# Print all the paths from root, with a specified sum in Binary tree

Given a Binary tree and a sum S, print all the paths, starting from root, that sums upto the given sum.

Note that this problem is different from root to leaf paths. Here path doesn’t need to end on a leaf node.

Examples:

```Input :
Input : sum = 8,
Root of tree
1
/   \
20      3
/    \
4       15
/  \     /  \
6    7   8    9
Output :
Path: 1 3 4

Input : sum = 38,
Root of tree
10
/     \
28       13
/     \
14       15
/   \     /  \
21   22   23   24
Output : Path found: 10 28
Path found: 10 13 15
```

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

For this problem, preorder traversal is best suited as we have to add up a key value as we land on that node.

We start from the root and start traversing by preorder traversal, adding key value to the sum_so_far and checking whether it is equal to the required sum.
Also, as tree node doesn’t have a pointer pointing to its parent, we have to explicitly save from where we have moved. We use a vector path to store the path for this.

Every node in this path contributes to the sum_so_far.

## C++

 `// C++ program to print all paths begiinning with ` `// root and sum as given sum ` `#include ` `using` `namespace` `std; ` ` `  `// A Tree node ` `struct` `Node ` `{ ` `    ``int` `key; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// Utility function to create a new node ` `Node* newNode(``int` `key) ` `{ ` `    ``Node* temp = ``new` `Node; ` `    ``temp->key = key; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `(temp); ` `} ` ` `  ` `  `void` `printPathsUtil(Node* curr_node, ``int` `sum, ` `             ``int` `sum_so_far, vector<``int``> &path) ` `{ ` `    ``if` `(curr_node == NULL) ` `        ``return``; ` ` `  `    ``// add the current node's value ` `    ``sum_so_far += curr_node->key; ` ` `  `    ``// add the value to path ` `    ``path.push_back(curr_node->key); ` ` `  `    ``// print the required path ` `    ``if` `(sum_so_far == sum ) ` `    ``{ ` `        ``cout << ``"Path found: "``; ` `        ``for` `(``int` `i=0; ileft != NULL) ` `        ``printPathsUtil(curr_node->left, sum, sum_so_far, path); ` ` `  `    ``// if right child exists ` `    ``if` `(curr_node->right != NULL) ` `        ``printPathsUtil(curr_node->right, sum, sum_so_far, path); ` ` `  ` `  `    ``// Remove last element from path ` `    ``// and move back to parent ` `    ``path.pop_back(); ` `} ` ` `  `// Wrapper over printPathsUtil ` `void` `printPaths(Node *root, ``int` `sum) ` `{ ` `    ``vector<``int``> path; ` `    ``printPathsUtil(root, sum, 0, path); ` `} ` ` `  `// Driver program ` `int` `main () ` `{ ` `    ``/*   10 ` `       ``/     \ ` `     ``28       13 ` `           ``/     \ ` `         ``14       15 ` `        ``/   \     /  \ ` `       ``21   22   23   24*/` `    ``Node *root  = newNode(10); ` `    ``root->left  = newNode(28); ` `    ``root->right = newNode(13); ` ` `  `    ``root->right->left   = newNode(14); ` `    ``root->right->right  = newNode(15); ` ` `  `    ``root->right->left->left   = newNode(21); ` `    ``root->right->left->right  = newNode(22); ` `    ``root->right->right->left  = newNode(23); ` `    ``root->right->right->right = newNode(24); ` ` `  `    ``int` `sum = 38; ` ` `  `    ``printPaths(root, sum); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 program to Print all the  ` `# paths from root, with a specified ` `# sum in Binary tree ` `     `  `# Binary Tree Node  ` `""" utility that allocates a newNode  ` `with the given key """` `class` `newNode:  ` ` `  `    ``# Construct to create a newNode  ` `    ``def` `__init__(``self``, key):  ` `        ``self``.key ``=` `key ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# This function prints all paths ` `# that have sum k  ` `def` `printPathsUtil(curr_node, ``sum``,  ` `                   ``sum_so_far, path):  ` ` `  `    ``# empty node  ` `    ``if` `(``not` `curr_node) : ` `        ``return` `    ``sum_so_far ``+``=` `curr_node.key ` `     `  `    ``# add current node to the path  ` `    ``path.append(curr_node.key)  ` ` `  `    ``# prthe required path  ` `    ``if` `(sum_so_far ``=``=` `sum` `) : ` `     `  `        ``print``(``"Path found:"``, end ``=` `" "``)  ` `        ``for` `i ``in` `range``(``len``(path)): ` `            ``print``(path[i], end ``=` `" "``)  ` ` `  `        ``print``()  ` `     `  `    ``# if left child exists  ` `    ``if` `(curr_node.left !``=` `None``) : ` `        ``printPathsUtil(curr_node.left, ``sum``,  ` `                       ``sum_so_far, path)  ` ` `  `    ``# if right child exists  ` `    ``if` `(curr_node.right !``=` `None``) : ` `        ``printPathsUtil(curr_node.right, ``sum``,  ` `                       ``sum_so_far, path) ` ` `  `    ``# Remove the current element  ` `    ``# from the path  ` `    ``path.pop(``-``1``)  ` ` `  `# A wrapper over printKPathUtil()  ` `def` `printPaths(root, ``sum``): ` ` `  `    ``path ``=` `[] ` `    ``printPathsUtil(root, ``sum``, ``0``, path)  ` ` `  `# Driver Code  ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``""" 10  ` `    ``/     \  ` `    ``28     13  ` `        ``/     \  ` `        ``14     15  ` `        ``/ \     / \  ` `    ``21 22 23 24"""` `    ``root ``=` `newNode(``10``)  ` `    ``root.left ``=` `newNode(``28``)  ` `    ``root.right ``=` `newNode(``13``)  ` ` `  `    ``root.right.left ``=` `newNode(``14``)  ` `    ``root.right.right ``=` `newNode(``15``)  ` ` `  `    ``root.right.left.left ``=` `newNode(``21``)  ` `    ``root.right.left.right ``=` `newNode(``22``)  ` `    ``root.right.right.left ``=` `newNode(``23``)  ` `    ``root.right.right.right ``=` `newNode(``24``)  ` ` `  `    ``sum` `=` `38` ` `  `    ``printPaths(root, ``sum``) ` ` `  `# This code is contributed by ` `# Shubham Singh(SHUBHAMSINGH10) `

Output:

```Path found: 10 28
Path found: 10 13 15
```

This article is contributed by Shubham Gupta. 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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Improved By : SHUBHAMSINGH10

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