ZOJ 3822 Domination The 2014 ACM-ICPC 牡丹江区域赛 概率dp 先算概率,再转成期望
2014-10-12 20:57
387 查看
DominationTime Limit: 8 Seconds Memory Limit: 131072 KB Special JudgeEdward is the headmaster of Marjar University. He is enthusiastic about chess and often plays chess with his friends. What's more, he bought a large decorative chessboard with N rows and M columns.Every day after work, Edward will place a chess piece on a random empty cell. A few days later, he found the chessboard was dominated by the chess pieces. That means there is at least one chess piece in every row. Also, there is at least one chess piece in every column."That's interesting!" Edward said. He wants to know the expectation number of days to make an empty chessboard of N × M dominated. Please write a program to help him.
Input
There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:There are only two integers N and M (1 <= N, M <= 50).Output
For each test case, output the expectation number of days.Any solution with a relative or absolute error of at most 10-8 will be accepted.Sample Input
2 1 3 2 2
Sample Output
3.000000000000 2.666666666667
以前做的期望题都是直接从后往前推,但是这题是要先从前往后算出概率,然后再计算期望。给跪了,思路是别人的。。。
dp数组里没维代表【当前步数】【当前覆盖行数】【当前覆盖列数】
然后注意下当全覆盖后,就不能再转移了。所以dp【i】【n】【m】 是不能再转移给 dp【i+1】【n】【m】的.因当全覆盖的时候已经结束了。
其他的转移都有备注
#include<stdio.h>#include<string.h>double dp[3000][55][55];int main(){ double ans; int t,n,m,tem; scanf("%d",&t); while(t--) { scanf("%d%d",&n,&m); memset(dp,0,sizeof(dp)); dp[0][0][0]=1.0; ans=0; for(int i=1;i<=n*m;i++)//步数 { //printf("第%d步\n",i); for(int j=1;j<=n;j++)//覆盖了几行 { for(int k=1;k<=m;k++)//覆盖了几列 { tem=n*m-i+1; //总数 if(j==n&&k==m)//这就不能再从本来的全覆盖转移过来了, dp[i][j][k]= dp[i-1][j-1][k-1]*((double)(n-(j-1))*(m-(k-1))/tem)//下的那块 行列都没被覆盖过 +dp[i-1][j-1][k]*((double)(n-(j-1))*k/tem)//行没被覆盖 列已经被覆盖 +dp[i-1][j][k-1]*((double)j*(m-(k-1))/tem);//行已经被覆盖 列还没被覆盖 else dp[i][j][k]= dp[i-1][j-1][k-1]*((double)(n-(j-1))*(m-(k-1))/tem)//下的那块 行列都没被覆盖过 +dp[i-1][j-1][k]*((double)(n-(j-1))*k/tem)//行没被覆盖 列已经被覆盖 +dp[i-1][j][k-1]*((double)j*(m-(k-1))/tem)//行已经被覆盖 列还没被覆盖 +dp[i-1][j][k]*((double)(j*k-(i-1))/tem);//被覆盖过的那些点中 还未被覆盖的点 //上面这行 较上面要减去(i-1)是因为这里将要下的地方是行列都被覆盖过的,所以其中的点有(i-1)个已经被覆盖过,要减去 //printf("%.1lf ",dp[i][j][k]); } //puts("\n"); } } for(int i=1;i<=n*m;i++) { ans+=dp[i][m]*i;//i天后 全覆盖的概率 乘上i 就是期望 } printf("%.12lf\n",ans); } return 0;}/*30 100 70100 130 30-100 -70 40*/
相关文章推荐
- [zoj 3822]2014牡丹江区域赛 Domination 概率dp求期望
- ZOJ 3822 Domination 概率DP 2014年ACM_ICPC亚洲区域赛牡丹江现场赛D题
- ZOJ3822 ACM-ICPC 2014 亚洲区域赛牡丹江赛区现场赛D题Domination 概率DP
- zoj 3822 Domination(2014牡丹江区域赛D题) (概率dp)
- ZOJ3822 ACM-ICPC 2014 亚洲区域赛牡丹江赛区现场赛D题Domination 概率DP(两种解法)
- ACM学习历程——ZOJ 3822 Domination (2014牡丹江区域赛 D题)(概率,数学递推)
- ZOJ3819 ACM-ICPC 2014 亚洲区域赛牡丹江赛区现场赛A题 Average Score 签到题
- 2014ACM/ICPC亚洲区域赛牡丹江站现场赛-D ( ZOJ 3822 ) Domonation
- ZOJ-3822-Domination【概率dp】【2014牡丹江赛区】
- 2014牡丹江现场赛A题D题I题(水,概率Dp,水)ZOJ 3819,3822,3827
- 2014 ACM-ICPC亚洲区域赛牡丹江站网络预选赛 C Untrusted Patrol
- zoj 3809 水 2014 ACM牡丹江区域赛网赛
- The 2014 ACM-ICPC Asia Mudanjiang Regional Contest(2014牡丹江区域赛)
- ZOJ 3822 Domination / The 2014 ACM-ICPC Asia Mudanjiang Regional Contest
- hdu 5045 - Contest(2014 ACM/ICPC Asia Regional Shanghai Online )概率dp
- ZOJ3819 ACM-ICPC 2014 亚洲区域赛的比赛现场牡丹江司A称号 Average Score 注册标题
- ZOJ 3822 Domination(概率dp 牡丹江现场赛)
- zoj 3822 Domination 概率dp 2014牡丹江站D题
- 2014ACM/ICPC亚洲区域赛牡丹江站现场赛-A ( ZOJ 3819 ) Average Score
- 2014ACM/ICPC亚洲区域赛牡丹江站现场赛-I ( ZOJ 3827 ) Information Entropy