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最新推荐文章于 2022-03-06 15:46:56 发布

Helloat123

最新推荐文章于 2022-03-06 15:46:56 发布

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分类专栏：网络流文章标签：网络流

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本文介绍了一种使用费用流算法解决特定线性规划问题的方法。通过实例演示了如何构造网络并应用最大费用最小流算法求解最优解。适用于算法竞赛及线性规划初学者。

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非常棒非常棒的费用流（线性规划）题目，我暂时不会simplex所以只能用费用流水水

这个题解很棒

//By Richard
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <ctime>
#define rep(x,y,z) for (int x=(y);(x)<=(z);(x)++)
#define per(x,y,z) for (int x=(y);(x)>=(z);(x)--)
#define log2(x) (31-__builtin_clz(x))
#define mod (int)(1e9+7)
#define inf 0x3f3f3f3f
#define cls(x) memset(x,0,sizeof(x))
#ifdef DEBUG
#define debugdo(X) X
#define debugndo(X)
#define debugout(X) cout<<(#X)<<"="<<(X)<<endl
#else
#define debugdo(X)
#define debugndo(X) X
#define debugout(X)
#endif // debug
#ifdef ONLINE_JUDGE
#define debugdo(X)
#define debugndo(X)
#define debugout(X)
#endif
#define putarray(x,n) rep(iiii,1,n) printf("%d ",x[iiii])
#define mp make_pair
using namespace std;
typedef pair<int,int> pairs;
typedef long long LL;
/////////////////////read4.0////////////////////////////////////
template <typename T>
inline void read(T &x){char ch;x=0;bool flag=false;ch=getchar();while (ch>'9'||ch<'0') {if (ch=='-') flag=true;ch=getchar();}while ((ch<='9'&&ch>='0')){x=x*10+ch-'0';ch=getchar();}if (flag) x*=-1;}
template <typename T>
inline void read(T &x,T &y){read(x);read(y);}
template <typename T>
inline void read(T &x,T &y,T &z){read(x);read(y);read(z);}
/////////////////////graph///////////////////////////////
const int MAXV=1111,MAXE=51111;
struct EDGE
{
    int u,v,w,cost;
};
struct GRAPH
{
    EDGE edge[MAXE];
    int next[MAXE],first[MAXV],cnt;
    inline void init()
    {
        cnt=0;
        cls(edge);
        cls(next);
        memset(first,-1,sizeof(first));
    }
    inline void addedge(int u,int v,int w,int cost)
    {
        edge[cnt].u=u;
        edge[cnt].v=v;
        edge[cnt].w=w;
        edge[cnt].cost=cost;
        next[cnt]=first[u];
        first[u]=cnt++;
        edge[cnt].u=v;
        edge[cnt].v=u;
        edge[cnt].w=0;
        edge[cnt].cost=-cost;
        next[cnt]=first[v];
        first[v]=cnt++;
    }
    int distance[MAXV],route[MAXV],maxflow;
    bool vis[MAXV];
    queue <int> qu;
    inline bool spfa(int s,int t)
    {
        memset(distance,0x3f,sizeof(distance));
        memset(route,-1,sizeof(route));
        cls(vis);
        distance[s]=0;
        vis[s]=true;
        qu.push(s);
        while (!qu.empty())
        {
            int p=qu.front();
            qu.pop();
            int q=first[p];
            vis[p]=false;
            while (q!=-1)
            {
                if (edge[q].w&&distance[edge[q].v]>distance[p]+edge[q].cost)
                {
                    distance[edge[q].v]=distance[p]+edge[q].cost;
                    route[edge[q].v]=q;
                    if (!vis[edge[q].v])
                    {
                        qu.push(edge[q].v);
                        vis[edge[q].v]=true;
                    }
                }
                q=next[q];
            }
        }
        if (distance[t]==inf) return false;
        return true;
    }
    int MCMF(int s,int t)
    {
        int mincost=0,nowflow=0,minflow;
        while (spfa(s,t))
        {
            minflow=inf+1;
            int q=route[t];
            while (q!=-1) 
            {
                minflow=min(minflow,edge[q].w);
                q=route[edge[q].u];
            }
            nowflow+=minflow;
            q=route[t];
            while (q!=-1)
            {
                edge[q].w-=minflow;
                edge[q^1].w+=minflow;
                q=route[edge[q].u];
            }
            mincost+=distance[t]*minflow;
        }
        maxflow=nowflow;
        return mincost;
    }
}graph;
int n,s,t,a[MAXV],m;
int main()
{
    read(n,m);
    s=0,t=n+2;
    graph.init();
    rep(i,1,n) read(a[i]);
    int x,y,z;
    rep(i,1,m)
    {
        read(x,y,z);
        graph.addedge(x,y+1,inf,z);
    }
    a[0]=a[n+1]=0;
    rep(i,1,n+1)
    {
        int temp=a[i]-a[i-1];
        if (temp>=0) graph.addedge(s,i,temp,0);
        else graph.addedge(i,t,-temp,0);
    }
    rep(i,1,n) graph.addedge(i+1,i,inf,0);
    printf("%d\n",graph.MCMF(s,t));
    return 0;
}