Minimum Number Game

Minimum Number Game

1. What is this problem about?

The Minimum Number Game coding problem presents a playful scenario involving two players, Alice and Bob, who are interacting with an array of numbers. In each round, Alice removes the smallest element, followed by Bob removing the next smallest. They then append these elements to a new "result" array, but in reverse order: Bob's element goes first, then Alice's. The task is to return the final state of this result array after all elements have been processed.

2. Why is this asked in interviews?

Companies like Meta, Amazon, and Google use the Minimum Number Game interview question to test a candidate's grasp of basic data structures and their ability to follow multi-step simulation rules. While the logic is straightforward, it requires careful synchronization between the "removal" phase and the "insertion" phase. It's an excellent way to see if a developer can write clean, readable code for a process that involves sorting or priority-based selection.

3. Algorithmic pattern used

This problem primarily utilizes the Array, Sorting, Heap (Priority Queue) interview pattern. The most efficient way to solve it is usually to sort the input array first. Once sorted, the elements are already in the order Alice and Bob would pick them. By iterating through the sorted array in steps of two, you can easily swap the positions of each pair to simulate the game's "Bob first" rule. Alternatively, a Min-Heap can be used to repeatedly extract the two smallest elements if the array is constantly changing, though sorting is usually sufficient here.

4. Example explanation

Suppose we have an input array: [5, 4, 2, 3]. First, we sort it: [2, 3, 4, 5]. Round 1: Alice picks 2 (smallest), Bob picks 3 (next smallest). They append them in reverse: result = [3, 2]. Round 2: Alice picks 4, Bob picks 5. They append them in reverse: result = [3, 2, 5, 4]. Final Output: [3, 2, 5, 4].

5. Common mistakes candidates make

The most frequent error is misinterpreting the "reverse order" rule and simply returning the sorted array. Another mistake is using an inefficient method to find the minimum in each round (like searching the whole array repeatedly), which leads to an O(n^2) solution when O(n log n) via sorting is expected. Candidates might also struggle with index management when skipping by two in a loop.

6. Interview preparation tip

For "Easy" difficulty problems like this, focus on code clarity and edge case handling. Ensure your solution handles empty arrays or arrays with an odd number of elements gracefully (though the problem usually guarantees an even length). Visualizing the process as "swapping adjacent elements in a sorted list" is a great mental shortcut that makes the implementation much simpler.