骑士共存问题

  1 #include<cstdio>
  2 #include<iostream>
  3 #include<cmath>
  4 #include<algorithm>
  5 #include<cstring>
  6 #include<cstdlib>
  7 #include<cctype>
  8 #include<vector>
  9 #include<stack>
 10 #include<queue>
 11 using namespace std;
 12 #define enter puts("") 
 13 #define space putchar(‘ ‘)
 14 #define Mem(a, x) memset(a, x, sizeof(a))
 15 #define rg register
 16 typedef long long ll;
 17 typedef double db;
 18 const int INF = 0x3f3f3f3f;
 19 const db eps = 1e-8;
 20 const int maxn = 4e4 + 5;
 21 inline ll read()
 22 {
 23     ll ans = 0;
 24     char ch = getchar(), last = ‘ ‘;
 25     while(!isdigit(ch)) {last = ch; ch = getchar();}
 26     while(isdigit(ch)) {ans = ans * 10 + ch - ‘0‘; ch = getchar();}
 27     if(last == ‘-‘) ans = -ans;
 28     return ans;
 29 }
 30 inline void write(ll x)
 31 {
 32     if(x < 0) x = -x, putchar(‘-‘);
 33     if(x >= 10) write(x / 10);
 34     putchar(x % 10 + ‘0‘);
 35 }
 36 
 37 const int dx[10] = {-1, -2, -2, -1, 1, 2, 2, 1}, dy[10] = {-2, -1, 1, 2, 2, 1, -1, -2};
 38 int n, m, t;
 39 bool vis[maxn];
 40 
 41 struct Edge
 42 {
 43     int from, to, cap, flow;
 44 };
 45 vector<Edge> edges;
 46 vector<int> G[maxn];
 47 void addEdge(int from, int to, int w)
 48 {
 49     edges.push_back((Edge){from, to, w, 0});
 50     edges.push_back((Edge){to, from, 0, 0});
 51     int sz = edges.size();
 52     G[from].push_back(sz - 2);
 53     G[to].push_back(sz - 1);
 54 }
 55 
 56 int getnum(int x, int y)
 57 {
 58     return (x - 1) * n + y;
 59 }
 60 
 61 void solve(int x, int y)
 62 {
 63     int u = getnum(x, y);
 64     for(int i = 0; i < 8; ++i)
 65     {
 66         int newx = x + dx[i], newy = y + dy[i];
 67         if(newx > 0 && newx <= n && newy > 0 && newy <= n) 
 68             addEdge(u, getnum(newx, newy), INF);
 69     }
 70 }
 71 
 72 int dis[maxn];
 73 bool bfs()
 74 {
 75     Mem(dis, 0); dis[0] = 1;
 76     queue<int> q; q.push(0);
 77     while(!q.empty())
 78     {
 79         int now = q.front(); q.pop();
 80         for(int i = 0; i < (int)G[now].size(); ++i)
 81         {
 82             Edge& e = edges[G[now][i]];
 83             if(!dis[e.to] && e.cap > e.flow)
 84             {
 85                 dis[e.to] = dis[now] + 1;
 86                 q.push(e.to);    
 87             }
 88         }
 89     }
 90     return dis[t];
 91 }
 92 int cur[maxn];
 93 int dfs(int now, int res)
 94 {
 95     if(now == t || res == 0) return res;
 96     int flow = 0, f;
 97     for(int& i = cur[now]; i < (int)G[now].size(); ++i)
 98     {
 99         Edge& e = edges[G[now][i]];
100         if(dis[e.to] == dis[now] + 1 && (f = dfs(e.to, min(res, e.cap - e.flow))) > 0)
101         {
102             e.flow += f;
103             edges[G[now][i] ^ 1].flow -= f;
104             flow += f; res -= f;
105             if(res == 0) break;
106         }
107     }
108     return flow;
109 }
110 
111 int minCut()
112 {
113     int flow = 0;
114     while(bfs())
115     {
116         Mem(cur, 0);
117         flow += dfs(0, INF);
118     }
119     return flow;
120 }
121 
122 int main()
123 {
124     n = read(); m = read();
125     t = n * n + 1;
126     for(int i = 1; i <= m; ++i)
127     {
128         int x = read(), y = read();
129         vis[getnum(x, y)] = 1;
130     }
131     for(int i = 1; i <= n; ++i)
132         for(int j = 1; j <= n; ++j) if(!vis[getnum(i, j)])
133         {
134             if((i + j) & 1) addEdge(getnum(i, j), t, 1);
135             else addEdge(0, getnum(i, j), 1), solve(i, j);
136         }
137     write(n * n - m - minCut()); enter;    
138     return 0;
139 }