Sum of Elements at Even Indices in an Array

Problem Statement

Given an array of integers, find the sum of elements present at even indices.

Important:
Even indices mean index positions, not even values.
Array indexing starts from 0.

Understanding Even Indices

In an array:

• Index 0 → even
• Index 1 → odd
• Index 2 → even
• Index 3 → odd
• and so on…

So, elements at indices 0, 2, 4, 6, ... are considered.

Example

Input

Array: [10, 20, 30, 40, 50]

Indices

Index:   0   1   2   3   4
Element:10  20  30  40  50

Elements at Even Indices

Index 0 → 10
Index 2 → 30
Index 4 → 50

Output

Sum = 10 + 30 + 50 = 90

Why This Problem Is Important

This problem helps you understand:

• Index-based traversal
• Conditional logic inside loops
• Difference between value-based and index-based operations
• Foundation for advanced problems like prefix sums and range queries

Approach / Logic

1. Initialize a variable sum = 0
2. Traverse the array from index 0 to n-1
3. Check if the index is even (i % 2 == 0)
4. If yes, add array[i] to sum
5. After traversal, print the sum

Algorithm (Step-by-Step)

1. Start
2. Read array and its size
3. Initialize sum = 0
4. Loop from i = 0 to n - 1
5. If i % 2 == 0
   • Add arr[i] to sum
6. Print sum
7. End

Pseudocode

sum = 0
for i = 0 to n-1:
    if i % 2 == 0:
        sum = sum + arr[i]
print sum

Dry Run

Array = [4, 7, 1, 9, 2]

i = 0 → even → sum = 4
i = 1 → odd  → skip
i = 2 → even → sum = 4 + 1 = 5
i = 3 → odd  → skip
i = 4 → even → sum = 5 + 2 = 7

Final Sum = 7

Time and Space Complexity

Only a single traversal is required, and no extra memory is used.

Language-wise Implementation

C Implementation

#include 

int main() {
    int arr[] = {10, 20, 30, 40, 50};
    int n = sizeof(arr) / sizeof(arr[0]);
    int sum = 0;

    for(int i = 0; i < n; i++) {
        if(i % 2 == 0) {
            sum += arr[i];
        }
    }

    printf("Sum of elements at even indices: %d", sum);
    return 0;
}

Output

Sum of elements at even indices: 90

C++ Implementation

#include 
using namespace std;

int main() {
    int arr[] = {10, 20, 30, 40, 50};
    int n = sizeof(arr) / sizeof(arr[0]);
    int sum = 0;

    for(int i = 0; i < n; i++) {
        if(i % 2 == 0) {
            sum += arr[i];
        }
    }

    cout << "Sum of elements at even indices: " << sum;
    return 0;
}

Output

Sum of elements at even indices: 90

Java Implementation

public class Main {
    public static void main(String[] args) {
        int[] arr = {10, 20, 30, 40, 50};
        int sum = 0;

        for(int i = 0; i < arr.length; i++) {
            if(i % 2 == 0) {
                sum += arr[i];
            }
        }

        System.out.println("Sum of elements at even indices: " + sum);
    }
}

Output

Sum of elements at even indices: 90

Python Implementation

arr = [10, 20, 30, 40, 50]
sum_even_index = 0

for i in range(len(arr)):
    if i % 2 == 0:
        sum_even_index += arr[i]

print("Sum of elements at even indices:", sum_even_index)

Output

Sum of elements at even indices: 90

C# Implementation

using System;

class Program {
    static void Main() {
        int[] arr = {10, 20, 30, 40, 50};
        int sum = 0;

        for(int i = 0; i < arr.Length; i++) {
            if(i % 2 == 0) {
                sum += arr[i];
            }
        }

        Console.WriteLine("Sum of elements at even indices: " + sum);
    }
}

Output

Sum of elements at even indices: 90

JavaScript Implementation

let arr = [10, 20, 30, 40, 50];
let sum = 0;

for (let i = 0; i < arr.length; i++) {
    if (i % 2 === 0) {
        sum += arr[i];
    }
}

console.log("Sum of elements at even indices:", sum);

Output

Sum of elements at even indices: 90

Common Mistakes to Avoid

• Confusing even indices with even numbers
• Starting indexing from 1 instead of 0
• Skipping index 0
• Using unnecessary extra arrays

Interview Variations

• Sum of elements at odd indices
• Sum of even-index elements greater than a given value
• Separate sums of even and odd indices
• Prefix sum of even indices

Detailed Summary

The problem of finding the sum of elements at even indices focuses on index-based traversal rather than value-based filtering. By iterating through the array and selectively adding elements whose indices satisfy a condition, we reinforce a critical concept used throughout array manipulation and algorithm design. This problem builds a strong foundation for understanding indexed access, loop control, and conditional logic, which are essential for more advanced array techniques such as sliding window, prefix sum, and hashing-based optimizations.

Next Problem in the Series

Sum of Elements at Odd Indices