# Sum of cousins of a given node in a Binary Tree

Given a binary tree and data value of a node. The task is to find the sum of cousin nodes of given node. If given node has no cousins then return -1.
Note: It is given that all nodes have distinct values and the given node exists in the tree.

Examples:

```Input:
1
/  \
3    7
/  \  / \
6   5  4  13
/  / \
10 17 15
key = 13
Output: 11
Cousin nodes are 5 and 6 which gives sum 11.

Input:
1
/  \
3    7
/  \  / \
6   5  4  13
/  / \
10 17 15
key = 7
Output: -1
No cousin nodes of node having value 7.
```

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

Approach: The approach is to do a level order traversal of the tree. While performing level order traversal, find the sum of child nodes of next level. Add a child node’s value to the sum and check if either of the children nodes is the target node or not. If yes, then do not add the value of either child to the sum. After traversing current level if the target node is present in next level, then end the level order traversal and sum found is the sum of cousin nodes.

Below is the implementation of the above approach:

 `// CPP program to find sum of cousins ` `// of given node in binary tree. ` `#include ` `using` `namespace` `std; ` ` `  `// A Binary Tree Node ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// A utility function to create a new ` `// Binary Tree Node ` `struct` `Node* newNode(``int` `item) ` `{ ` `    ``struct` `Node* temp = (``struct` `Node*)``malloc``(``sizeof``(``struct` `Node)); ` `    ``temp->data = item; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `// Function to find sum of cousins of ` `// a given node. ` `int` `findCousinSum(Node* root, ``int` `key) ` `{ ` `    ``if` `(root == NULL) ` `        ``return` `-1; ` ` `  `    ``// Root node has no cousins so return -1. ` `    ``if` `(root->data == key) { ` `        ``return` `-1; ` `    ``} ` ` `  `    ``// To store sum of cousins. ` `    ``int` `currSum = 0; ` ` `  `    ``// To store size of current level. ` `    ``int` `size; ` ` `  `    ``// To perform level order traversal. ` `    ``queue q; ` `    ``q.push(root); ` ` `  `    ``// To represent that target node is ` `    ``// found. ` `    ``bool` `found = ``false``; ` ` `  `    ``while` `(!q.empty()) { ` ` `  `        ``// If target node is present at ` `        ``// current level, then return ` `        ``// sum of cousins stored in currSum. ` `        ``if` `(found == ``true``) { ` `            ``return` `currSum; ` `        ``} ` ` `  `        ``// Find size of current level and ` `        ``// traverse entire level. ` `        ``size = q.size(); ` `        ``currSum = 0; ` ` `  `        ``while` `(size) { ` `            ``root = q.front(); ` `            ``q.pop(); ` ` `  `            ``// Check if either of the existing ` `            ``// children of given node is target ` `            ``// node or not. If yes then set ` `            ``// found equal to true. ` `            ``if` `((root->left && root->left->data == key) ` `                ``|| (root->right && root->right->data == key)) { ` `                ``found = ``true``; ` `            ``} ` ` `  `            ``// If target node is not children of ` `            ``// current node, then its childeren can be cousin ` `            ``// of target node, so add their value to sum. ` `            ``else` `{ ` `                ``if` `(root->left) { ` `                    ``currSum += root->left->data; ` `                    ``q.push(root->left); ` `                ``} ` ` `  `                ``if` `(root->right) { ` `                    ``currSum += root->right->data; ` `                    ``q.push(root->right); ` `                ``} ` `            ``} ` ` `  `            ``size--; ` `        ``} ` `    ``} ` ` `  `    ``return` `-1; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``/* ` `                ``1 ` `              ``/  \ ` `             ``3    7 ` `           ``/  \  / \ ` `          ``6   5  4  13 ` `             ``/  / \ ` `            ``10 17 15 ` `    ``*/` ` `  `    ``struct` `Node* root = newNode(1); ` `    ``root->left = newNode(3); ` `    ``root->right = newNode(7); ` `    ``root->left->left = newNode(6); ` `    ``root->left->right = newNode(5); ` `    ``root->left->right->left = newNode(10); ` `    ``root->right->left = newNode(4); ` `    ``root->right->right = newNode(13); ` `    ``root->right->left->left = newNode(17); ` `    ``root->right->left->right = newNode(15); ` ` `  `    ``cout << findCousinSum(root, 13) << ``"\n"``; ` ` `  `    ``cout << findCousinSum(root, 7) << ``"\n"``; ` `    ``return` `0; ` `} `

Output:

```11
-1
```

Time Complexity: O(N)
Auxiliary Space: O(N)

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