1921

1921. Eliminate Maximum Number of Monsters (Medium)

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

Companies: Google

Related Topics:
Array, Greedy, Sorting

Similar Questions:

• Minimum Health to Beat Game (Medium)
• Minimum Time to Kill All Monsters (Hard)

Hints:

• Find the amount of time it takes each monster to arrive.
• Find the order in which the monsters will arrive.

Solution 1. Sorting

// OJ: https://leetcode.com/problems/eliminate-maximum-number-of-monsters/
// Author: github.com/lzl124631x
// Time: O(NlogN)
// Space: O(N)
class Solution {
public:
    int eliminateMaximum(vector<int>& dist, vector<int>& speed) {
        vector<int> time;
        int N = dist.size();
        for (int i = 0; i < N; ++i) {
            time.push_back((dist[i] + speed[i] - 1) / speed[i]); // round up the time.
        }
        sort(begin(time), end(time));
        for (int i = 1; i < N; ++i) {
            if (time[i] < i + 1) return i;
        }
        return N;
    }
};