Introduction

Sum of Array Elements means:

  • adding all values
  • present inside an array

The task is to:

  • traverse array
  • calculate total sum
  • return final answer

Example:

Input:
1 2 3 4 5

Output:
15

Explanation:

1 + 2 + 3 + 4 + 5 = 15

This problem is one of the most important applications of:

Recursion on Arrays

Constraints

1 <= Array Size <= 10^5

Approach 1 : Iterative Solution

Explanations:

Explanation:

The idea is:

  • traverse array
  • add every element

Steps:

  1. Initialize sum as 0.
  2. Traverse array.
  3. Add elements one by one.
  4. Print final sum.

This approach:

  • is simple
  • avoids recursion

Dry Run

Array:
1 2 3 4 5
sum = 0

0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15

Practice :

Complexity Analysis

Time Complexity:- O(n)Explanation :
Array is traversed once.

Space Complexity:- O(1)
Explanation :
No extra space is used.

Approach 2 : Recursive Solution

Explanations:

Explanation:

This is the most important recursion-based solution.

The idea is:

  • current element
  • recursive sum of remaining array

Base Case:

  • when index reaches end

Recursive Case:

  • add current element
  • recurse for next index

Dry Run

Array:
1 2 3 4 5

1 + sum(2 3 4 5)
1 + 2 + sum(3 4 5)
1 + 2 + 3 + sum(4 5)
1 + 2 + 3 + 4 + 5 = 15

Practice :

Complexity Analysis :

Time Complexity:- O(n)Explanation :
Recursive calls run n times.

Space Complexity:- O(n)
Explanation :
Recursion stack is used.

Why This Problem is Important

This problem builds the foundation for:

  • Recursion on arrays
  • Recursive traversal
  • Array processing
  • Recursive thinking
  • Mathematical recursion

Real-World Applications

Array summation concepts are used in:

  • Data analytics
  • Financial calculations
  • Statistical systems
  • Scientific computing
  • Database operations

Common Beginner Mistakes

  • Missing base case
  • Wrong recursion index
  • Infinite recursion
  • Incorrect addition logic
  • Index out of bounds

Interview Tip

Interviewers often expect:

  • recursion understanding
  • proper base case
  • recursive traversal logic
  • iterative vs recursive comparison

Always explain:

  • base condition
  • recursive call
  • accumulation process

Related Questions

  • Check Sorted Array
  • Factorial
  • Fibonacci
  • Maximum Element in Array
  • Recursion Basics

Final Takeaway

The Sum of Array Elements problem is one of the most important beginner recursion array problems.

It teaches:

  • recursion on arrays
  • recursive traversal
  • accumulation logic
  • recursive thinking

Understanding this problem builds a strong foundation for:

  • advanced recursion problems
  • divide and conquer
  • interview-level data structure questions.