LOOPS
http://acm.hdu.edu.cn/showproblem.php?pid=3853
Time Limit: 15000/5000 MS (Java/Others) Memory Limit: 125536/65536 K (Java/Others)
Total Submission(s): 6292 Accepted Submission(s):
2516
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.
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
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
Source
Recommend
题意：r*c的网格，人在左上角，出口在右下角
人有三种选择，不走，向下走，向右走，每种选择都有一定的概率，每种选择都会花费2魔力值
问到达出口的期望魔力值
dp[i][j]表示从（i，j）到出口的期望值
dp[i][j]=dp[i][j]*p1[i][j]+dp[i][j+1]*p2[i][j]+dp[i+1][j]*p3[i][j]+2
将dp[i][j]*p1[i][j]移到左边，得到状态转移方程
dp[i][j]=(dp[i][j+1]*p[2][i][j]+dp[i+1][j]*p[3][i][j]+2)/(1-p[1][i][j]);
#include<cstdio> #include<cstring> #define N 1002 using namespace std; double p[4][N][N],dp[N][N]; int main() { int n,m; while(scanf("%d%d",&n,&m)!=EOF) { memset(dp,0,sizeof(dp)); for(int i=1;i<=n;i++) for(int j=1;j<=m;j++) for(int k=1;k<=3;k++) scanf("%lf",&p[k][i][j]); for(int i=n;i;i--) for(int j=m;j;j--) { if(p[1][i][j]==1) continue; dp[i][j]=(dp[i][j+1]*p[2][i][j]+dp[i+1][j]*p[3][i][j]+2)/(1-p[1][i][j]); } printf("%.3lf ",dp[1][1]); } }