Prefix Sum Array Implementation (original) (raw)

Last Updated : 13 Jul, 2025

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Given an array **arr[], Find the prefix sum of the array. A prefix sum array is another array **prefixSum[] of the same size, such that **prefixSum[i] is **arr[0] + arr[1] + arr[2] . . . arr[i].

**Examples:

**Input: arr[] = [10, 20, 10, 5, 15]
**Output: [10, 30, 40, 45, 60]
**Explanation: For each index i, add all the elements from 0 to i:
prefixSum[0] = 10,
prefixSum[1] = 10 + 20 = 30,
prefixSum[2] = 10 + 20 + 10 = 40 and so on.

**Input: arr[] = [30, 10, 10, 5, 50]
**Output: [30, 40, 50, 55, 105]
**Explanation: For each index i, add all the elements from 0 to i:
prefixSum[0] = 30,
prefixSum[1] = 30 + 10 = 40,
prefixSum[2] = 30 + 10+ 10 = 50 and so on.

Prefix Sum Implementation

The idea is to create an array prefixSum[] of size n, and for each index i in range 1 to n - 1, set prefixSum[i] = prefixSum[i - 1] + arr[i].

To solve the problem follow the given steps:

• Declare a new array **prefixSum[] of the same size as the input array
• Run a for loop to traverse the input array
• For each index add the value of the current element and the previous value of the prefix sum array

Below is the implementation of the above approach:

C++ `

#include #include using namespace std;

// function to find the prefix sum array vector prefSum(vector &arr) { int n = arr.size();

// to store the prefix sum
vector<int> prefixSum(n);

// initialize the first element
prefixSum[0] = arr[0];

// Adding present element with previous element
for (int i = 1; i < n; i++)
    prefixSum[i] = prefixSum[i - 1] + arr[i];

return prefixSum;

}

int main() { vector arr = {10, 20, 10, 5, 15}; vector prefixSum = prefSum(arr); for(auto i: prefixSum) { cout << i << " " ; } return 0; }

Java

import java.util.ArrayList;

public class GfG {

// function to find the prefix sum array
public static ArrayList<Integer> prefSum(int[] arr) {
    int n = arr.length;

    // to store the prefix sum
    ArrayList<Integer> prefixSum = new ArrayList<>();

    // initialize the first element
    prefixSum.add(arr[0]);

    // Adding present element with previous element
    for (int i = 1; i < n; i++)
        prefixSum.add(prefixSum.get(i - 1) + arr[i]);

    return prefixSum;
}

public static void main(String[] args) {
    int[] arr = {10, 20, 10, 5, 15};
    ArrayList<Integer> prefixSum = prefSum(arr);
    for (int i : prefixSum) {
        System.out.print(i + " ");
    }
}

}

Python

function to find the prefix sum array

def prefSum(arr): n = len(arr)

# to store the prefix sum
prefixSum = [0] * n

# initialize the first element
prefixSum[0] = arr[0]

# Adding present element with previous element
for i in range(1, n):
    prefixSum[i] = prefixSum[i - 1] + arr[i]

return prefixSum

if name == "main": arr = [10, 20, 10, 5, 15] prefixSum = prefSum(arr) for i in prefixSum: print(i, end=" ")

C#

using System; using System.Collections.Generic;

class GfG {

// function to find the prefix sum array
static List<int> prefSum(int[] arr) {
    int n = arr.Length;
    
    // to store the prefix sum
    List<int> prefixSum = new List<int>(new int[n]);

    // initialize the first element
    prefixSum[0] = arr[0];

    // Adding present element with previous element
    for (int i = 1; i < n; i++)
        prefixSum[i] = prefixSum[i - 1] + arr[i];
    
    return prefixSum;
}

static void Main() {
    int[] arr = {10, 20, 10, 5, 15};
    List<int> prefixSum = prefSum(arr);
    foreach (int i in prefixSum) {
        Console.Write(i + " ");
    }
}

}

JavaScript

// function to find the prefix sum array function prefSum(arr) { let n = arr.length;

// to store the prefix sum
let prefixSum = new Array(n);

// initialize the first element
prefixSum[0] = arr[0];

// Adding present element with previous element
for (let i = 1; i < n; i++)
    prefixSum[i] = prefixSum[i - 1] + arr[i];

return prefixSum;

}

// Driver Code let arr = [10, 20, 10, 5, 15]; let prefixSum = prefSum(arr); for (let i of prefixSum) { process.stdout.write(i + " "); }

`

**Time Complexity: O(n)
**Auxiliary Space: O(n)

Please refer Top Problems on Prefix Sum Technique for Interviews for more prefix sum problems.