UVA 10817 - Headmaster's Headache（三进制状压dp）

题目：https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=20&page=show_problem&problem=1758

状态压缩的DP，dp[i][st]表示状态为st考虑后面i个人所有人最小花费，

因为每个科目有三种状态，可以用一个三进制数表示，

状态不是很多，所以可以把预先把每个数的三进制预处理出来，

决策为选和不选。

#include<bits/stdc++.h>
using namespace std;
const int maxs = ;
const int MAXSTA = +;
const int maxn = ;
int base[maxs+],trp[MAXSTA][maxs+];
int dp[maxn][MAXSTA];
int tch[maxn],cost[maxn],sa;
int s,m,n;
const int INF = 0x3fffffff;
void preDeal()
{
    base[] = ;
    for(int i = ; i <= maxs; i++){
        base[i] = *base[i-];
    }
    for(int i = ; i < MAXSTA; i++){
        int x = i, cnt = ;
        while(x){
            trp[i][cnt++] = x%;
            x /= ;
        }
    }
}

int dfs(int i,int st)
{
    if(i == n) return st == sa? :INF;
    int &ans = dp[i][st];
    if(~ans) return ans;
    ans = dfs(i+,st);
    //int nst = st;
    for(int j = ; j < s; j++){
        if(trp[tch[i]][j] && trp[st][j] != ){
            st += base[j];
        }
    }
    ans = min(ans,dfs(i+,st)+cost[i]);
    return ans;
}

int work()
{
    sa = base[s]-;
    int st = ,sum = ;
    for(int i = ; i < m; i++){
        int c; scanf("%d",&c);
        sum += c;
        while(getchar()!='\n'){
            int sub = getchar()-'';
            int t = trp[st][sub] ;
            if(t != ){
                st += base[sub];
            }
        }
    }
    for(int i = ; i < n; i++){
        scanf("%d",cost+i);
        tch[i] = ;
        while(getchar()!='\n'){
            tch[i] += base[getchar()-''];
        }
    }
    memset(dp,-,sizeof(dp));
    return sum + dfs(,st);
}

int main()
{
    //freopen("in.txt","r",stdin);
    preDeal();
    while(scanf("%d%d%d",&s,&m,&n),s){
        printf("%d\n",work());
    }
    return ;
}