codeforces1599C.BubbleStrike

题意

Little Johnny Bubbles enjoys spending hours in front of his computer playing video games. His favorite game is Bubble Strike, fast-paced bubble shooting online game for two players.Each game is set in one of the N maps, each having different terrain configuration. First phase of each game decides on which map the game will be played. The game system randomly selects three maps and shows them to the players. Each player must pick one of those three maps to be discarded. The game system then randomly selects one of the maps that were not picked by any of the players and starts the game.Johnny is deeply enthusiastic about the game and wants to spend some time studying maps, thus increasing chances to win games played on those maps. However, he also needs to do his homework, so he does not have time to study all the maps. That is why he asked himself the following question: "What is the minimum number of maps I have to study, so that the probability to play one of those maps is at least P"?Can you help Johnny find the answer for this question? You can assume Johnny&＃39;s opponents do not know him, and they will randomly pick maps.


思路

首先n只有1000
当然肯定是看的地图越多越有把握达到p的概率
所以就是暴力做法
一个一个涂色&＃xff0c;当然可以二分&＃xff0c;这里数剧太小就直接O(3e3)
对于每一局&＃xff0c;如果恰好是一个熟悉的地图都没有&＃xff0c;那么增加的概率必是0
如果恰好认识一个地图&＃xff0c;那么选择另一个不认识的淘汰&＃xff0c;有1/2的概率
如果恰好认识两个地图&＃xff0c;那么选择另一个不认识的淘汰&＃xff0c;必选中熟悉地图
如果三个地图&＃xff0c;必选中熟悉地图
这就像高中的超几何分布吧


AC

#include
using namespace std;
#define ll long long
int n;//1e3
double p;//0~1int C(int x, int t)//Cx^t
{ll ret &＃61; 1;for (int i &＃61; 1; i <&＃61; t; i&＃43;&＃43;)ret *&＃61; x - i &＃43; 1;for (int i &＃61; 1; i <&＃61; t; i&＃43;&＃43;)ret /&＃61; i;return ret;
}int main()
{cin >> n >> p;for (int i &＃61; 0; i <&＃61; n; i&＃43;&＃43;){double ans &＃61; 0;for (int j &＃61; 1; j <&＃61; 3; j&＃43;&＃43;){int res &＃61; C(i, j) * C(n - i, 3 - j);if (j &＃61;&＃61; 1)ans &＃43;&＃61; res * 0.5;if (j >&＃61; 2)ans &＃43;&＃61; res;}ans /&＃61; C(n, 3);if (ans >&＃61; p)return cout << i << endl, 0;}return 0;
}