hdoj 1853 Cyclic Tour 【最小费用最大流 or KM算法】【构图后可以判断图中是否存在哈密顿环】

6 9
1 2 5
2 3 5
3 1 10
3 4 12
4 1 8
4 6 11
5 4 7
5 6 9
6 5 4
6 5
1 2 1
2 3 1
3 4 1
4 5 1
5 6 1

42
-1

Hint In the first sample, there are two cycles, (1->2->3->1) and (6->5->4->6) whose length is 20 + 22 = 42.

#include <cstdio>
#include <cstring>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
#define MAXN 200+10
#define MAXM 30000+10
#define INF 0x3f3f3f3f
using namespace std;
struct Edge
{
    int from, to, cap, flow, cost, next;
};
Edge edge[MAXM];
int head[MAXN], edgenum;
int pre[MAXN], dist[MAXN];
bool vis[MAXN];
int N, M;
int source, sink;//超级源点 超级汇点
void init()
{
    edgenum = 0;
    memset(head, -1, sizeof(head));
}
void addEdge(int u, int v, int w, int c)
{
    Edge E1 = {u, v, w, 0, c, head[u]};
    edge[edgenum] = E1;
    head[u] = edgenum++;
    Edge E2 = {v, u, 0, 0, -c, head[v]};
    edge[edgenum] = E2;
    head[v] = edgenum++;
}
void getMap()
{
    int a, b, c;
    source = 0, sink = 2*N+1;
    for(int i = 1; i <= N; i++)
        addEdge(source, i, 1, 0),//超级源点 连左点
        addEdge(i + N, sink, 1, 0);//右点 连超级汇点
    while(M--)
    {
        scanf("%d%d%d", &a, &b, &c);
        addEdge(a, b+N, 1, c);//左点 连 右点
    }
}
bool SPFA(int s, int t)
{
    queue<int> Q;
    memset(dist, INF, sizeof(dist));
    memset(vis, false, sizeof(vis));
    memset(pre, -1, sizeof(pre));
    dist[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)
        {
            Edge E = edge[i];
            if(dist[E.to] > dist[u] + E.cost && E.cap > E.flow)
            {
                dist[E.to] = dist[u] + E.cost;
                pre[E.to] = i;
                if(!vis[E.to])
                {
                    vis[E.to] = true;
                    Q.push(E.to);
                }
            }
        }
    }
    return pre[t] != -1;
}
void MCMF(int s, int t, int &cost, int &flow)
{
    cost = flow = 0;
    while(SPFA(s, t))
    {
        int Min = INF;
        for(int i = pre[t]; i != -1; i = pre[edge[i^1].to])
        {
            Edge E = edge[i];
            Min = min(Min, E.cap-E.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;
    }
}
int main()
{
    while(scanf("%d%d", &N, &M) != EOF)
    {
        init();
        getMap();
        int cost, flow;
        MCMF(source, sink, cost, flow);
        if(flow == N)//满流
            printf("%d\n", cost);
        else
            printf("-1\n");
    }
    return 0;
}

#include <cstdio>
#include <cstring>
#include <algorithm>
#define INF 0x3f3f3f3f
using namespace std;
int lx[110], ly[110];
int Map[110][110];
bool visx[110], visy[110];
int slack[110];
int match[110];
int N, M;
void getMap()
{
    for(int i = 1; i <= N; i++)
    {
        for(int j = 1; j <= N; j++)
            Map[i][j] = -INF;
    }
    int a, b, c;
    while(M--)
    {
        scanf("%d%d%d", &a, &b, &c);
        if(-c > Map[a][b])
            Map[a][b] = -c;
    }
}
int DFS(int x)
{
    visx[x] = true;
    for(int y = 1; y <= N; y++)
    {
        if(visy[y]) continue;
        int t = lx[x] + ly[y] - Map[x][y];
        if(t == 0)
        {
            visy[y] = true;
            if(match[y] == -1 || DFS(match[y]))
            {
                match[y] = x;
                return 1;
            }
        }
        else if(slack[y] > t)
            slack[y] = t;
    }
    return 0;
}
void KM()
{
    memset(match, -1, sizeof(match));
    memset(ly, 0, sizeof(ly));
    for(int x = 1; x <= N; x++)
    {
        lx[x] = -INF;
        for(int y = 1; y <= N; y++)
            lx[x] = max(lx[x], Map[x][y]);
    }
    for(int x = 1; x <= N; x++)
    {
        for(int i = 1; i <= N; i++)
            slack[i] = INF;
        while(1)
        {
            memset(visx, false, sizeof(visx));
            memset(visy, false, sizeof(visy));
            if(DFS(x)) break;
            int d = INF;
            for(int i = 1; i <= N; i++)
            {
                if(!visy[i] && slack[i] < d)
                    d = slack[i];
            }
            for(int i = 1; i <= N; i++)
            {
                if(visx[i])
                   lx[i] -= d;
            }
            for(int i = 1; i <= N; i++)
            {
                if(visy[i])
                    ly[i] += d;
                else
                    slack[i] -= d;
            }
        }
    }
    //判断是否存在完美匹配
    int ans = 0;
    bool flag = true;
    for(int i = 1; i <= N; i++)
    {
        if(match[i] == -1 || Map[match[i]][i] == -INF)
        {
            flag = false;
            break;
        }
        ans += Map[match[i]][i];
    }
    if(flag)
        printf("%d\n", -ans);
    else
        printf("-1\n");
}
int main()
{
    while(scanf("%d%d", &N, &M) != EOF)
    {
        getMap();
        KM();
    }
    return 0;
}