hdoj 4307 Matrix 【最大流 求解矩阵乘最值】【经典构图！】

1
3
1 2 1
3 1 0
1 2 3
2 3 7

2
HintFor sample, A=[1, 1, 0] or A=[1, 1, 1] would get the maximum D.

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
#define MAXN 1010
#define MAXM 3000000
#define INF 0x3f3f3f3f
using namespace std;
struct Edge
{
    int from, to, cap, flow, next;
};
Edge edge[MAXM];
int head[MAXN], edgenum;
int dist[MAXN], cur[MAXN];
bool vis[MAXN];
int N;
void init()
{
    edgenum = 0;
    memset(head, -1, sizeof(head));
}
void addEdge(int u, int v, int w)
{
    Edge E1 = {u, v, w, 0, head[u]};
    edge[edgenum] = E1;
    head[u] = edgenum++;
    Edge E2 = {v, u, 0, 0, head[v]};
    edge[edgenum] = E2;
    head[v] = edgenum++;
}
int sum;//记录矩阵B中所有元素之和
int source, sink;
void getMap()
{
    init();
    scanf("%d", &N);
    int a;
    sum = 0;
    source = 0, sink = N+1;
    //B矩阵 构图
    for(int i = 1; i <= N; i++)
    {
        int sumcul = 0;
        for(int j = 1; j <= N; j++)
        {
            scanf("%d", &a);
            sumcul += a;
            sum += a;
            addEdge(i, j, a);
        }
        addEdge(source, i, sumcul);
    }
    //C矩阵 构图
    for(int i = 1; i <= N; i++)
    {
        scanf("%d", &a);
        addEdge(i, sink, a);
    }
}
bool BFS(int s, int t)
{
    queue<int> Q;
    memset(dist, -1, sizeof(dist));
    memset(vis, false, sizeof(vis));
    dist[s] = 0;
    vis[s] = true;
    Q.push(s);
    while(!Q.empty())
    {
        int u = Q.front();
        Q.pop();
        for(int i = head[u]; i != -1; i = edge[i].next)
        {
            Edge E = edge[i];
            if(!vis[E.to] && E.cap > E.flow)
            {
                dist[E.to] = dist[u] + 1;
                if(E.to == t) return true;
                vis[E.to] = true;
                Q.push(E.to);
            }
        }
    }
    return false;
}
int DFS(int x, int a, int t)
{
    if(x == t || a == 0) return a;
    int flow = 0, f;
    for(int &i = cur[x]; i != -1; i = edge[i].next)
    {
        Edge &E = edge[i];
        if(dist[E.to] == dist[x] + 1 && (f = DFS(E.to, min(a, E.cap-E.flow), t)) > 0)
        {
            edge[i].flow += f;
            edge[i^1].flow -= f;
            flow += f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}
int Maxflow(int s, int t)
{
    int flow = 0;
    while(BFS(s, t))
    {
        memcpy(cur, head, sizeof(head));
        flow += DFS(s, INF, t);
    }
    return flow;
}
int main()
{
    int t;
    scanf("%d", &t);
    while(t--)
    {
        getMap();
        printf("%d\n", sum - Maxflow(source, sink));
    }
    return 0;
}