LOOPS(HDU 3853)

最新推荐文章于 2020-01-20 11:33:56 发布

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最新推荐文章于 2020-01-20 11:33:56 发布

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原文链接：http://www.cnblogs.com/sunus/p/4446023.html

本文介绍了一个名为LOOPS的迷宫问题，该问题要求计算魔法少女Homura从迷宫逃脱所需的平均魔法能量。通过使用概率动态规划的方法，文章提供了一种有效的解决方案，并给出了具体的代码实现。

LOOPS

Time Limit: 15000/5000 MS (Java/Others) Memory Limit: 125536/65536 K (Java/Others)
Total Submission(s): 3163 Accepted Submission(s): 1279

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

Source

2011 Invitational Contest Host by BUPT

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chenyongfu

比较简单的概率dp

简单求期望，常规逆推

d[i][j]表示距出口的期望能量消耗

d[i][j] = p1 * d[i + 1][j] + p2 * d[i][j + 1] + p3 * d[i][j] + 2;

#include <cstdio>
#include <iostream>
#include <sstream>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>
using namespace std;
#define ll long long
#define _cle(m, a) memset(m, a, sizeof(m))
#define repu(i, a, b) for(int i = a; i < b; i++)
#define repd(i, a, b) for(int i = b; i >= a; i--)
#define MAXN 1005

struct P{
  double o, d, r;
}ma[MAXN][MAXN];
double d[MAXN][MAXN];
int main()
{
    int r, c;
    while(~scanf("%d%d", &r, &c))
    {
        repu(i, 1, r + 1)
           repu(j, 1, c + 1) scanf("%lf%lf%lf", &ma[i][j].o, &ma[i][j].r, &ma[i][j].d);

        repd(i, 1, r) repd(j, 1, c) {
            if(i == r && j == c) d[r][c] = 0.0;
            else {
                if(ma[i][j].o != 1.0)
                d[i][j] = (d[i + 1][j] * ma[i][j].d + d[i][j + 1] * ma[i][j].r + 2.0) / (1.0 - ma[i][j].o);
                else d[i][j] += 2.0;
            }
          }
        printf("%.3lf\n", d[1][1]);
    }
    return 0;
}