Array Reduce Transformation - Video Solutions

Problem Overview: You receive an array nums, a reducer function fn, and an initial value init. The task is to repeatedly apply the function so that each array element updates an accumulator value, eventually producing a single final result.

This mirrors how the classic reduce operation works in functional programming. Starting with init, the reducer combines the accumulator with each element in order: acc = fn(acc, nums[i]). After processing every element, the final accumulator value is returned.

Approach 1: Iterative Loop Reduction (O(n) time, O(1) space)

The most direct implementation uses a simple loop. Initialize a variable accumulator with init. Then iterate through the array from index 0 to n-1. For every element, call the reducer function and update the accumulator: accumulator = fn(accumulator, nums[i]). After the loop finishes, return the accumulator.

This approach works because reduction is inherently sequential. Each step depends on the previous accumulator value. The algorithm performs exactly one pass over the array, making the time complexity O(n). Only a single variable is maintained regardless of input size, so the space complexity remains O(1). This pattern appears frequently in problems involving arrays and aggregation tasks such as sums, products, or custom accumulations.

Approach 2: Recursive Reduction (O(n) time, O(n) space)

The same reduction logic can be expressed recursively. Define a recursive function that processes the array index by index. At each step, compute a new accumulator using the current element, then call the function for the next index.

The recursion terminates when the index reaches the end of the array. The final accumulator value is returned back through the call stack. While the algorithm still processes each element once for O(n) time complexity, recursion adds stack frames for every call, resulting in O(n) auxiliary space.

This version is conceptually aligned with functional programming patterns and demonstrates how reduction can be defined in terms of smaller subproblems. It’s a good exercise when practicing recursion or understanding functional abstractions used in languages like JavaScript.

Recommended for interviews: The iterative loop reduction is the expected approach. It is simpler, avoids recursion overhead, and clearly demonstrates how reduction accumulates results across an array. The recursive version still shows strong understanding of functional decomposition, but interviewers generally prefer the iterative implementation because it uses constant space and mirrors real-world implementations of reduce.