Sum of Elements at Odd Indices in an Array

Problem Statement

Given an array of integers, calculate the sum of elements present at odd indices.

Note:
Odd indices refer to index positions, not odd-valued elements.
Array indexing always starts from 0.

Understanding Odd Indices

In an array:

• Index 0 → even
• Index 1 → odd
• Index 2 → even
• Index 3 → odd
• Index 5, 7, 9, … → odd indices

So, we consider elements at indices:

1, 3, 5, 7, ...

Example

Input

Array: [5, 15, 25, 35, 45]

Index Mapping

Index:    0   1   2   3   4
Element:  5  15  25  35  45

Elements at Odd Indices

Index 1 → 15
Index 3 → 35

Output

Sum = 15 + 35 = 50

Why This Problem Is Important

This problem helps in understanding:

• Index-based filtering
• Conditional checks within loops
• Difference between index and element properties
• Logical thinking for selective traversal

It also prepares you for:

• Alternate index problems
• Range-based queries
• Prefix sum optimizations

Approach / Logic

1. Initialize a variable sum = 0
2. Traverse the array using a loop
3. Check if the index is odd (i % 2 != 0)
4. Add the element at that index to sum
5. Print the final sum

Step-by-Step Algorithm

1. Start
2. Read the 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 Example

Array = [2, 4, 6, 8, 10, 12]

i = 0 → even → skip
i = 1 → odd  → sum = 4
i = 2 → even → skip
i = 3 → odd  → sum = 4 + 8 = 12
i = 4 → even → skip
i = 5 → odd  → sum = 12 + 12 = 24

Final Sum = 24

Time and Space Complexity

Only a single traversal is required, with no extra memory usage.

Language-wise Implementation

C Implementation

#include 

int main() {
    int arr[] = {5, 15, 25, 35, 45};
    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 odd indices: %d", sum);
    return 0;
}

Output

Sum of elements at odd indices: 50

C++ Implementation

#include 
using namespace std;

int main() {
    int arr[] = {5, 15, 25, 35, 45};
    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 odd indices: " << sum;
    return 0;
}

Output

Sum of elements at odd indices: 50

Java Implementation

public class Main {
    public static void main(String[] args) {
        int[] arr = {5, 15, 25, 35, 45};
        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 odd indices: " + sum);
    }
}

Output

Sum of elements at odd indices: 50

Python Implementation

arr = [5, 15, 25, 35, 45]
sum_odd_index = 0

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

print("Sum of elements at odd indices:", sum_odd_index)

Output

Sum of elements at odd indices: 50

C# Implementation

using System;

class Program {
    static void Main() {
        int[] arr = {5, 15, 25, 35, 45};
        int sum = 0;

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

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

Output

Sum of elements at odd indices: 50

JavaScript Implementation

let arr = [5, 15, 25, 35, 45];
let sum = 0;

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

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

Output

Sum of elements at odd indices: 50

Common Mistakes to Avoid

• Confusing odd indices with odd values
• Starting indexing from 1
• Forgetting index 1
• Using unnecessary extra arrays

Interview Variations

• Compare sum of even vs odd indices
• Find maximum sum among even or odd indices
• Prefix sum of odd index elements
• Alternate index summation

Detailed Summary

The problem of summing elements at odd indices reinforces the importance of index-based operations in arrays. By focusing on position rather than value, this problem strengthens loop control, conditional logic, and array traversal fundamentals. It also builds a solid base for more advanced concepts such as range-based calculations, prefix sums, and sliding window techniques, which frequently rely on selective index processing.

Next Problem in the Series

Find the Average of Array Elements