# Print path from root to a given node in a binary tree

Given a binary tree with distinct nodes(no two nodes have the same have data values). The problem is to print the path from root to a given node x. If node x is not present then print “No Path”.

Examples:

```Input :          1
/   \
2     3
/ \   /  \
4   5  6   7

x = 5

Output : 1->2->5
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Create a recursive function that traverses the different path in the binary tree to find the required node x. If node x is present then it returns true and accumulates the path nodes in some array arr[]. Else it returns false.

Following are the cases during the traversal:

1. If root = NULL, return false.
2. push the root’s data into arr[].
3. if root’s data = x, return true.
4. if node x is present in root’s left or right subtree, return true.
5. Else remove root’s data value from arr[] and return false.

This recursive function can be accessed from other function to check whether node x is present or not and if it is present, then the path nodes can be accessed from arr[]. You can define arr[] globally or pass its reference to the recursive function.

```// C++ implementation to print the path from root
// to a given node in a binary tree
#include <bits/stdc++.h>
using namespace std;

// structure of a node of binary tree
struct Node
{
int data;
Node *left, *right;
};

/* Helper function that allocates a new node with the
given data and NULL left and right pointers. */
struct Node* getNode(int data)
{
struct Node *newNode = new Node;
newNode->data = data;
newNode->left = newNode->right = NULL;
return newNode;
}

// Returns true if there is a path from root
// to the given node. It also populates
// 'arr' with the given path
bool hasPath(Node *root, vector<int>& arr, int x)
{
// if root is NULL
// there is no path
if (!root)
return false;

// push the node's value in 'arr'
arr.push_back(root->data);

// if it is the required node
// return true
if (root->data == x)
return true;

// else check whether the required node lies
// in the left subtree or right subtree of
// the current node
if (hasPath(root->left, arr, x) ||
hasPath(root->right, arr, x))
return true;

// required node does not lie either in the
// left or right subtree of the current node
// Thus, remove current node's value from
// 'arr'and then return false
arr.pop_back();
return false;
}

// function to print the path from root to the
// given node if the node lies in the binary tree
void printPath(Node *root, int x)
{
// vector to store the path
vector<int> arr;

// if required node 'x' is present
// then print the path
if (hasPath(root, arr, x))
{
for (int i=0; i<arr.size()-1; i++)
cout << arr[i] << "->";
cout << arr[arr.size() - 1];
}

// 'x' is not present in the binary tree
else
cout << "No Path";
}

// Driver program to test above
int main()
{
// binary tree formation
struct Node *root = getNode(1);
root->left = getNode(2);
root->right = getNode(3);
root->left->left = getNode(4);
root->left->right = getNode(5);
root->right->left = getNode(6);
root->right->right = getNode(7);

int x = 5;
printPath(root, x);
return 0;
}
```

Output:

```1->2->5
```

Time complexity: O(n) in worst case, where n is the number of nodes in the binary tree.

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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