left path and Right path
        return Math.max(maxPathLenUtil(root.left, cur_val, prev_len+1),
                maxPathLenUtil(root.right, cur_val, prev_len+1));
    }

    // Find length of the maximum path under subtree rooted with this
    // node (The path may or may not include this node)
    int newPathLen = Math.max(maxPathLenUtil(root.left, cur_val, 1),
                        maxPathLenUtil(root.right, cur_val, 1));

    // Take the maximum previous path and path under subtree rooted
    // with this node.
    return Math.max(prev_len, newPathLen);
}

// A wrapper over maxPathLenUtil().
static int maxConsecutivePathLength(Node root)
{
    // Return 0 if root is NULL
    if (root == null)
        return 0;

    // Else compute Maximum Consecutive Increasing Path
    // Length using maxPathLenUtil.
    return maxPathLenUtil(root, root.val-1, 0);
}

//Driver program to test above function
public static void main(String[] args)
{
    Node root = newNode(10);
    root.left = newNode(11);
    root.right = newNode(9);
    root.left.left = newNode(13);
    root.left.right = newNode(12);
    root.right.left = newNode(13);
    root.right.right = newNode(8);

    System.out.println("Maximum Consecutive Increasing Path Length is "+maxConsecutivePathLength(root));

}
}

Python3

# Python program to find Maximum consecutive
# path length in binary tree

# A binary tree node
class Node:

    # Constructor to create a new node
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

# Returns the maximum consecutive path length
def maxPathLenUtil(root, prev_val, prev_len):
    if root is None:
        return prev_len

    # Get the value of current node
    # The value of the current node will be
    # prev node for its left and right children
    curr_val =  root.val

    # If current node has to be a part of the
    # consecutive path then it should be 1 greater
    # than the value of the previous node
    if curr_val == prev_val +1 :

        # a) Find the length of the left path
        # b) Find the length of the right path
        # Return the maximum of left path and right path
        return max(maxPathLenUtil(root.left, curr_val, prev_len+1),
                   maxPathLenUtil(root.right, curr_val, prev_len+1))

    # Find the length of the maximum path under subtree
    # rooted with this node
    newPathLen = max(maxPathLenUtil(root.left, curr_val, 1),
                    maxPathLenUtil(root.right, curr_val, 1))

    # Take the maximum previous path and path under subtree
    # rooted with this node
    return max(prev_len , newPathLen)

# A Wrapper over maxPathLenUtil()
def maxConsecutivePathLength(root):

    # Return 0 if root is None
    if root is None:
        return 0

    # Else compute maximum consecutive increasing path
    # length using maxPathLenUtil
    return maxPathLenUtil(root, root.val -1 , 0)

# Driver program to test above function
root = Node(10)
root.left = Node(11)
root.right = Node(9)
root.left.left = Node(13)
root.left.right = Node(12)
root.right.left = Node(13)
root.right.right = Node(8)

print ("Maximum Consecutive Increasing Path Length is",)
print (maxConsecutivePathLength(root))

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

// C# Program to find Maximum Consecutive
// Path Length in a Binary Tree
using System;

class GfG
{

    // To represent a node of a Binary Tree
    class Node
    {
        public Node left, right;
        public int val;
    }

    // Create a new Node and return its address
    static Node newNode(int val)
    {
        Node temp = new Node();
        temp.val = val;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    // Returns the maximum consecutive Path Length
    static int maxPathLenUtil(Node root,
                int prev_val, int prev_len)
    {
        if (root == null)
            return prev_len;

        // Get the value of Current Node
        // The value of the current node will be
        // prev Node for its left and right children
        int cur_val = root.val;

        // If current node has to be a part of the
        // consecutive path then it should be 1 greater
        // than the value of the previous node
        if (cur_val == prev_val+1)
        {

            // a) Find the length of the Left Path
            // b) Find the length of the Right Path
            // Return the maximum of Left path and Right path
            return Math.Max(maxPathLenUtil(root.left, cur_val, prev_len+1),
                    maxPathLenUtil(root.right, cur_val, prev_len+1));
        }

        // Find length of the maximum path under subtree rooted with this
        // node (The path may or may not include this node)
        int newPathLen = Math.Max(maxPathLenUtil(root.left, cur_val, 1),
                            maxPathLenUtil(root.right, cur_val, 1));

        // Take the maximum previous path and path under subtree rooted
        // with this node.
        return Math.Max(prev_len, newPathLen);
    }

    // A wrapper over maxPathLenUtil().
    static int maxConsecutivePathLength(Node root)
    {
        // Return 0 if root is NULL
        if (root == null)
            return 0;

        // Else compute Maximum Consecutive Increasing Path
        // Length using maxPathLenUtil.
        return maxPathLenUtil(root, root.val - 1, 0);
    }

    // Driver code
    public static void Main(String[] args)
    {
        Node root = newNode(10);
        root.left = newNode(11);
        root.right = newNode(9);
        root.left.left = newNode(13);
        root.left.right = newNode(12);
        root.right.left = newNode(13);
        root.right.right = newNode(8);

        Console.WriteLine("Maximum Consecutive" +
                        " Increasing Path Length is "+
                            maxConsecutivePathLength(root));
    }
}

// This code has been contributed by 29AjayKumar

Javascript

<script>
// Javascript Program to find Maximum Consecutive
// Path Length in a Binary Tree

// To represent a node of a Binary Tree
class Node
{
    constructor(val)
    {
        this.val = val;
        this.left = this.right = null;
    }
}

// Returns the maximum consecutive Path Length
function maxPathLenUtil(root,prev_val,prev_len)
{
    if (root == null)
        return prev_len;

    // Get the value of Current Node
    // The value of the current node will be
    // prev Node for its left and right children
    let cur_val = root.val;

    // If current node has to be a part of the
    // consecutive path then it should be 1 greater
    // than the value of the previous node
    if (cur_val == prev_val+1)
    {

        // a) Find the length of the Left Path
        // b) Find the length of the Right Path
        // Return the maximum of Left path and Right path
        return Math.max(maxPathLenUtil(root.left, cur_val, prev_len+1),
                maxPathLenUtil(root.right, cur_val, prev_len+1));
    }

    // Find length of the maximum path under subtree rooted with this
    // node (The path may or may not include this node)
    let newPathLen = Math.max(maxPathLenUtil(root.left, cur_val, 1),
                        maxPathLenUtil(root.right, cur_val, 1));

    // Take the maximum previous path and path under subtree rooted
    // with this node.
    return Math.max(prev_len, newPathLen);
}

// A wrapper over maxPathLenUtil().
function maxConsecutivePathLength(root)
{
    // Return 0 if root is NULL
    if (root == null)
        return 0;

    // Else compute Maximum Consecutive Increasing Path
    // Length using maxPathLenUtil.
    return maxPathLenUtil(root, root.val-1, 0);
}

// Driver program to test above function
let root = new Node(10);
root.left = new Node(11);
root.right = new Node(9);
root.left.left = new Node(13);
root.left.right = new Node(12);
root.right.left = new Node(13);
root.right.right = new Node(8);

document.write("Maximum Consecutive Increasing Path Length is "+
maxConsecutivePathLength(root)+"<br>");

// This code is contributed by rag2127
</script>

Output

Maximum Consecutive Increasing Path Length is 3

Time Complexity: O(n^2), where n is the number of nodes in the given binary tree.
Auxiliary Space: O(log(n))