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

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++

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// C++ implementation to find array 
// elements equal to the sum
// of any subarray of at least size 2
  
#include <bits/stdc++.h>
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[0] = arr[0];
  
    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[0]);
  
    findElements(arr1, n1);
  
    return 0;
}

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Python3

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# 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

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Output:

3 5 6

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Improved By : AnkitRai01