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Count of root to leaf paths in a Binary Tree that form an AP

  • Last Updated : 23 Aug, 2021

Given a Binary Tree, the task is to count all paths from root to leaf which forms an Arithmetic Progression.

Examples: 

Input: 
 

Output:
Explanation: 
The paths that form an AP in the given tree from root to leaf are: 



  • 1->3->5 (A.P. with common difference 2)
  • 1->6->11 (A.P. with common difference 5)

Input: 
 

Output:
Explanation: 
The path that form an AP in the given tree from root to leaf is 1->10->19 (A.P. with difference 9) 
 

Approach: The problem can be solved using the Preorder Traversal. Follow the steps below to solve the problem: 

  • Perform Preorder Traversal on the given binary tree.
  • Initialize an array arr[] to store the path.
  • Initialize count = 0, to store the count of paths which forms an A.P.
  • After reaching the leaf node, check if the current elements in the array(i.e. the node values from root to leaf path) forms an A.P..
    • If so, increment the count
    • After the complete traversal of the tree, print the count.

Below is the implementation of above approach: 

C++




// C++ implementation to count
// the path which forms an A.P.
#include <bits/stdc++.h>
using namespace std;
 
int count = 0;
 
// Node structure
struct Node {
    int val;
    // left and right child of the node
    Node *left, *right;
    // initialization constructor
    Node(int x)
    {
        val = x;
        left = NULL;
        right = NULL;
    }
};
 
// Function to check if path
// format A.P. or not
bool check(vector<int> arr)
{
 
    if (arr.size() == 1)
        return true;
 
    // if size of arr is greater than 2
    int d = arr[1] - arr[0];
 
    for (int i = 2; i < arr.size(); i++) {
        if (arr[i] - arr[i - 1] != d)
            return false;
    }
 
    return true;
}
 
// Function to find the maximum
// setbits sum from root to leaf
int countAP(Node* root, vector<int> arr)
{
    if (!root)
        return 0;
 
    arr.push_back(root->val);
 
    // If the node is a leaf node
    if (root->left == NULL
        && root->right == NULL) {
        if (check(arr))
            return 1;
        return 0;
    }
 
    // Traverse left subtree
    int x = countAP(root->left, arr);
 
    // Traverse the right subtree
    int y = countAP(root->right, arr);
 
    return x + y;
}
 
// Driver Code
int main()
{
    Node* root = new Node(1);
    root->left = new Node(3);
    root->right = new Node(6);
    root->left->left = new Node(5);
    root->left->right = new Node(7);
    root->right->left = new Node(11);
    root->right->right = new Node(23);
 
    cout << countAP(root, {});
 
    return 0;
}

Java




// Java implementation to count
// the path which forms an A.P.
import java.util.*;
 
class GFG{
 
int count = 0;
 
// Node structure
static class Node
{
    int val;
     
    // left and right child of the node
    Node left, right;
     
    // Initialization constructor
    Node(int x)
    {
        val = x;
        left = null;
        right = null;
    }
};
 
// Function to check if path
// format A.P. or not
static boolean check(Vector<Integer> arr)
{
    if (arr.size() == 1)
        return true;
 
    // If size of arr is greater than 2
    int d = arr.get(1) - arr.get(0);
 
    for(int i = 2; i < arr.size(); i++)
    {
        if (arr.get(i) - arr.get(i - 1) != d)
            return false;
    }
    return true;
}
 
// Function to find the maximum
// setbits sum from root to leaf
static int countAP(Node root,
                   Vector<Integer> arr)
{
    if (root == null)
        return 0;
 
    arr.add(root.val);
 
    // If the node is a leaf node
    if (root.left == null &&
        root.right == null)
    {
        if (check(arr))
            return 1;
        return 0;
    }
 
    // Traverse left subtree
    int x = countAP(root.left, arr);
 
    // Traverse the right subtree
    int y = countAP(root.right, arr);
 
    return x + y;
}
 
// Driver Code
public static void main(String[] args)
{
    Node root = new Node(1);
    root.left = new Node(3);
    root.right = new Node(6);
    root.left.left = new Node(5);
    root.left.right = new Node(7);
    root.right.left = new Node(11);
    root.right.right = new Node(23);
 
    System.out.print(countAP(root, new Vector<Integer>()));
}
}
 
// This code is contributed by gauravrajput1

Python3




# Python3 implementation to count
# the path which forms an A.P.
 
# Node structure
class Node:
    def __init__(self, x):
         
        self.val = x
        self.left = None
        self.right = None
         
# Function to check if path
# format A.P. or not
def check(arr):
     
    if len(arr) == 1:
        return True
     
    # If size of arr is greater than 2
    d = arr[1] - arr[0]
     
    for i in range(2, len(arr)):
        if arr[i] - arr[i - 1] != d:
            return False
             
    return True
 
# Function to find the maximum
# setbits sum from root to leaf
def countAP(root, arr):
     
    if not root:
        return 0
     
    arr.append(root.val)
     
    # If the node is a leaf node
    if (root.left == None and
        root.right == None):
        if check(arr):
            return 1
        return 0
     
    # Traverse the left subtree
    x = countAP(root.left, arr)
     
    # Traverse the right subtree
    y = countAP(root.right, arr)
     
    return x + y
 
# Driver code
root = Node(1)
root.left = Node(3)
root.right = Node(6)
root.left.left = Node(5)
root.left.right = Node(7)
root.right.left = Node(11)
root.right.right = Node(23)
 
print(countAP(root, []))
 
# This code is contributed by stutipathak31jan

C#




// C# implementation to count
// the path which forms an A.P.
using System;
using System.Collections.Generic;
 
class GFG{
 
//int count = 0;
 
// Node structure
class Node
{
    public int val;
     
    // left and right child of the node
    public Node left, right;
     
    // Initialization constructor
    public Node(int x)
    {
        val = x;
        left = null;
        right = null;
    }
};
 
// Function to check if path
// format A.P. or not
static bool check(List<int> arr)
{
    if (arr.Count == 1)
        return true;
 
    // If size of arr is greater than 2
    int d = arr[1] - arr[0];
 
    for(int i = 2; i < arr.Count; i++)
    {
        if (arr[i] - arr[i - 1] != d)
            return false;
    }
    return true;
}
 
// Function to find the maximum
// setbits sum from root to leaf
static int countAP(Node root,
                   List<int> arr)
{
    if (root == null)
        return 0;
 
    arr.Add(root.val);
 
    // If the node is a leaf node
    if (root.left == null &&
       root.right == null)
    {
        if (check(arr))
            return 1;
        return 0;
    }
 
    // Traverse left subtree
    int x = countAP(root.left, arr);
 
    // Traverse the right subtree
    int y = countAP(root.right, arr);
 
    return x + y;
}
 
// Driver Code
public static void Main(String[] args)
{
    Node root = new Node(1);
    root.left = new Node(3);
    root.right = new Node(6);
    root.left.left = new Node(5);
    root.left.right = new Node(7);
    root.right.left = new Node(11);
    root.right.right = new Node(23);
 
    Console.Write(countAP(root, new List<int>()));
}
}
 
// This code is contributed by amal kumar choubey

Javascript




<script>
 
// JavaScript implementation to count
// the path which forms an A.P.
let count = 0;
 
// Node structure
class Node
{
     
    // Initialize constructor
    constructor(x)
    {
        this.val = x;
        this.left = null;
        this.right = null;
    }
}
 
var root;
 
// Function to check if path
// format A.P. or not
function check(arr)
{
    if (arr.length == 1)
        return true;
 
    // If size of arr is greater than 2
    let d = arr[1] - arr[0];
 
    for(let i = 2; i < arr.length; i++)
    {
        if (arr[i] - arr[i - 1] != d)
            return false;
    }
    return true;
}
 
// Function to find the maximum
// setbits sum from root to leaf
function countAP(root, arr)
{
    if (!root)
        return 0;
 
    arr.push(root.val);
 
    // If the node is a leaf node
    if (root.left == null &&
       root.right == null)
    {
        if (check(arr))
            return 1;
        return 0;
    }
 
    // Traverse left subtree
    let x = countAP(root.left, arr);
 
    // Traverse the right subtree
    let y = countAP(root.right, arr);
 
    return x + y;
}
 
// Driver Code
root = new Node(1);
root.left = new Node(3);
root.right = new Node(6);
root.left.left = new Node(5);
root.left.right = new Node(7);
root.right.left = new Node(11);
root.right.right = new Node(23);
 
let arr = [];
document.write(countAP(root, arr));
 
// This code is contributed by Dharanendra L V.
 
</script>

Output: 

2

Time Complexity: O(N) 
Auxiliary Space: O(h), where h is the height of binary tree.

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