# Find the root of the sub-tree whose weighted sum is minimum

Given a tree, and the weights of all the nodes, the task is to find the root of the sub-tree whose weighted sum is minimum.

Examples:

Input: Output: 5
Weight of sub-tree for parent 1 = ((-1) + (5) + (-2) + (-1) + (3)) = 4
Weight of sub-tree for parent 2 = ((5) + (-1) + (3)) = 7
Weight of sub-tree for parent 3 = -1
Weight of sub-tree for parent 4 = 3
Weight of sub-tree for parent 5 = -2
Node 5 gives the minimum sub-tree weighted sum.

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

Approach: Perform dfs on the tree, and for every node calculate the sub-tree weighted sum rooted at the current node then find the minimum sum value for a node.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `int` `ans = 0, mini = INT_MAX; ` ` `  `vector<``int``> graph; ` `vector<``int``> weight(100); ` ` `  `// Function to perform dfs and update the tree ` `// such that every node's weight is the sum of ` `// the weights of all the nodes in the sub-tree ` `// of the current node including itself ` `void` `dfs(``int` `node, ``int` `parent) ` `{ ` `    ``for` `(``int` `to : graph[node]) { ` `        ``if` `(to == parent) ` `            ``continue``; ` `        ``dfs(to, node); ` ` `  `        ``// Calculating the weighted ` `        ``// sum of the subtree ` `        ``weight[node] += weight[to]; ` `    ``} ` `} ` ` `  `// Function to find the node ` `// having minimum sub-tree sum ` `void` `findMin(``int` `n) ` `{ ` ` `  `    ``// For every node ` `    ``for` `(``int` `i = 1; i <= n; i++) { ` ` `  `        ``// If current node's weight ` `        ``// is minimum so far ` `        ``if` `(mini > weight[i]) { ` `            ``mini = weight[i]; ` `            ``ans = i; ` `        ``} ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` ` `  `    ``// Weights of the node ` `    ``weight = -1; ` `    ``weight = 5; ` `    ``weight = -1; ` `    ``weight = 3; ` `    ``weight = -2; ` ` `  `    ``// Edges of the tree ` `    ``graph.push_back(2); ` `    ``graph.push_back(3); ` `    ``graph.push_back(4); ` `    ``graph.push_back(5); ` ` `  `    ``dfs(1, 1); ` `    ``findMin(n); ` ` `  `    ``cout << ans; ` ` `  `    ``return` `0; ` `} `

Output:

```5
```

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