[网络流24题]骑士共存问题 二分图/最大点权独立集

题目链接

把棋盘黑白染色,构建二分图,然后s点连黑1 ,黑连白INF ,白连t 1,注意黑白相连为一步可达

#include<bits/stdc++.h>using namespace std;typedef long long ll;const int  MAXN = 41000;const int  MAXM = 10000010;const int  INF  = 0x3f3f3f3f;//const ll MOD = 998244353;int dir[8][2]={ {2,1},{-2,1},{2,-1},{-2,-1} , {1,2},{1,-2},{-1,2},{-1,-2} };inline int read(){int ra,fh;char rx;rx=getchar(),ra=0,fh=1;while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();if(rx=='-')fh=-1,rx=getchar();while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48,rx=getchar();return ra*fh;}struct Edge{    int from, to, cap, flow, next;};Edge edge[MAXM];int head[MAXN], cur[MAXN], edgenum;int dist[MAXN];bool vis[MAXN];int N, M,ss,tt;void init(){    edgenum = 0;    memset(head, -1, sizeof(head));}void addEdge(int u, int v, int w){    Edge E1 = {u, v, w, 0, head[u]};    edge[edgenum] = E1;    head[u] = edgenum++;    Edge E2 = {v, u, 0, 0, head[v]};    edge[edgenum] = E2;    head[v] = edgenum++;}bool BFS(int s, int t){    queue<int> Q;    memset(dist, -1, sizeof(dist));    memset(vis, false, sizeof(vis));    dist[s] = 0;    vis[s] = true;    Q.push(s);    while(!Q.empty())    {        int u = Q.front();        Q.pop();        for(int i = head[u]; i != -1; i = edge[i].next)        {            Edge E = edge[i];            if(!vis[E.to] && E.cap > E.flow)            {                dist[E.to] = dist[u] + 1;                if(E.to == t) return true;                vis[E.to] = true;                Q.push(E.to);            }        }    }    return false;}int DFS(int x, int a, int t){    if(x == t || a == 0) return a;    int flow = 0, f;    for(int &i = cur[x]; i != -1; i = edge[i].next)    {        Edge &E = edge[i];        if(dist[E.to] == dist[x] + 1 && (f = DFS(E.to, min(a, E.cap - E.flow), t)) > 0)        {            edge[i].flow += f;            edge[i^1].flow -= f;            flow += f;            a -= f;            if(a == 0) break;        }    }    return flow;}int Maxflow(int s, int t){    int flow = 0;    while(BFS(s, t))    {        memcpy(cur, head, sizeof(head));        flow += DFS(s, INF, t);    }    return flow;}int mm[205][205];int m,n;int u,v;int getnum(int x,int y){    return (x-1)*n+y;}void dfs(int curx,int cury,int now){    mm[curx][cury] = now;    for(int i=0 ;i<8;i++)    {        int xx = curx + dir[i][0];        int yy = cury + dir[i][1];        if(xx<1||xx>n||yy<1||yy>n||mm[xx][yy])        {            continue;        }        if(now==2)        {//            addEdge(getnum(curx,cury),getnum(xx,yy),INF);            dfs(xx,yy,3);        }        else        {//            addEdge(getnum(xx,yy),getnum(curx,cury),INF);            dfs(xx,yy,2);        }    }}int main(){//    freopen("data.txt","r",stdin);    ios_base::sync_with_stdio(false);    cin >> n>>m;    init();    int s = 0;    int t = n*n+1;    for(int i=0;i<m;i++)    {        cin >> u>>v;        mm[u][v]=1;    }    for(int i=1;i<=n;i++)    {        for(int j=1;j<=n;j++)        {            if(mm[i][j]==0)            {                dfs(i,j,2);            }        }    }//    for(int i=1;i<=n;i++)//    {//        for(int j=1;j<=n;j++)//        {//            cout << mm[i][j]<<" ";//        }//        cout <<endl;//    }    for(int i=1;i<=n;i++)    {        for(int j=1;j<=n;j++)        {            if(mm[i][j]==2)            {                addEdge(s,getnum(i,j),1);                for(int d=0 ;d<8;d++)                {                    int xx = i + dir[d][0];                    int yy = j + dir[d][1];                    if(xx<1||xx>n||yy<1||yy>n)                    {                        continue;                    }                    if(mm[xx][yy]==3)                    {                        addEdge(getnum(i,j),getnum(xx,yy),INF);                    }                }            }            if(mm[i][j]==3)            {                addEdge(getnum(i,j),t,1);            }        }    }    cout << n*n-m-Maxflow(s,t)<<endl;    return 0;}