【TopCoder SRM570】Curvy on Rails







  1. 回路中的每一个点的度一定是 $ 2$
  2. 如果每一个点的度都是 $ 2$ ,那么这一定是由一些回路构成的图

这样的话,这个 $ Subcase$ 就可以通过染色后二分图匹配来解决了

现在来考虑 towns with Curvies

在上一个 $ Subcase$ 中使用的二分图匹配,实际上是对 进行匹配

  1. 横向的度
  2. 纵向的度

对于 towns with Curvies 来说:如果同类的度匹配,那么就得付出代价

将二分图匹配改造成费用流,已建的边费用全部为 $ 0$
然后在同一个格子拆开的点之间连一条双向、流量为 $ 1$、费用为 $ 0$ 的边
这样的话,就相当于两个匹配都使用同一类度的时候得付出 $ 1$ 的代价


#define LL long long
using namespace std;

const int L = 30;
const int N = 2000;
const int M = 50000;
const int INF = 1000000000;

int S,T,head[N],nxt[M],to[M],flow[M],cost[M];
int dx[]={0,1,0,-1,0},dy[]={0,0,1,0,-1};

class Minimum_Cost_Flow{
    int dis[N],sur[N],inq[N];
    queue<int> que;
        inline pair<int,int> MaxFlow() {
        	int ret_cost = 0, ret_flow = 0;
            for (int f=INF,w;SPFA();f=INF) {
                for (w=T;w!=S;w=to[sur[w]^1]) f = min(f, flow[sur[w]]);
                for (w=T;w!=S;w=to[sur[w]^1]) flow[sur[w]] -= f, flow[sur[w]^1] += f;
                ret_cost += dis[T] * f;
                ret_flow += f;
            return make_pair(ret_cost, ret_flow);
        bool SPFA() {
            que.push(S); dis[S] = 0;
            while (!que.empty()) {
                int w = que.front(); que.pop(); inq[w] = 0;
                for (int i=head[w];i;i=nxt[i]) {
                    if (dis[to[i]] > dis[w] + cost[i] && flow[i]) {
                        dis[to[i]] = dis[w] + cost[i];
                        sur[to[i]] = i;
                        if (!inq[to[i]]) inq[to[i]] = 1, que.push(to[i]);
            return dis[T] < INF;

class CurvyonRails {
	int n,m,cnt,E;
	char pat[L][L];
    	int getmin(vector<string> field) {
    	    m = field.size();
    	    n = field[0].size();
    	    for (int j=0;j<m;j++) {
				for (int i=0;i<n;i++) {
					pat[i+1][j+1] = field[j][i];
			for (int j=1;j<=m;j++) {
				for (int i=1;i<=n;i++) {
					if (pat[i][j] == 'w') continue;
					else {
						if (++cnt, i + j & 1) {
							Add_Edge(id(i,j,0), T, 1);
							Add_Edge(id(i,j,1), T, 1);
						} else {
							Add_Edge(S, id(i,j,0), 1);
							Add_Edge(S, id(i,j,1), 1);
							for (int k=1,x,y;k<=4;k++) {
								x = i + dx[k];
								y = j + dy[k];
								if (1 <= x && x <= n && 1 <= y && y <= m) {
									if (x == i) Add_Edge(id(i,j,1), id(x,y,1), 1);
									if (y == j) Add_Edge(id(i,j,0), id(x,y,0), 1);
						if (pat[i][j] == '.') {
							Add_Edge(id(i,j,0), id(i,j,1), 1);
							Add_Edge(id(i,j,1), id(i,j,0), 1);
						if (pat[i][j] == 'C') {
							Add_Edge(id(i,j,0), id(i,j,1), 1, 1);
							Add_Edge(id(i,j,1), id(i,j,0), 1, 1);
			pair<int,int> vout = MCMF.MaxFlow();
			if (vout.second < cnt) return -1;
			else return vout.first;
   		inline int id(int x, int y, int t) {
			return ((y-1)*n + (x-1)) * 2 + 1 + t;   
   		inline void init() {
			E = 1; S = cnt = 0; T = N - 1;
   		inline void Add_Edge(int u, int v, int f, int c = 0) {
			to[++E] = v; nxt[E] = head[u]; head[u] = E; flow[E] = f; cost[E] = c;
			to[++E] = u; nxt[E] = head[v]; head[v] = E; flow[E] = 0; cost[E] = -c;

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