How do you solve Eliminate Maximum Number of Monsters on LeetCode?

Eliminate Maximum Number of Monsters (LeetCode #1921) 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: Monsters must be eliminated in the order of their arrival times to maximize the number eliminated.

What is the brute force solution for Eliminate Maximum Number of Monsters?

The brute force approach for Eliminate Maximum Number of Monsters is Brute Force, with O(n log n) time complexity and O(n) space complexity. The brute-force approach involves calculating the time it takes for each monster to reach the city and then simulating the elimination process minute by minute. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Eliminate Maximum Number of Monsters?

Eliminate Maximum Number of Monsters uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Eliminate Maximum Number of Monsters?

Always clarify the problem constraints and edge cases before jumping into coding. Think about how you can optimize your solution after writing a brute-force version. Explain your thought process clearly while coding, as it shows your understanding.

What are common mistakes when solving Eliminate Maximum Number of Monsters?

Forgetting to sort the arrival times before processing. Not handling the case where the weapon is charged exactly when a monster arrives.

#1921

Eliminate Maximum Number of Monsters

Medium

ArrayGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

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

The optimal solution leverages sorting and a greedy approach to ensure that we eliminate monsters in the order of their arrival times while keeping track of the time taken to eliminate each monster. This approach is efficient and avoids unnecessary calculations.

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Algorithm

3 steps

1Step 1: Calculate the time for each monster to reach the city and store it in an array.
2Step 2: Sort the array of times.
3Step 3: Iterate through the sorted times, and for each monster, check if the current time (number of monsters eliminated) is less than the monster's arrival time. If true, eliminate the monster; otherwise, return the count.

solution.py6 lines

1def eliminateMaximum(dist, speed):
2    times = sorted(dist[i] / speed[i] for i in range(len(dist)))
3    for i in range(len(times)):
4        if i >= times[i]:
5            return i
6    return len(dist)

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Complexity note: The optimal solution also has a time complexity of O(n log n) due to sorting, but it is more efficient in practice because it minimizes unnecessary checks and calculations.

1Monsters must be eliminated in the order of their arrival times to maximize the number eliminated.
2Sorting the arrival times allows for a simple linear pass to determine how many can be eliminated.

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