【最大流】【HDU3338】【Kakuro Extension】

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3338

题目大意：填数字，使白色区域的值得和等于有值得黑色区域的相对应的值，用网络流来做

题目思路：增加一个源点和汇点，然后左进上出，用源点连左面，容量为相对应的值，汇点连上面，容量是相对应的值，然后左面连空白区域的，容量为8，因为数字为1-9，有下限，但因每个空白必须有值，所以至少为一，所以容量空间为0-8；然后空白区域来连上面，容量同样为8；

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
#define INF 999999999
#define maxn 14000

#define RE(x) (x)^1
int head[maxn];
int st,ed;//开始节点，结束节点
struct Edge
{
    int v,next;
    int val;
    Edge() {}
    Edge( int V , int NEXT , int W = 0 ):v(V),next(NEXT),val(W) {}
} edge[500000];
int lvl[maxn], gap[maxn];
int cnt_edge;
int map[maxn][maxn];
struct gg
{
    int x,y;
    int val;
} row[maxn],col[maxn];
int emp,row_num,col_num;
int n,m,T;
void Insert_Edge( int u , int v , int flow = 0 )
{

    edge[cnt_edge] = Edge(v,head[u],flow);
    head[u] = cnt_edge++;
    edge[cnt_edge] = Edge(u,head[v]);
    head[v] = cnt_edge++;

}
void Init()
{
    cnt_edge = 0;
    memset(head,-1,sizeof(head));
    memset(lvl, 0, sizeof (lvl));
    memset(gap, 0, sizeof (gap));
}
int dfs(int u, int flow)
{
    if (u==ed)
    {
        return flow;
    }
    int tf = 0, sf, mlvl = ed-1;
    for (int i= head[u]; i != -1; i = edge[i].next)
    {
        if (edge[i].val > 0)
        {
            if (lvl[u] ==lvl[edge[i].v]+1)
            {
                sf = dfs(edge[i].v, min(flow-tf, edge[i].val));
                edge[i].val -= sf;
                edge[RE(i)].val += sf;
                tf += sf;
                if (lvl[st] >=ed)
                {
                    return tf;
                }
                if (tf == flow)
                {
                    break;
                }
            }
            mlvl = min(mlvl, lvl[edge[i].v]);
        }
    }
    if (tf == 0)
    {
        --gap[lvl[u]];
        if (!gap[lvl[u]])
        {
            lvl[st] =ed;
        }
        else
        {
            lvl[u] = mlvl+1;
            ++gap[lvl[u]];
        }
    }
    return tf;
}
int sap()
{
    int ans = 0;
    gap[0]=ed;
    while (lvl[st] <ed)
    {
        ans += dfs(st, INF);
    }
    return ans;
}
int print( int tp )
{
    int ans = 0;
    int id = tp + row_num+1;
    for( int i = head[id] ; i != -1 ; i = edge[i].next )
    {
        int v = edge[i].v;
        if( v <=row_num+1 )
        {
            ans+= edge[i].val;
            break;
        }
    }
    return ans+1;
}
int main()
{
    int i,j;
    char s[15];
    //freopen("F://ACMInput/input.txt","r",stdin);
    while(scanf("%d%d",&n,&m)!=-1)
    {
        emp=row_num=col_num=0;
        for(i=0; i<n; i++)
            for(j=0; j<m; j++)
            {
                scanf("%s",s);
                if(s[0]=='.')
                {
                    map[i][j]=++emp;
                }
                else
                {
                    map[i][j]=-1;
                    if(s[4]!='X')
                    {
                        int tp=(s[4]-'0')*100+(s[5]-'0')*10+s[6]-'0';
                        row[++row_num].x=i;
                        row[row_num].y=j;
                        row[row_num].val=tp;
                    }
                    if(s[0]!= 'X' )
                    {
                        int tp = (s[0]-'0')*100+(s[1]-'0')*10+s[2]-'0';
                        col[++col_num].x = i;
                        col[col_num].y = j;
                        col[col_num].val = tp;
                    }
                }
            }
        T=emp+col_num+row_num+2;
        st=1;
        ed=T;
        Init();
        for(i=1; i<=row_num; i++)
        {
            int pos = i;
            int x = row[i].x;
            int y = row[i].y;
            int cnt_len = 0;
            for( y=y+1; y <m ; y++ )
            {
                if( map[x][y] != -1 )
                {
                    cnt_len++;
                    Insert_Edge(i+1, row_num+ map[x][y]+1,8);
                }
                else break;
            }
            Insert_Edge(st,pos+1,row[i].val-cnt_len);
        }

        for( i = 1 ; i <=col_num ; i++ )
        {
            int pos =i+1+row_num+emp;
            int x = col[i].x;
            int y = col[i].y;
            int cnt_len = 0;
            for( x=x+1 ; x < n ; x++ )
            {
                if( map[x][y] != -1 )
                {
                    cnt_len++;
                    Insert_Edge(row_num+ map[x][y]+1,pos,8);

                }
                else break;
            }
            Insert_Edge(pos,ed,col[i].val-cnt_len);
        }
        sap();
        for(i=0; i<n; i++)
        {
            for(j=0; j<m; j++)
            {

                if(map[i][j]==-1)
                    printf("_ ");
                else
                    printf("%d ",print(map[i][j]));
            }
            printf("\n");
        }
    }
    return 0;
}