Make Array Elements Equal to Zero - Video Solutions

Problem Overview: You are given an integer array and must determine whether the elements can be reduced so the entire array becomes zero under the allowed operations. The key challenge is tracking how values change as operations propagate across the array.

Approach 1: Simulation with State Changes (O(n) time, O(1) space)

The most direct strategy is to simulate the process exactly as defined. Iterate through the array and apply the allowed operation whenever a valid state appears. Each operation updates the current element and may influence neighboring positions, so you maintain the array state as you move through it. The insight is that every value eventually contributes to a sequence of decrements that propagate across the array. Because each element is processed a constant number of times, the total time complexity remains O(n) with O(1) extra space. This approach is ideal when the constraints are small or when the goal is to mirror the problem statement precisely using straightforward array traversal.

Approach 2: Prefix Sum Based Reasoning (O(n) time, O(1) space)

Instead of explicitly performing every state change, you can track the cumulative effect of operations using a running prefix balance. Each operation contributes a predictable change that affects future positions. By maintaining a prefix sum that represents the total operations applied so far, you can determine the effective value of the current element without modifying the entire array. If the adjusted value becomes invalid at any step, the configuration cannot reach all zeros. This reduces unnecessary updates and keeps the algorithm strictly linear. Prefix tracking is a common optimization pattern when operations apply cumulative changes across an prefix sum structure.

Approach 3: Graph Perspective with BFS (O(n) time, O(n) space)

The array can also be viewed as a graph where each index is a node and operations propagate changes to adjacent indices. In this interpretation, nodes that become zero act as starting points that trigger updates to neighbors. Using a queue, perform a breadth‑first search that processes indices whose state allows further propagation. Each node is visited when its value reaches the required condition, and the BFS ensures updates spread in the correct order. This framing is helpful when reasoning about chained effects or when the operation behaves like a wave spreading through the array. The queue introduces O(n) auxiliary space but keeps the runtime linear. This method combines array traversal with classic simulation ideas.

Recommended for interviews: The simulation approach is usually the first step because it mirrors the problem statement and proves you understand the state transitions. Interviewers typically expect you to then optimize the reasoning using a prefix‑sum style running balance, which avoids repeated updates and achieves a clean O(n) solution.