Transformed Array - Solution & Explanation

Problem Overview: You are given an integer array nums. For each index i, move nums[i] steps in the array (right for positive values, left for negative values) using circular indexing. The value at the destination index becomes result[i]. The task is to build this transformed array.

Approach 1: Step-by-Step Simulation (O(n²) time, O(n) space)

The most direct approach simulates movement one step at a time. For every index i, repeatedly move left or right depending on the sign of nums[i]. Since the array is circular, wrap around when the pointer moves past either end. After completing the required number of steps, record the element at the final index. This method mirrors the problem statement closely and is easy to reason about, but repeated stepping can make the total work quadratic in the worst case.

Approach 2: Direct Circular Index Calculation (O(n) time, O(n) space)

You can compute the final position directly using modular arithmetic instead of moving step by step. For index i, the destination becomes (i + nums[i]) % n, where n is the array length. If the result is negative, add n to normalize it into the valid range [0, n-1]. This works because circular movement in an array is equivalent to modular index wrapping. Once the destination index is known, copy the value from nums[dest] into the output array.

This technique is a classic simulation optimization. Instead of simulating each move, you compute the final state directly using arithmetic. The algorithm performs a single pass through the array, making it linear time while using a separate result array.

Recommended for interviews: The direct circular index calculation is what interviewers expect. Explaining the step-by-step simulation first shows you understand the mechanics of the problem. Converting it into a modular arithmetic formula demonstrates strong reasoning about circular arrays and produces the optimal O(n) solution.