# Find array elements equal to sum of any subarray of at least size 2

Given an array arr[], the task is to find the elements from the array which are equal to the sum of any sub-array of size greater than 1.

Examples:

Input: arr[] = {1, 2, 3, 4, 5, 6}
Output: 3, 5, 6
Explanation:
The elements 3, 5, 6 are equal to sum of subarrays {1, 2},{2, 3} and {1, 2, 3} respectively.

Input: arr[] = {5, 6, 10, 1, 3, 4, 8, 16}
Output: 4, 8, 16
Explanation:
The elements 4, 8, 16 are equal to the sum of subarrays {1, 3}, {1, 3, 4}, {1, 3, 4, 8} respectively

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

Approach: The idea is to use prefix sum array to solve the given problem. Create a prefix[] array that stores the prefix sum of all its preceding elements for every index. Store the sum of all subarrays in a map and search if any array element is present in the map or not.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to find array  ` `// elements equal to the sum ` `// of any subarray of at least size 2 ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find all elements ` `void` `findElements(``int``* arr, ``int` `n) ` `{ ` `    ``if` `(n == 1) ` `        ``return``; ` ` `  `    ``int` `pre[n]; ` ` `  `    ``// Create a prefix array ` `    ``pre = arr; ` ` `  `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``pre[i] = arr[i] + pre[i - 1]; ` ` `  `    ``unordered_map<``int``, ``bool``> mp; ` ` `  `    ``// Mark the sum of all sub arrays as true ` `    ``for` `(``int` `i = 1; i < n - 1; i++) { ` `        ``mp[pre[i]] = ``true``; ` ` `  `        ``for` `(``int` `j = i + 1; j < n; j++) { ` `            ``mp[pre[j] - pre[i - 1]] = ``true``; ` `        ``} ` `    ``} ` ` `  `    ``// Check all elements ` `    ``// which are marked ` `    ``// true in the map ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(mp[arr[i]]) { ` `            ``cout << arr[i] << ``" "``; ` `        ``} ` `    ``} ` `    ``cout << endl; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `arr1[] = { 1, 2, 3, 4, 5, 6 }; ` ` `  `    ``int` `n1 = ``sizeof``(arr1) / ``sizeof``(arr1); ` ` `  `    ``findElements(arr1, n1); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 implementation to find array  ` `# elements equal to the sum of any ` `# subarray of at least size 2  ` ` `  `# Function to find all elements  ` `def` `findElements(arr, n):  ` ` `  `    ``if` `(n ``=``=` `1``): ` `        ``return``;  ` ` `  `    ``pre ``=` `[``0``] ``*` `n;  ` ` `  `    ``# Create a prefix array  ` `    ``pre[``0``] ``=` `arr[``0``];  ` ` `  `    ``for` `i ``in` `range``(``1``, n):  ` `        ``pre[i] ``=` `arr[i] ``+` `pre[i ``-` `1``];  ` ` `  `    ``mp ``=` `{};  ` ` `  `    ``# Mark the sum of all sub arrays as true  ` `    ``for` `i ``in` `range``(``1``, n ``-` `1``): ` `        ``mp[pre[i]] ``=` `True``;  ` ` `  `        ``for` `j ``in` `range``(i ``+` `1``, n): ` `            ``mp[pre[j] ``-` `pre[i ``-` `1``]] ``=` `True``;  ` ` `  `    ``# Check all elements which  ` `    ``# are marked true in the map  ` `    ``for` `i ``in` `range``(n): ` `        ``if` `arr[i] ``in` `mp: ` `            ``print``(arr[i], end ``=` `" "``);  ` `        ``else``: ` `            ``pass` `     `  `    ``print``() ` ` `  `# Driver Code  ` `if` `__name__ ``=``=` `"__main__"``:  ` ` `  `    ``arr1 ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5``, ``6` `];  ` `    ``n1 ``=` `len``(arr1);  ` ` `  `    ``findElements(arr1, n1);  ` `     `  `# This code is contributed by AnkitRai01`

Output:

```3 5 6
```

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