out ima def 參考 immediate col test case esc only

Problem Description A murder happened in the hotel. As the best detective in the town, you should examine all the N rooms of the hotel immediately. However, all the doors of the rooms are locked, and the keys are just locked in the rooms, what a trap! You know that there is exactly one key in each room, and all the possible distributions are of equal possibility. For example, if N = 3, there are 6 possible distributions, the possibility of each is 1/6. For convenience, we number the rooms from 1 to N, and the key for Room 1 is numbered Key 1, the key for Room 2 is Key 2, etc.
To examine all the rooms, you have to destroy some doors by force. But you don’t want to destroy too many, so you take the following strategy: At first, you have no keys in hand, so you randomly destroy a locked door, get into the room, examine it and fetch the key in it. Then maybe you can open another room with the new key, examine it and get the second key. Repeat this until you can’t open any new rooms. If there are still rooms un-examined, you have to randomly pick another unopened door to destroy by force, then repeat the procedure above, until all the rooms are examined.
Now you are only allowed to destroy at most K doors by force. What’s more, there lives a Very Important Person in Room 1. You are not allowed to destroy the doors of Room 1, that is, the only way to examine Room 1 is opening it with the corresponding key. You want to know what is the possibility of that you can examine all the rooms finally.

Input The first line of the input contains an integer T (T ≤ 200), indicating the number of test cases. Then T cases follow. Each case contains a line with two numbers N and K. (1 < N ≤ 20, 1 ≤ K < N)

Output Output one line for each case, indicating the corresponding possibility. Four digits after decimal point are preserved by rounding. 參考：http://blog.csdn.net/queuelovestack/article/details/47970827 鑰匙和門的關系是類似環狀的，打開一個門之後，該環內的所有房間都可以進入，怎麽說呢，就拿Hint裏的#6來舉例，Room1 Room2 Room3是在一個環當中的，假設我破壞了Room3，那麽我取出Room3內的鑰匙Key2就可以打開Room2，而Room2裏有鑰匙Key1，那我們又可以打開Room1。 第一類斯特林數可以求解把包含n個元素的集合分成k個環排列的方法數

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <bitset>
using namespace std;
typedef long long LL;
#define MOD 1000000007
LL fac[25],s[25][25],n,k,T;
int main(){
  // freopen("test.in","r",stdin);
  cin >> T;
  fac[
 
1] = 1; s[0][0] = 0; s[1][1] = 1; s[1][0] = 0;
  for (int i=2;i<=21;i++){
    fac[i] = fac[i-1] * i;
    s[i][0] = 0;
    for (int j=1;j<=i;j++){
      s[i][j] = s[i-1][j-1] + (i-1) * s[i-1][j];
    }
  }
  for (int i=1;i<=T;i++){
    cin >> n >> k;
    LL ans = 0;
    for (int j=1;j<=k;j++){
      ans += s[n][j] - s[n-1][j-1];
    }
    double anss = ans * 1.0;
    printf("%.4lf\n",anss/fac[n]);
  }
  return 0;
}

View Code

HDU 3625 Examining the Rooms