BZOJ 2424: [HAOI2010]订货 费用流

2424: [HAOI2010]订货

Time Limit: 1 Sec

Memory Limit: 256 MB

题目连接

http://www.lydsy.com/JudgeOnline/problem.php?id=2424

Description

某公司估计市场在第i个月对某产品的需求量为Ui，已知在第i月该产品的订货单价为di，上个月月底未销完的单位产品要付存贮费用m，假定第一月月初的库存量为零，第n月月底的库存量也为零，问如何安排这n个月订购计划，才能使成本最低？每月月初订购，订购后产品立即到货，进库并供应市场，于当月被售掉则不必付存贮费。假设仓库容量为S。

Input

第1行：n, m, S (0<=n<=50, 0<=m<=10, 0<=S<=10000)

第2行：U1 , U2 , ... , Ui , ... , Un (0<=Ui<=10000)

第3行：d1 , d2 , ..., di , ... , dn (0<=di<=100)

Output

只有1行，一个整数，代表最低成本

Sample Input

3 1 1000
2 4 8
1 2 4

Sample Output

34

HINT

题意

题解：

费用流，S--月--T

|

　　　　  下个月

代码：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <cmath>
using namespace std;
const int MAXN = 10000;
const int MAXM = 100000;
const int INF = 0x3f3f3f3f;
struct Edge
{
    int to, next, cap, flow, cost;
    int x, y;
} edge[MAXM],HH[MAXN],MM[MAXN];
int head[MAXN],tol;
int pre[MAXN],dis[MAXN];
bool vis[MAXN];
int N, M;
char map[MAXN][MAXN];
void init()
{
    N = MAXN;
    tol = 0;
    memset(head, -1, sizeof(head));
}
void addedge(int u, int v, int cap, int cost)//左端点，右端点，容量，花费
{
    edge[tol]. to = v;
    edge[tol]. cap = cap;
    edge[tol]. cost = cost;
    edge[tol]. flow = 0;
    edge[tol]. next = head[u];
    head[u] = tol++;
    edge[tol]. to = u;
    edge[tol]. cap = 0;
    edge[tol]. cost = -cost;
    edge[tol]. flow = 0;
    edge[tol]. next = head[v];
    head[v] = tol++;
}
bool spfa(int s, int t)
{
    queue<int>q;
    for(int i = 0; i < N; i++)
    {
        dis[i] = INF;
        vis[i] = false;
        pre[i] = -1;
    }
    dis[s] = 0;
    vis[s] = true;
    q.push(s);
    while(!q.empty())
    {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for(int i = head[u]; i != -1; i = edge[i]. next)
        {
            int v = edge[i]. to;
            if(edge[i]. cap > edge[i]. flow &&
                    dis[v] > dis[u] + edge[i]. cost )
            {
                dis[v] = dis[u] + edge[i]. cost;
                pre[v] = i;
                if(!vis[v])
                {
                    vis[v] = true;
                    q.push(v);
                }
            }
        }
    }
    if(pre[t] == -1) return false;
    else return true;
}
//返回的是最大流， cost存的是最小费用
int minCostMaxflow(int s, int t, int &cost)
{
    int flow = 0;
    cost = 0;
    while(spfa(s,t))
    {
        int Min = INF;
        for(int i = pre[t]; i != -1; i = pre[edge[i^1]. to])
        {
            if(Min > edge[i]. cap - edge[i]. flow)
                Min = edge[i]. cap - edge[i]. flow;
        }
        for(int i = pre[t]; i != -1; i = pre[edge[i^1]. to])
        {
            edge[i]. flow += Min;
            edge[i^1]. flow -= Min;
            cost += edge[i]. cost * Min;
        }
        flow += Min;
    }
    return flow;
}

int main()
{
    int n, m, ss;
    scanf("%d%d%d",&n,&m,&ss);
    int ch = 0, cm = 0;
    init();//注意
    int beg = 0;//超级起点
    int end = 3000;//超级汇点
    for(int i=1;i<=n;i++)
    {
        int x;scanf("%d",&x);
        addedge(i,end,x,0);
    }
    for(int i=1;i<=n;i++)
    {
        int x;scanf("%d",&x);
        addedge(0,i,9999999,x);
    }
    for(int i=1;i<n;i++)addedge(i,i+1,ss,m);
    int ans = 0;
    minCostMaxflow(beg,end,ans);
    printf("%d\n",ans);
}