学步园

经典的奇偶建图，这个模型有必要记一下。

网络流过了。

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <map>
using namespace std;

const int maxn = 40*40;
const int INF = 0x3f3f3f3f;

struct Edge
{
	int from, to, cap, flow;
	Edge(int from, int to, int cap, int flow): from(from), to(to), cap(cap), flow(flow) {}
};

struct Dinic
{
	int n, m, s, t;
	vector<Edge> edges;
	vector<int> G[maxn];
	bool vis[maxn];
	int d[maxn];
	int cur[maxn];
	
	void init(int n)
	{
		this->n = n;
		for(int i = 0; i <= n; i++) G[i].clear();
		edges.clear();
	}
	
	void ClearFlow ()
	{
		for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;
	}
	
	void AddEdge(int from, int to, int cap)
	{
		edges.push_back(Edge (from, to, cap, 0));
		edges.push_back(Edge (to, from, 0, 0));
		m = edges.size();
		G[from].push_back(m-2);
		G[to].push_back(m-1);
	}
	
	bool BFS()
	{
		memset(vis, 0, sizeof(vis));
		queue<int> Q;
		Q.push(s);
		d[s] = 0;
		vis[s] = 1;
		while(!Q.empty())
		{
			int x = Q.front(); Q.pop();
			for(int i = 0; i < G[x].size(); i++)
			{
				Edge& e = edges[G[x][i]];
				if(!vis[e.to] && e.cap > e.flow)
				{
					vis[e.to] = 1;
					d[e.to] = d[x]+1;
					Q.push(e.to);
				}
			}
		}
		return vis[t];
	}
	
	int DFS(int x, int a)
	{
		if(x == t || a == 0) return a;
		int flow = 0, f;
		for(int &i = cur[x]; i < G[x].size(); i++)
		{
			Edge& e = edges[G[x][i]];
			if(d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap-e.flow))) > 0)
			{
				e.flow += f;
				edges[G[x][i]^1].flow -= f;
				flow += f;
				a -= f;
				if(a == 0) break;
			}
		}
		return flow;
	}
	
	int Maxflow(int s, int t)
	{
		this->s = s; this->t = t;
		int flow = 0;
		while(BFS())
		{
			memset(cur, 0, sizeof(cur));
			flow += DFS(s, INF);
		}
		return flow;
	}
};
 
void readint(int &x)
{
    char c;
    while(!isdigit(c)) c = getchar();
    
    x = 0;
    while(isdigit(c))
    {
        x = x*10 + c-'0';
        c = getchar();
    }
}

void writeint(int x)
{
    if(x > 9) writeint(x/10);
    putchar(x%10+'0');
}

///////////////////////////////////////

Dinic solver;
int n, m, s, t;

int k;
struct Point
{
	int x, y;
	Point(int x=0, int y=0): x(x), y(y) {}
    bool check(Point a)
    {
        if(x == a.x && (a.y == y+1 || a.y == y-1)) return 1;
        if(y == a.y && (a.x == x+1 || a.x == x-1)) return 1;
        return 0;
    }
};

Point P1[maxn], P2[maxn];
int p1, p2;

void read_case()
{
	p1 = p2 = 0;
	
	bool is[40][40] = {0};
	
	for(int i = 0; i < k; i++)
	{
		int x, y;
		readint(y), readint(x);
		is[x][y] = 1;
	}
	
	for(int i = 1; i <= n; i++)
	for(int j = 1; j <= m; j++) if(!is[i][j])
	{
		if((i+j) & 1) P1[p1++] = Point(i, j);
		else P2[p2++] = Point(i, j);
	}
	
	solver.init(p1+p2+5);
	s = p1+p2+1, t = p1+p2+2;
	
	for(int i = 0; i < p1; i++)
	for(int j = 0; j < p2; j++)
	{
		if(P1[i].check(P2[j])) solver.AddEdge(i, j+p1, 1);
	}
	
	for(int i = 0; i < p1; i++) solver.AddEdge(s, i, 1);
	for(int i = 0; i < p2; i++) solver.AddEdge(i+p1, t, 1);
}

void solve()
{
    read_case();
    if(solver.Maxflow(s, t)*2 + k == m*n) printf("YES\n");
    else printf("NO\n");
}

int main()
{
	while(~scanf("%d%d%d", &n, &m, &k)) solve();
	return 0;
}