sgu206 分类： sgu 2015-06-10 17:00 29人阅读 评论(0) 收藏

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首先很显然，生成树上的边权应减小，非生成树上的边权应增大。

令 xi=ci−di , yj=dj−cj (xi>=0,yj>=0)
若树边 i 在非树边 j 和生成树形成的环上，
有 di<=dj⟹ci−xi<=yj+cj⟹xi+yj>=ci−cj

建立二分图，其中 wi,j=ci−cj，KM 算法求最大权匹配，满足
Ai+Bj>=wi,j，即可满足该不等式。

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与 差分约束系统 有着异曲同工之妙 ^_^。

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#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>

const int MAXN = 70, MAXM = 405, INF = 0x3f3f3f3f;

int n, m; 
int a[MAXM], b[MAXM], c[MAXM]; 
int g[MAXN][MAXN];

int nx, ny, w[MAXM][MAXM];
int link[MAXM], slack[MAXM];
int lx[MAXM], ly[MAXM];
bool visx[MAXM], visy[MAXM];

bool DFS(int fr,int a,int to,int id)
{
    if(a == to) return true;

    for(int i = 1; i <= n; i++)
    {
        if(i == fr || !g[a][i]) continue;

        if(DFS(a, i, to, id))
        {
            int &newrc = w[g[a][i]][id];
            newrc = std::max(newrc, c[g[a][i]] - c[id]);
            return true;
        }
    }
    return false;
}
void PreWork()
{
    scanf("%d%d",&n,&m);

    for(int i = 1; i <= m; i++)
    {
         scanf("%d%d%d",&a[i],&b[i],&c[i]);
         if(i < n) g[a[i]][b[i]] = g[b[i]][a[i]] = i;
    }
    for(int i = n; i <= m; i++)
        DFS(0,a[i],b[i],i);

    nx = m, ny = m;
}
bool find(int x)
{
    visx[x] = true;

    for(int y = 1; y <= ny; y++)
        if(!visy[y])
        {
            int cal = lx[x] + ly[y] - w[x][y];

            if(cal == 0)
            {
                visy[y] = true;
                if(!link[y] || find(link[y]))
                {
                    link[y] = x;
                    return true;
                }
            }
            slack[y] = std::min(cal, slack[y]); 
        }
    return false;   
}

void Solve()
{
    memset(lx,0,sizeof(lx));
    memset(ly,0,sizeof(ly));

    for(int i = 1; i <= nx; i++)
        for(int j = 1; j <= ny; j++)
            lx[i] = std::max(lx[i], w[i][j]);

    for(int i = 1; i <= nx; i++)
    {
        memset(slack,INF,sizeof(slack)); 

        while(true)
        {
            memset(visx,false,sizeof(visx));
            memset(visy,false,sizeof(visy));

            if(find(i)) break;

            int d = INF;

            for(int j = 1; j <= ny; j++)
                if(!visy[j]) d = std::min(d, slack[j]);

            for(int j = 1; j <= nx; j++)
                if(visx[j])lx[j] -= d;
            for(int j = 1; j <= ny; j++)
                if(visy[j])ly[j] += d;
                else  slack[j] -= d;        
        }
    }

}

void Output()
{
    for(int i = 1; i < n; i++)
        printf("%d\n",c[i]-lx[i]);
    for(int i = n; i <= m; i++)
        printf("%d\n",c[i]+ly[i]);
}

int main()
{
#ifndef ONLINE_JUDGE
    freopen("sgu206.in","r",stdin);
    freopen("sgu206.out","w",stdout);
#endif

    PreWork();
    Solve();
    Output();

#ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout); 
#endif
    return 0;   
}

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