[LOJ] #2360. 「NOIP2016」换教室

期望DP

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cctype>

using namespace std;

inline int rd(){
	int ret=0,f=1;char c;
	while(c=getchar(),!isdigit(c))f=c=='-'?-1:1;
	while(isdigit(c))ret=ret*10+c-'0',c=getchar();
	return ret*f;
}

const int MAXN = 2048;

int t1[MAXN],t2[MAXN];
double p[MAXN],f[MAXN][MAXN][2],mp[305][305];
int n,m,v,e;

void init(){
	memset(f,127,sizeof(f));
	memset(mp,127,sizeof(mp));
}

int main(){
	init();
	n=rd();m=rd();v=rd();e=rd();
	for(int i=1;i<=n;i++)t1[i]=rd();
	for(int i=1;i<=n;i++)t2[i]=rd();
	for(int i=1;i<=n;i++)scanf("%lf",&p[i]);
	int x,y;double w;
	for(int i=1;i<=e;i++){
		x=rd();y=rd();scanf("%lf",&w);
		mp[x][y]=mp[y][x]=min(w,mp[x][y]);
	}
	for(int i=1;i<=v;i++)mp[i][i]=0;//??!!
	for(int k=1;k<=v;k++){
		for(int i=1;i<=v;i++){
			for(int j=1;j<=v;j++){
				mp[i][j]=min(mp[i][j],mp[i][k]+mp[k][j]);
			}
		}
	}
	f[1][0][0]=f[1][1][1]=0;
	for(int i=2;i<=n;i++){
		for(int j=0;j<=m;j++){
			//1
			f[i][j][0]=min(f[i][j][0],min(
			f[i-1][j][0]+mp[t1[i-1]][t1[i]],//上一个不换
			f[i-1][j][1]+p[i-1]*mp[t2[i-1]][t1[i]]+(1.0-p[i-1])*mp[t1[i-1]][t1[i]]));//上一个换
			//2
			if(j==0)continue;
			f[i][j][1]=min(f[i][j][1],min(//当前换
			f[i-1][j-1][0]+p[i]*mp[t1[i-1]][t2[i]]+(1.0-p[i])*mp[t1[i-1]][t1[i]],//上一个不换
			f[i-1][j-1][1]+p[i-1]*p[i]*mp[t2[i-1]][t2[i]]
			+p[i-1]*(1.0-p[i])*mp[t2[i-1]][t1[i]]
			+(1.0-p[i-1])*p[i]*mp[t1[i-1]][t2[i]]
			+(1.0-p[i-1])*(1.0-p[i])*mp[t1[i-1]][t1[i]]));
		}
	}
	double ans=1e9;
	for(int j=0;j<=m;j++){
		ans=min(ans,min(f[n][j][0],f[n][j][1]));
	}
	printf("%.2lf",ans);
	return 0;
}