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 meters 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 meters per minute.
The monsters start moving at minute 0. You have a weapon that you can choose to use at the start of every minute, including minute 0. You cannot use the weapon in the middle of a minute. The weapon can eliminate any monster that is still alive. You lose when any monster reaches your city. If a monster reaches the city exactly at the start of a minute, it counts as a loss, and the game ends before you can use your weapon in that minute.
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: At the start of minute 0, the distances of the monsters are [1,3,4], you eliminate the first monster. At the start of minute 1, the distances of the monsters are [X,2,3], you don't do anything. At the start of minute 2, the distances of the monsters are [X,1,2], you eliminate the second monster. At the start of minute 3, the distances of the monsters are [X,X,1], you eliminate the third monster. All 3 monsters can be eliminated.
Example 2:
Input: dist = [1,1,2,3], speed = [1,1,1,1] Output: 1 Explanation: At the start of minute 0, the distances of the monsters are [1,1,2,3], you eliminate the first monster. At the start of minute 1, 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: At the start of minute 0, the distances of the monsters are [3,2,4], you eliminate the first monster. At the start of minute 1, the distances of the monsters are [X,0,2], so you lose. You can only eliminate 1 monster.
Constraints:
n == dist.length == speed.length1 <= n <= 1051 <= dist[i], speed[i] <= 105
// 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]);
}
sort(begin(time), end(time));
for (int i = 1; i < N; ++i) {
if (time[i] < i + 1) return i;
}
return N;
}
};