1921 Eliminate Maximum Number of Monsters - Medium

Problem:

You are playing a video game where you are defending your city from a group of n monsters. You are given a 0-indexed integer array dist of size n, where dist[i] is the initial distance in kilometers of the ith monster from the city.

The monsters walk toward the city at a constant speed. The speed of each monster is given to you in an integer array speed of size n, where speed[i] is the speed of the ith monster in kilometers per minute.

You have a weapon that, once fully charged, can eliminate a single monster. However, the weapon takes one minute to charge. The weapon is fully charged at the very start.

You lose when any monster reaches your city. If a monster reaches the city at the exact moment the weapon is fully charged, it counts as a loss, and the game ends before you can use your weapon.

Return the maximum number of monsters that you can eliminate before you lose, or n if you can eliminate all the monsters before they reach the city.

Example 1:

Input: dist = [1,3,4], speed = [1,1,1] Output: 3 Explanation: In the beginning, the distances of the monsters are [1,3,4]. You eliminate the first monster. After a minute, the distances of the monsters are [X,2,3]. You eliminate the second monster. After a minute, the distances of the monsters are [X,X,2]. You eliminate the thrid monster. All 3 monsters can be eliminated.

Example 2:

Input: dist = [1,1,2,3], speed = [1,1,1,1] Output: 1 Explanation: In the beginning, the distances of the monsters are [1,1,2,3]. You eliminate the first monster. After a minute, the distances of the monsters are [X,0,1,2], so you lose. You can only eliminate 1 monster.

Example 3:

Input: dist = [3,2,4], speed = [5,3,2] Output: 1 Explanation: In the beginning, the distances of the monsters are [3,2,4]. You eliminate the first monster. After a minute, the distances of the monsters are [X,0,2], so you lose. You can only eliminate 1 monster.

Constraints:

• n == dist.length == speed.length
• 1 <= n <= 105
• 1 <= dist[i], speed[i] <= 105

Problem Analysis:

• Calculate the minimum time it takes for each element to reach its destination given its speed and distance.
• Sort the minimum reach times in ascending order.
• Iterate through the sorted times and keep track of how many elements can be eliminated based on the constraints.
• O(nlogn) time complexity

Solutions:

class Solution:
    def eliminateMaximum(self, dist: List[int], speed: List[int]) -> int:
        minReach = [math.ceil(d / s) for d, s in zip(dist, speed)]
        
        minReach.sort()
        res = 0

        for i, m in enumerate(minReach):
            if i >= m:
                break  
            res += 1
        
        return res

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