线性规划与网络流24题の17 运输问题（最小费用最大流、最大费用最大流）

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有m个仓库，n个商店，每个仓库有一定的货物ai，每个商店需要供货bi，仓库i到商店j的运输费用是cij。求运输的最小费用和最大费用。

http://wikioi.com/problem/1914/

分别求最小费用最大流和最大费用最大流

//#pragma comment(linker,"/STACK:1024000000,1024000000")#include <map>#include <set>#include <cmath>#include <queue>#include <stack>#include <cstdio>#include <string>#include <vector>#include <cstring>#include <iostream>#include <algorithm>using namespace std;typedef double DB;typedef long long ll;typedef pair<int, int> PII;#define pb push_back#define MP make_pair#define lson l, m, rt << 1#define rson m + 1, r, rt << 1 | 1const DB eps = 1e-6;const int inf = ~0U>>1;const ll INF = 0x3f3f3f3f3f3f3f3f;const int mod = 1000000007;const int maxn = 1000 + 10;/*mincost 为最小费用。若要求最大费用，加边时将费用取反，最后-mincost是最大费用*////先调用init，然后while(Find());const int maxv = 1000 + 10;///顶点数const int maxe = 1000000 + 10;///边数struct node{    int v, w, cap, next; ///cap = 容量, w = 费用}edge[maxe];struct fnode{    int e, cap, w;///上一条边，容量，费用}fn[maxv];int head[maxv], cnt, st, ed, maxflow, mincost;bool vis[maxv];void addedge(int u, int v, int cap, int w){    edge[cnt].v = v; edge[cnt].w = w; edge[cnt].cap = cap; edge[cnt].next = head[u]; head[u] = cnt++;    edge[cnt].v = u; edge[cnt].w = -w; edge[cnt].cap = 0; edge[cnt].next = head[v]; head[v] = cnt++;//    printf("u:%d, v:%d, cap:%d, w:%d, cnt:%d\n", u, v, cap, w, cnt - 1);}bool Find(){///找最短路    memset(vis, false, sizeof(vis));    for(int i=st; i<=ed; i++) fn[i].w = inf;    fn[st].w = 0;    vis[st] = 1; fn[st].cap = inf;    queue<int> Q;    Q.push(st);    while(!Q.empty()){        int now = Q.front(); Q.pop();        vis[now] = 0;        for(int i=head[now]; ~i; i=edge[i].next){            int k = edge[i].v;            if(edge[i].cap && fn[now].w + edge[i].w < fn[k].w){                fn[k].w = fn[now].w + edge[i].w;                fn[k].cap = min(fn[now].cap, edge[i].cap);                fn[k].e = i;                if(!vis[k]){                    vis[k] = 1; Q.push(k);                }            }        }    }    if(fn[ed].w == inf) return 0;    mincost += fn[ed].cap * fn[ed].w;    maxflow += fn[ed].cap;    int i = ed;    while(i != st){        edge[fn[i].e].cap -= fn[ed].cap;        edge[fn[i].e ^ 1].cap += fn[ed].cap;        i = edge[fn[i].e ^ 1].v;    }    return 1;}void init(int source, int sink){    memset(head, -1, sizeof(head)); cnt = 0;    st = source; ed = sink;///源点和汇点    maxflow = mincost = 0;///最大流和最小费用}int n, m, a[maxn], b[maxn], c[maxn][maxn];int main(){    scanf("%d%d", &m, &n);    init(0, m + n + 1);    for(int i=1; i<=m; i++){        scanf("%d", &a[i]);        addedge(st, i, a[i], 0);    }    for(int i=1; i<=n; i++){        scanf("%d", &b[i]);        addedge(i + m, ed, b[i], 0);    }    for(int i=1; i<=m; i++)    for(int j=1; j<=n; j++){        scanf("%d", &c[i][j]);        addedge(i, j + m, inf, c[i][j]);    }    while(Find());    printf("%d\n", mincost);    init(0, n + m + 1);    for(int i=1; i<=m; i++)        addedge(st, i, a[i], 0);    for(int j=1; j<=n; j++)        addedge(j + m, ed, b[j], 0);    for(int i=1; i<=m; i++)    for(int j=1; j<=n; j++)        addedge(i, j + m, inf, -c[i][j]);    while(Find());    printf("%d\n", -mincost);    return 0;}

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