BZOJ 2424 DP OR 费用流

思路：

1.DP

f[i][j]表示第i个月的月底 还剩j的容量

转移还是相对比较好想的……

f[i][j+1]=min(f[i][j+1],f[i][j]+d[i]);
if(j>=u[i+1])f[i+1][j-u[i+1]]=min(f[i+1][j-u[i+1]],f[i][j]+m*j);
else f[i+1][0]=min(f[i+1][0],f[i][j]+d[i+1]*(u[i+1]-j)+m*j);

//By SiriusRen
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int n,m,s,u[55],d[55],f[55][10005];
int main(){
    scanf("%d%d%d",&n,&m,&s);
    for(int i=1;i<=n;i++)scanf("%d",&u[i]);
    for(int i=1;i<=n;i++)scanf("%d",&d[i]);
    memset(f,0x3f,sizeof(f));
    f[1][0]=d[1]*u[1];
    for(int i=1;i<=n;i++)
        for(int j=0;j<=s;j++){
            f[i][j+1]=min(f[i][j+1],f[i][j]+d[i]);
            if(j>=u[i+1])f[i+1][j-u[i+1]]=min(f[i+1][j-u[i+1]],f[i][j]+m*j);
            else f[i+1][0]=min(f[i+1][0],f[i][j]+d[i+1]*(u[i+1]-j)+m*j);
        }
    printf("%d\n",f[n][0]);
}

2.

费用流 裸的建图吧

源->i 流量inf 费用d[i]

i->汇 流量u[i] 费用0

i->i+1 （i!=n） 流量S 费用m

跑一哈 搞定~

//By SiriusRen
#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;
#define N 55
#define M 55555
#define inf 0x3f3f3f3f
#define mem(x,y) memset(x,y,sizeof(x))
int n,m,S,xx,T,edge[M],v[M],cost[M],first[N],nxt[M],vis[N],minn[N],d[N],with[N],tot,ans;
void Add(int x,int y,int C,int E){edge[tot]=E,cost[tot]=C,v[tot]=y,nxt[tot]=first[x],first[x]=tot++;}
void add(int x,int y,int C,int E){Add(x,y,C,E),Add(y,x,-C,0);}
bool tell(){
    mem(vis,0),mem(with,0),mem(d,0x3f),mem(minn,0x3f);
    queue<int>q;q.push(0),d[0]=0;
    while(!q.empty()){
        int t=q.front();q.pop();vis[t]=0;
        for(int i=first[t];~i;i=nxt[i])
            if(d[v[i]]>d[t]+cost[i]&&edge[i]){
                with[v[i]]=i,d[v[i]]=d[t]+cost[i],minn[v[i]]=min(minn[t],edge[i]);
                if(!vis[v[i]])vis[v[i]]=1,q.push(v[i]);
            }
    }return d[T]!=0x3f3f3f3f;
}
int zeng(){
    for(int i=T;i;i=v[with[i]^1])
        edge[with[i]]-=minn[T],edge[with[i]^1]+=minn[T];
    return minn[T]*d[T];
}
int main(){
    mem(first,-1);
    scanf("%d%d%d",&n,&m,&S),T=n+1;
    for(int i=1;i<=n;i++)scanf("%d",&xx),add(i,T,0,xx);
    for(int i=1;i<=n;i++){
        scanf("%d",&xx),add(0,i,xx,inf);
        if(i!=n)add(i,i+1,m,S);
    }
    while(tell())ans+=zeng();
    printf("%d\n",ans);
}

这道题 费用流还是要稍微快一点儿的……