最大流最小割合集 II

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hdu 1569 方格取数(2)（最大点权独立集）

点覆盖集：无向图G的一个点集，使得该图中所有边都至少有一个端点在该集合内；
最小点权覆盖集：在带点权无向图G中，点权之和最小的覆盖集；
点独立集：无向图G的一个点集，使得任两个在该集合中的点在原图中都不相邻；
最大点权独立集：在带权无向图G中，点权之和最大的独立集；

解法：

对图中所有点进行0|1染色

0色：S向其连权值为该点权值的边，向相邻点连权值为inf的边

1色：向T连权值为该点权值的边

#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>#include <vector>using namespace std;const int MAXN = 55*55, inf = 0x3f3f3f3f;const int MAXM = MAXN*10;int n, m;struct _edge{    int v, nxt;    int w;    _edge(int vv, int ww, int nnxt):v(vv),w(ww),nxt(nnxt){}    _edge(){}}ee[MAXM];int head[MAXN], cnt;int cur[MAXN], dis[MAXN], gap[MAXN], pre[MAXN];void add(int u, int v, int w){    ee[cnt] = _edge(v,w,head[u]); head[u] = cnt++;    ee[cnt] = _edge(u,0,head[v]); head[v] = cnt++;}int sap(int start,int end,int nodenum){    memset(dis,0,4*MAXN);    memset(gap,0,4*MAXN);    memcpy(cur,head,4*MAXN);    int u=pre[start]=start;    int maxflow=0,aug=-1;    gap[0]=nodenum;    while(dis[start]<nodenum)    {        loop:        for(int &i=cur[u];i!=-1;i=ee[i].nxt)        {            int v=ee[i].v;            if(ee[i].w&&dis[u]==dis[v]+1)            {                if(aug==-1||aug>ee[i].w)                    aug=ee[i].w;                pre[v]=u;                u=v;                if(v==end)                {                    maxflow+=aug;                    for(u=pre[u];v!=start;v=u,u=pre[u])                    {                        ee[cur[u]].w-=aug;                        ee[cur[u]^1].w+=aug;                    }                    aug=-1;                }                goto loop;            }        }        int mindis=nodenum;        for(int i=head[u];i!=-1;i=ee[i].nxt)        {            int v=ee[i].v;            if(ee[i].w && mindis>dis[v])            {                cur[u]=i;                mindis=dis[v];            }        }        if((--gap[dis[u]])==0)break;        gap[dis[u]=mindis+1]++;        u=pre[u];    }    return maxflow;}void init(){    cnt = 0;    memset(head, -1, sizeof head);}int main()   {#ifndef ONLINE_JUDGE    freopen("in.txt", "r", stdin);#endif    while (scanf("%d%d", &n, &m) != EOF)    {        int S = n*m, T = S+1, a, res = 0;        init();        for (int i = 0; i< n; ++i)        {            for (int j = 0; j< m; ++j)            {                scanf("%d", &a);                res += a;                int p = i*m+j;                if ((i+j) & 1)                    add(p, T, a);                else                {                    add(S, p, a);                    if (j > 0) add(p, p-1, inf);                    if (j+1 < m) add(p, p+1, inf);                    if (i > 0) add(p, p-m, inf);                    if (i+1 < n) add(p, p+m, inf);                }            }        }        printf("%d\n", res - sap(S, T, T+1));    }    return 0;}

hdu 4859 海岸线

推荐这篇博客的解法： http://blog.csdn.net/t1019256391/article/details/38036355

#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>#include <vector>using namespace std;const int MAXN = 55*55, inf = 0x3f3f3f3f;const int MAXM = MAXN*10;int n, m;char mmp[55][55];struct _edge{    int v, nxt;    int w;    _edge(int vv, int ww, int nnxt):v(vv),w(ww),nxt(nnxt){}    _edge(){}}ee[MAXM];int head[MAXN], cnt;int cur[MAXN], dis[MAXN], gap[MAXN], pre[MAXN];void add(int u, int v, int w){    ee[cnt] = _edge(v,w,head[u]); head[u] = cnt++;    ee[cnt] = _edge(u,0,head[v]); head[v] = cnt++;}int sap(int start,int end,int nodenum){    memset(dis,0,4*MAXN);    memset(gap,0,4*MAXN);    memcpy(cur,head,4*MAXN);    int u=pre[start]=start;    int maxflow=0,aug=-1;    gap[0]=nodenum;    while(dis[start]<nodenum)    {        loop:        for(int &i=cur[u];i!=-1;i=ee[i].nxt)        {            int v=ee[i].v;            if(ee[i].w&&dis[u]==dis[v]+1)            {                if(aug==-1||aug>ee[i].w)                    aug=ee[i].w;                pre[v]=u;                u=v;                if(v==end)                {                    maxflow+=aug;                    for(u=pre[u];v!=start;v=u,u=pre[u])                    {                        ee[cur[u]].w-=aug;                        ee[cur[u]^1].w+=aug;                    }                    aug=-1;                }                goto loop;            }        }        int mindis=nodenum;        for(int i=head[u];i!=-1;i=ee[i].nxt)        {            int v=ee[i].v;            if(ee[i].w && mindis>dis[v])            {                cur[u]=i;                mindis=dis[v];            }        }        if((--gap[dis[u]])==0)break;        gap[dis[u]=mindis+1]++;        u=pre[u];    }    return maxflow;}void init(){    cnt = 0;    memset(head, -1, sizeof head);}int main()   {#ifndef ONLINE_JUDGE    freopen("in.txt", "r", stdin);#endifint t, S, T, cs = 0, p;scanf("%d", &t);    while (t--)    {        scanf("%d%d", &n, &m);    init();    S = (n+2)*(m+2); T = S+1;    for (int i = 1; i<= n; ++i)    scanf("%s", mmp[i]+1);for (int i = 0; i<= n+1; ++i)for (int j = 0; j<= m+1; ++j){if (i == 0 || j == 0 || i==n+1 || j == m+1)   mmp[i][j] = 'D';p = i*(m+2)+j;if ((i+j) & 1){if (mmp[i][j] == 'D') add(p, T, inf);if (mmp[i][j] == '.') add(S, p, inf);}else{if (mmp[i][j] == '.') add(p, T, inf);if (mmp[i][j] == 'D') add(S, p, inf);}if (i-1 >= 0) add(p, p-m-2, 1);if (i+1 < n+2) add(p, p+m+2, 1);if (j-1 >= 0) add(p, p-1, 1);if (j+1 < m+2) add(p, p+1, 1);}printf("Case %d: %d\n", ++cs, (n+1)*(m+2)+(n+2)*(m+1) - sap(S, T, T+1));    }    return 0;}

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