Find the Score Difference in a Game - Video Solutions

Problem Overview: You are given an array representing moves or scoring events in a game. Each element affects the score of one of the players according to the rules. The task is to simulate the sequence and compute the final score difference between the two sides.

Approach 1: Direct Simulation (O(n) time, O(1) space)

The straightforward solution iterates through the array and updates scores exactly as the game rules describe. Maintain two variables representing each player's score or maintain a single running difference. For every element, apply the rule that determines which player gains points and update the totals accordingly. This approach works because the game outcome depends entirely on sequential processing of events, making a simple pass sufficient. Time complexity is O(n) since each move is processed once, and space complexity is O(1) because only a few counters are stored.

Approach 2: Running Difference Simulation (O(n) time, O(1) space)

Instead of storing two separate scores, track the score difference directly. When player A scores, add the value to a running variable; when player B scores, subtract it. This removes the need for multiple variables and simplifies the final calculation since the running value already represents the difference. The algorithm still performs a single pass through the array and applies constant-time updates for each element. Time complexity remains O(n), and space complexity stays O(1).

Approach 3: Structured Game Simulation (O(n) time, O(1) space)

If the game includes turn-based behavior or conditional scoring, you can explicitly simulate each round. Maintain a variable representing the current player and update scores depending on the move type. This method mirrors how the game would run in reality and is easy to extend when rules involve extra conditions such as streak bonuses or skipped turns. The algorithm still processes each event once using simulation logic with constant additional memory. Time complexity is O(n) and space complexity is O(1).

Recommended for interviews: The direct simulation approach is what most interviewers expect. The problem is fundamentally about carefully translating rules into code and iterating through the input once. Mentioning a brute-force interpretation helps demonstrate understanding of the scoring process, but the optimal answer is the single-pass simulation using an array traversal with constant space.