How do you solve Minimum Number Game on LeetCode?

Minimum Number Game (LeetCode #2974) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Sorting the array simplifies the problem.

What is the time complexity of Minimum Number Game?

The optimal solution for Minimum Number Game runs in O(n log n) time and uses O(n) space. The time complexity is O(n log n) due to the sorting step, while the space complexity is O(n) for storing the result array.

What is the brute force solution for Minimum Number Game?

The brute force approach for Minimum Number Game is Brute Force, with O(n²) time complexity and O(1) space complexity. We can simulate the game by repeatedly finding and removing the minimum elements from the array. This approach is straightforward but inefficient because it requires searching for the minimum element each time. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Number Game?

Minimum Number Game uses the following concepts: Array, Sorting, Heap (Priority Queue), Simulation. The recommended patterns to study are: Sorting, Array Manipulation.

What are the interview tips for Minimum Number Game?

Explain your thought process clearly. Consider edge cases, such as the smallest input size. Practice similar problems to strengthen your understanding.

What are common mistakes when solving Minimum Number Game?

Not sorting the array before processing. Confusing the order of appending elements to arr.

#2974

Minimum Number Game

Easy

ArraySortingHeap (Priority Queue)SimulationSortingArray Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

Instead of simulating the game step by step, we can sort the array first and then rearrange the elements based on the game rules. This is efficient because sorting allows us to easily access the minimum elements in the correct order.

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Algorithm

4 steps

1Step 1: Sort the nums array in ascending order.
2Step 2: Create an empty array arr to store the results.
3Step 3: Iterate through the sorted array, taking elements in pairs: first take the second element (Bob's turn), then take the first element (Alice's turn), and append them to arr.
4Step 4: Return the resulting array arr.

solution.py7 lines

1def minNumberGame(nums):
2    nums.sort()
3    arr = []
4    for i in range(0, len(nums), 2):
5        arr.append(nums[i + 1])
6        arr.append(nums[i])
7    return arr

ℹ

Complexity note: The time complexity is O(n log n) due to the sorting step, while the space complexity is O(n) for storing the result array.

1Sorting the array simplifies the problem.
2Understanding the order of operations is crucial.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.