Maximum Number of Operations With the Same Score I - Video Solutions

Problem Overview: You are given an integer array nums. Each operation removes the first two elements and produces a score equal to their sum. Every operation must produce the same score. The task is to determine the maximum number of valid operations you can perform before the rule breaks.

Approach 1: Brute Force Simulation (O(n) time, O(1) space)

The direct strategy simulates the process exactly as described. Start by computing the score from the first pair: target = nums[0] + nums[1]. Then repeatedly remove the next two elements and check whether their sum equals target. If the sum differs, the sequence of operations must stop. Because each step processes exactly two elements, the algorithm scans the array once. This approach uses simple iteration and conditional checks, making it easy to implement. It fits naturally with problems categorized under Array and Simulation since you mimic the operations step by step without additional data structures.

Approach 2: Optimized Two-Pointer Scan (O(n) time, O(1) space)

A cleaner implementation uses a pointer that moves across the array in steps of two. First compute the required score using the first pair. Then maintain a pointer i starting at index 2. At each step, check whether nums[i] + nums[i+1] equals the target score. If it matches, increment the operation count and move the pointer forward by two positions. If it does not match, terminate immediately because future operations would violate the constant-score rule. This pattern resembles a simplified Two Pointers traversal where the pointer jumps across fixed-size segments instead of sliding element by element.

The key insight is that the score is fixed by the first operation. After that, the array must naturally split into consecutive pairs producing the same sum. No rearrangement or searching is allowed, so the problem reduces to verifying each pair sequentially. Because every element is visited at most once, the runtime stays linear and memory usage remains constant.

Recommended for interviews: The two-pointer style scan is the approach interviewers typically expect. It demonstrates that you recognized the greedy constraint: the first pair determines the only valid score. The brute force simulation still shows clear understanding of the problem mechanics, but the optimized pointer traversal communicates stronger pattern recognition and cleaner implementation.