HDU - 6201 - transaction transaction transaction（SPFA最长路 or 费用流）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=6201

题意：每个地点的商品都有一个价格，你可以在任意两个地点买卖，两个地点之间还有一个路费。求最终获得的最大利润。

思路：题目要求的是最大利润，我们建立超级源点超级汇点，超级源点到每一个点是买东西花掉的-val，每一个点到超级汇点是卖东西挣得的val。然后建立权值为负的边表示路费，然后跑一遍spfa最长路，或者费用流即可。

spfa：

#include <bits/stdc++.h>
using namespace std;
#define inf 0x3f3f3f3f
#define GT() int T;scanf("%d",&T);while(T--)
const int maxn = 1e5+7;
int n,m;
int d[maxn], vis[maxn], v[maxn];
int s, t;
vector<pair<int,int> >E[maxn];
void init()
{
    memset(vis,0,sizeof(vis));
    for(int i = 0; i <= n + 1; i++)
        E[i].clear(), d[i] = -inf;
}
void spfa()
{
    queue <int> Q;
    Q.push(s);
    while(!Q.empty())
    {
        int now = Q.front();
        Q.pop(); vis[now] = 0;
        for(int j = 0; j < E[now].size(); j++)
        {
            int v = E[now][j].first;
            if(d[v] < d[now] + E[now][j].second)
            {
                d[v] = d[now] + E[now][j].second;
                if(vis[v]) continue;
                vis[v] = 1;
                Q.push(v);
            }
        }
    }
}
int main()
{
    int T; scanf("%d",&T);
    while(T--)
    {
        scanf("%d", &n); init();
        for(int i = 1; i <= n; i++)
            scanf("%d", &v[i]);
        int a, b, x;
        for(int i = 0; i < n-1; i++)
        {
            scanf("%d%d%d",&a, &b, &x);
            E[a].push_back({b, -x});
            E[b].push_back({a, -x});
        }
        s = 0, t = n + 1;
        for(int i = 1; i <= n; i++)
        {
            E[s].push_back({i, -v[i]});
            E[i].push_back({t, v[i]});
        }
        d[s] = 0; vis[s] = 1; spfa();
        printf("%d\n",d[t]);
    }
    return 0;
}
/*
1
4
10 40 15 30
1 2 30
1 3 2
3 4 10
*/

费用流：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#define inf 0x3f3f3f3f
using namespace std;
const int maxn = 1e6 + 7;

bool vis[maxn];
int n,m,x,y,z,f,dis[maxn],pre[maxn],last[maxn],flow[maxn],maxflow,mincost;
struct node{int next,to,flow,dis;}edge[maxn];
int head[maxn],cnt;
queue <int> q;

void add(int u,int v,int flow,int dis)
{
    edge[cnt] = (node){head[u],v,flow,dis}; head[u] = cnt++;
    edge[cnt] = (node){head[v],u,0,-dis}; head[v] = cnt++;
}

bool spfa(int s,int t)
{
    for(int i = 0; i < t + 10; i++)
        dis[i] = inf, flow[i] = inf, vis[i] = 0;
    q.push(s); vis[s] = 1; dis[s] = 0; pre[t] = -1;
    while (!q.empty())
    {
        int now = q.front();
        q.pop();
        vis[now] = 0;
        for (int i = head[now]; i != -1; i = edge[i].next)
        {
            if (edge[i].flow > 0 && dis[edge[i].to] > dis[now] + edge[i].dis)
            {
                dis[edge[i].to] = dis[now] + edge[i].dis;
                pre[edge[i].to] = now;
                last[edge[i].to] = i;
                flow[edge[i].to] = min(flow[now],edge[i].flow);
                if (!vis[edge[i].to])
                {
                    vis[edge[i].to] = 1;
                    q.push(edge[i].to);
                }
            }
        }
    }
    return pre[t] != -1;
}

void MCMF(int s, int t)
{
    maxflow = 0, mincost = 0;
    while(spfa(s,t))
    {
        int now = t;
        maxflow += flow[t];
        mincost += flow[t]*dis[t];
        while (now != s)
        {
            edge[last[now]].flow -= flow[t];
            edge[last[now]^1].flow += flow[t];
            now = pre[now];
        }
    }
}

int main()
{
    int T; scanf("%d",&T);
    while(T--)
    {
        memset(head,-1,sizeof(head)); cnt = 0;
        scanf("%d",&n);
        int s = 0;
        int s1 = n + 1;
        int t = n + 2;
        add(s, s1, 1, 0);
        for(int i = 1; i <= n; i++)
        {
            int val;
            scanf("%d",&val);
            add(s1,i,1,-val);
            add(i,t,1,val);
        }
        for(int i = 1; i <= n - 1; i++)
        {
            scanf("%d%d%d",&x,&y,&f);
            add(x,y,1,f);
            add(y,x,1,f);
        }
        MCMF(s, t);
        printf("%d\n",abs(mincost));
    }
    return 0;
}
/*
1
4
10 40 15 30
1 2 30
1 3 2
3 4 10
*/

HDU - 6201 - transaction transaction transaction（SPFA最长路 or 费用流）

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