Find array elements equal to sum of any subarray of at least size 2
Last Updated :
15 Jul, 2025
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 a 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 <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;
}
// Java implementation to find array
// elements equal to the sum of any
// subarray of at least size 2
import java.util.*;
class GFG{
// Function to find all elements
static void findElements(int[] arr, int n)
{
if (n == 1)
return;
int pre[] = new int[n];
// Create a prefix array
pre[0] = arr[0];
for(int i = 1; i < n; i++)
pre[i] = arr[i] + pre[i - 1];
HashMap<Integer, Boolean> mp = new HashMap<>();
// Mark the sum of all sub arrays as true
for(int i = 1; i < n - 1; i++)
{
mp.put(pre[i], true);
for(int j = i + 1; j < n; j++)
{
mp.put(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.get(arr[i]) != null)
{
System.out.print(arr[i] + " ");
}
}
System.out.println();
}
// Driver Code
public static void main(String[] args)
{
int arr1[] = { 1, 2, 3, 4, 5, 6 };
int n1 = arr1.length;
findElements(arr1, n1);
}
}
// This code is contributed by jrishabh99
# 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
// C# implementation to find array
// elements equal to the sum of any
// subarray of at least size 2
using System;
using System.Collections.Generic;
class GFG{
// Function to find all elements
static void findElements(int[] arr,
int n)
{
if (n == 1)
return;
int []pre = new int[n];
// Create a prefix array
pre[0] = arr[0];
for(int i = 1; i < n; i++)
pre[i] = arr[i] + pre[i - 1];
Dictionary<int,
Boolean> mp = new Dictionary<int,
Boolean>();
// Mark the sum of all sub arrays as true
for(int i = 1; i < n - 1; i++)
{
if(!mp.ContainsKey(pre[i]))
mp.Add(pre[i], true);
for(int j = i + 1; j < n; j++)
{
if(!mp.ContainsKey(pre[j] - pre[i - 1]))
mp.Add(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.ContainsKey(arr[i]))
{
Console.Write(arr[i] + " ");
}
}
Console.WriteLine();
}
// Driver Code
public static void Main(String[] args)
{
int []arr1 = {1, 2, 3, 4, 5, 6};
int n1 = arr1.Length;
findElements(arr1, n1);
}
}
// This code is contributed by gauravrajput1
<script>
// Javascript implementation to find array
// elements equal to the sum of any
// subarray of at least size 2
// Function to find all elements
function findElements(arr, n)
{
if (n == 1)
return;
let pre = Array.from({length: n}, (_, i) => 0);
// Create a prefix array
pre[0] = arr[0];
for(let i = 1; i < n; i++)
pre[i] = arr[i] + pre[i - 1];
let mp = new Map();
// Mark the sum of all sub arrays as true
for(let i = 1; i < n - 1; i++)
{
mp.set(pre[i], true);
for(let j = i + 1; j < n; j++)
{
mp.set(pre[j] - pre[i - 1], true);
}
}
// Check all elements
// which are marked
// true in the map
for(let i = 0; i < n; i++)
{
if (mp.get(arr[i]) != null)
{
document.write(arr[i] + " ");
}
}
document.write("<br/>");
}
// Driver code
let arr1 = [ 1, 2, 3, 4, 5, 6 ];
let n1 = arr1.length;
findElements(arr1, n1);
// This code is contributed by souravghosh0416.
</script>
Time Complexity: O(N2)
Auxiliary Space: O(N)
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