HDU 3853 LOOPS 概率第一题 水题，还是被坑了很久

Problem Description

Akemi Homura is a Mahou Shoujo (Puella Magi/Magical Girl).

Homura wants to help her friend Madoka save the world. But because of the plot of the Boss Incubator, she is trapped in a labyrinth called LOOPS.

The planform of the LOOPS is a rectangle of R*C grids. There is a portal in each grid except the exit grid. It costs Homura 2 magic power to use a portal once. The portal in a grid G(r, c) will send Homura to the grid below G (grid(r+1, c)), the grid on the right of G (grid(r, c+1)), or even G itself at respective probability (How evil the Boss Incubator is)!
At the beginning Homura is in the top left corner of the LOOPS ((1, 1)), and the exit of the labyrinth is in the bottom right corner ((R, C)). Given the probability of transmissions of each portal, your task is help poor Homura calculate the EXPECT magic power she need to escape from the LOOPS.

 

 

Input

The first line contains two integers R and C (2 <= R, C <= 1000).

The following R lines, each contains C*3 real numbers, at 2 decimal places. Every three numbers make a group. The first, second and third number of the cth group of line r represent the probability of transportation to grid (r, c), grid (r, c+1), grid (r+1, c) of the portal in grid (r, c) respectively. Two groups of numbers are separated by 4 spaces.

It is ensured that the sum of three numbers in each group is 1, and the second numbers of the rightmost groups are 0 (as there are no grids on the right of them) while the third numbers of the downmost groups are 0 (as there are no grids below them).

You may ignore the last three numbers of the input data. They are printed just for looking neat.

The answer is ensured no greater than 1000000.

Terminal at EOF

 

 

Output

A real number at 3 decimal places (round to), representing the expect magic power Homura need to escape from the LOOPS.

 

 

Sample Input

2 2

0.00 0.50 0.50     0.50 0.00 0.50

0.50 0.50 0.00     1.00 0.00 0.00

 

 

Sample Output

6.000

 

 

 

 

就是推公式，使用全期望公式

 

 

注意：

 

double  输入用%lf， 输出用%f

 

记得提交的时候去掉freopen语句

 

数学式子的分母不能为0

 

递推的时候，注意处理起点

 

 

 

 

 

 

 1 #include<cstdio>

 2 #include<algorithm>

 3 #include<cstring>

 4 

 5 using namespace std;

 6 

 7 const int maxn=1005;

 8 

 9 double dp[maxn][maxn];

10 double loop_p[maxn][maxn];

11 double down_p[maxn][maxn];

12 double right_p[maxn][maxn];

13 

14 int main()

15 {

16     //freopen("in.txt","r",stdin);

17 

18     int r,c;

19 

20     while(scanf("%d%d",&r,&c)!=EOF)

21     {

22         for(int i=1;i<=r;i++)

23         {

24             for(int j=1;j<=c;j++)

25             {

26                 scanf("%lf",&loop_p[i][j]);

27                 scanf("%lf",&right_p[i][j]);

28                 scanf("%lf",&down_p[i][j]);

29             }

30         }

31 

32         for(int i=0;i<=r+1;i++)

33             for(int j=0;j<=c+1;j++)

34                 dp[i][j]=0.0;

35 

36         for(int i=r;i>0;i--)

37         {

38             for(int j=c;j>0;j--)

39             {

40 

41                 //忘了这一步，样例一直过不了

42                 if(i==r&&c==j)

43                     continue;

44 

45                 //式子分母不能为0

46                 if(loop_p[i][j]==1.0)

47                     continue;

48 

49                 dp[i][j]=(dp[i+1][j]*down_p[i][j]+

50                 dp[i][j+1]*right_p[i][j]+2.0)/(1.0-loop_p[i][j]);

51             }

52         }

53 

54         printf("%.3f\n",dp[1][1]);

55     }

56 

57     return 0;

58 }

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