hdu 4865 Peter's Hobby（概率dp）

#include <stdio.h>
#include <iostream>
#include <map>
#include <set>
#include <stack>
#include <vector>
#include <math.h>
#include <string.h>
#include <queue>
#include <string>
#include <stdlib.h>
#include <algorithm>
#define LL long long
#define _LL __int64
#define eps 1e-12
#define PI acos(-1.0)
using namespace std;

const int INF = 0x3f3f3f3f;
double wl[3][4] = {
{0.6,0.2,0.15,0.05},
{0.25,0.3,0.2,0.25},
{0.05,0.10,0.35,0.50}};

double ww[3][3] = {
{0.5,0.375,0.125},
{0.25,0.125,0.625},
{0.25,0.375,0.375}
};

double st[3] = {0.63,0.17,0.2};
int n;
char s[10];
int a[55];
double f[55][5];
double dp[55][5];
int pre[55][5];

stack <int> sta;

int init(char s[])
{
if(strcmp(s,"Dry") == 0)
return 0;
if(strcmp(s,"Dryish") == 0)
return 1;
if(strcmp(s,"Damp") == 0)
return 2;
if(strcmp(s,"Soggy") == 0)
return 3;
}

void To()
{
for(int i = 0; i < 3; i++)
{
for(int j = 0; j < 3; j++)
ww[i][j] = log(ww[i][j]);
}
for(int i = 0; i < 3; i++)
st[i] = log(st[i]);
}

int main()
{
To();
int test;
scanf("%d",&test);
for(int item = 1; item <= test; item++)
{
scanf("%d",&n);
memset(pre,-1,sizeof(pre));
memset(f,0,sizeof(f));
for(int i = 1; i <= n; i++)
{
scanf("%s",s);
a[i] = init(s);
}

for(int i = 1; i <= n; i++)
{
//对于当前天的叶子状态是固定的。如今的f[i][j]表示第i天在叶子固定的条件下天气为j的概率。
//所以f[i][j]为每种天气占总天气的比值
double t = 0;
for(int j = 0; j < 3; j++)
{
f[i][j] = wl[j][a[i]];
t += wl[j][a[i]];
}
for(int j = 0; j < 3; j++)
f[i][j] /= t;
}

for(int i = 1; i <= n; i++)
{
for(int j = 0; j < 3; j++)
f[i][j] = log(f[i][j]);
}
memset(dp,-INF,sizeof(dp));
for(int j = 0; j < 3; j++)
dp[1][j] = st[j] + f[1][j];

for(int i = 2; i <= n; i++)
{
for(int j = 0; j < 3; j++)
{
for(int k = 0; k < 3; k++)
{
double t = dp[i-1][k] + ww[k][j] + f[i][j];
if(dp[i][j] < t)
{
dp[i][j] = t;
pre[i][j] = k;
}
}
}
}
int p = n;
int c;
double Max = -INF;

for(int j = 0; j < 3; j++)
{
if(dp
[j] > Max)
{
Max = dp
[j];
c = j;
}
}

while(!sta.empty()) sta.pop();

sta.push(c);
while(pre[p][c] != -1)
{
sta.push(pre[p][c]);
c = pre[p][c];
p--;
}

printf("Case #%d:\n",item);
while(!sta.empty())
{
if(sta.top() == 0)
printf("Sunny\n");
if(sta.top() == 1)
printf("Cloudy\n");
if(sta.top() == 2)
printf("Rainy\n");
sta.pop();
}
}
return 0;
}