「loj - 3022」「cqoi 2017」老 C 的方块

link。

good题，考虑像 国家集训队 - happiness 一样在棋盘上搞染色，我毛张 @shadowice1987 的图给你看啊

你像这样奇数层以 red -> blue -> green -> yellow 为一个周期，偶数层 yellow -> green -> blue -> red，就会发现给出的形状都包括恰好四种颜色和一条黑线。那现在就好搞了，就是要在每个连通块里面删除至少一种颜色的全部方块（包括黑线），有这样几种选择：全绿 / 全黄 / 全黑线（即破环红或蓝中的一个），像图右侧一样建图就好了。

#include<bits/stdc++.h>
using namespace std;
enum Color { red=1,blue,yellow,green };
const long long INF=0x3f3f3f3f;
template<class Kap> struct Net {
	const long long n;
	struct Arc {
		long long to, rev; Kap cap;
	};
	vector<long long> lev,iter;
	vector<vector<Arc>> e;
	std::queue<long long> q;
	Net(long long n):n(n),e(n),lev(n),iter(n) {}
	void add(long long one,long long ano,Kap cap) {
		// printf("  %lld  %lld  %lld\n",one,ano,cap);
		e[one-1].push_back((Arc){ano-1,(long long)(e[ano-1].size())+(one==ano),cap});
		e[ano-1].push_back((Arc){one-1,(long long)(e[one-1].size())-1,0});
	}
	Kap solve(long long s,long long t) { return solve(s-1,t-1,std::numeric_limits<Kap>::max()); }
	bool Getlayer(long long s,long long t) {
		lev.assign(n,0);
		while(q.size())	q.pop();
		lev[s]=1;
		q.emplace(s);
		while(q.size()) {
			long long now=q.front();
			q.pop();
			if(now==t)	break;
			for(long long i=0; i<(long long)(e[now].size()); ++i) {
				long long y=e[now][i].to; Kap cap=e[now][i].cap;
				if(!lev[y] && cap)	lev[y]=lev[now]+1,q.emplace(y);
			}
		}
		return lev[t];
	};
	Kap Augment(long long now,Kap up,long long t) {
		if(now==t)	return up;
		Kap rlow=0;
		for(long long& i=iter[now]; i<(long long)(e[now].size()); ++i) {
			if(!up)	break;
			long long y=e[now][i].to; Kap& cap=e[now][i].cap;
			if(lev[y]==lev[now]+1 && cap) {
				Kap f=Augment(y,min(up,cap),t);
				if(f<=0)	continue;
				cap-=f; e[y][e[now][i].rev].cap+=f; up-=f; rlow+=f;
			}
		}
		if(!rlow)	lev[now]=n+1;
		return rlow;
	};
	Kap solve(long long s,long long t,const Kap inf) {
		lev.assign(n,0); iter.assign(n,0); Kap res=0,tmp;
		while (Getlayer(s,t)) {
			iter.assign(n, 0);
			if((tmp=Augment(s,inf,t)))	res+=tmp;
			else	break;
		}
		return res;
	}
};
long long r,c,n,celx[100100],cely[100100],celw[100100],S,T,co[100100];
map<long long,long long> mp;
bool valid(long long x,long long y) { return x>=1 && x<=r && y>=1 && y<=c; }
long long getid(long long x,long long y) { return 1ll*(x-1)*c+y; }
signed main() {
	scanf("%lld %lld %lld",&c,&r,&n);
	for(long long i=1; i<=n; ++i)	scanf("%lld %lld %lld",&cely[i],&celx[i],&celw[i]),mp[getid(celx[i],cely[i])]=i;
	// for(long long i=1; i<=n; ++i)	printf("  ---- %lld %lld %lld\n",celx[i],cely[i],celw[i]);
	for(long long i=1; i<=n; ++i) {
		if(cely[i]%4==0)	co[i]=(celx[i]&1)?3:1;
		else if(cely[i]%4==1)	co[i]=(celx[i]&1)?1:3;
		else if(cely[i]%4==2)	co[i]=(celx[i]&1)?2:4;
		else	co[i]=(celx[i]&1)?4:2;
	}
	// char tmp[5][10]={"tmp","red","blue","yellow","green"};
	// for(long long i=1; i<=n; ++i)	puts(tmp[co[i]]);
	// for(long long i=1; i<=n; ++i)	printf(" %lld",co[i]);
	// puts("");
	// 1 for red, 2 for blue, 3 for yellow, 4 for green
	Net<long long> G(n+2); S=n+1; T=n+2;
	for(long long i=1; i<=n; ++i) {
		if(co[i]==yellow /*yellow*/) {
			G.add(S,i,celw[i]);
			if(valid(celx[i],cely[i]-1)) {
				long long j=mp[getid(celx[i],cely[i]-1)];
				if(j && co[j]==red)	G.add(i,j,INF);
			}
			if(valid(celx[i],cely[i]+1)) {
				long long j=mp[getid(celx[i],cely[i]+1)];
				if(j && co[j]==red)	G.add(i,j,INF);
			}
			// printf(" --- %lld %lld\n",celx[i],cely[i]);
			if(valid(celx[i]-1,cely[i])) {
				long long j=mp[getid(celx[i]-1,cely[i])];
				if(j && co[j]==red)	G.add(i,j,INF);
			}
			if(valid(celx[i]+1,cely[i])) {
				long long j=mp[getid(celx[i]+1,cely[i])];
				if(j && co[j]==red)	G.add(i,j,INF);
			}
		}
		else if(co[i]==green /*green*/) {
			G.add(i,T,celw[i]);
			if(valid(celx[i],cely[i]-1)) {
				long long j=mp[getid(celx[i],cely[i]-1)];
				if(j && co[j]==blue)	G.add(j,i,INF);
			}
			if(valid(celx[i],cely[i]+1)) {
				long long j=mp[getid(celx[i],cely[i]+1)];
				if(j && co[j]==blue)	G.add(j,i,INF);
			}
			if(valid(celx[i]+1,cely[i])) {
				long long j=mp[getid(celx[i]+1,cely[i])];
				if(j && co[j]==blue)	G.add(j,i,INF);
			}
			if(valid(celx[i]-1,cely[i])) {
				long long j=mp[getid(celx[i]-1,cely[i])];
				if(j && co[j]==blue)	G.add(j,i,INF);
			}
		}
		else if(co[i]==red) {
			if(valid(celx[i],cely[i]+1)) {
				long long j=mp[getid(celx[i],cely[i]+1)];
				// if(celx[i]==1 && cely[i]==1 && j)	printf("  --  %lld %lld %lld %lld %lld\n",celx[i],cely[i],celw[i],getid(celx[i],cely[i]),mp[getid(celx[i],cely[i])]);
				if(j && co[j]==blue)	G.add(i,j,min(celw[i],celw[j]));
			}
			if(valid(celx[i],cely[i]-1)) {
				long long j=mp[getid(celx[i],cely[i]-1)];
				// if(celx[i]==1 && cely[i]==1 && j)	printf("  --  %lld %lld %lld %lld %lld\n",celx[i],cely[i],celw[i],getid(celx[i],cely[i]),mp[getid(celx[i],cely[i])]);
				if(j && co[j]==blue)	G.add(i,j,min(celw[i],celw[j]));
			}
			if(valid(celx[i]+1,cely[i])) {
				long long j=mp[getid(celx[i]+1,cely[i])];
				// if(celx[i]==1 && cely[i]==1 && j)	printf("  --  %lld %lld %lld %lld %lld\n",celx[i],cely[i],celw[i],getid(celx[i],cely[i]),mp[getid(celx[i],cely[i])]);
				if(j && co[j]==blue)	G.add(i,j,min(celw[i],celw[j]));
			}
			if(valid(celx[i]-1,cely[i])) {
				long long j=mp[getid(celx[i]-1,cely[i])];
				// if(celx[i]==1 && cely[i]==1 && j)	printf("  --  %lld %lld %lld %lld %lld\n",celx[i],cely[i],celw[i],getid(celx[i],cely[i]),mp[getid(celx[i],cely[i])]);
				if(j && co[j]==blue)	G.add(i,j,min(celw[i],celw[j]));
			}
		}
	}
	printf("%lld\n",G.solve(S,T));
	return 0;
}