Codeforces Gym 100203I I WIN 最大流

原题链接：http://codeforces.com/gym/100203/attachments/download/1702/statements.pdf

题解

首先寻找每个I，然后枚举形状，如果匹配的话，就将源点连一条边到当前匹配的W，再从W连条边到I，I需要拆点，然后将拆点后面的那个点连接到N，从N连接到汇点。所有边的容量都是1。需要注意避免产生重边。然后最大流就是答案。

代码

#include<iostream>
#include<stack>
#include<vector>
#include<cstring>
#include<string>
#include<algorithm>
#include<queue>
#define MAX_V 1500
#define MAX_N 10004
#define INF 2500005
using namespace std;

struct edge{int to,cap,rev;bool isRev;};

vector<edge> G[MAX_N];
int level[MAX_V];
int iter[MAX_V];

void add_edge(int from,int to,int cap) {
    G[from].push_back((edge) {to, cap, G[to].size(),0});
    G[to].push_back((edge) {from, 0, G[from].size() - 1,1});
}

void bfs(int s) {
    memset(level, -1, sizeof(level));
    queue<int> que;
    level[s] = 0;
    que.push(s);
    while (!que.empty()) {
        int v = que.front();
        que.pop();
        for (int i = 0; i < G[v].size(); i++) {
            edge &e = G[v][i];
            if (e.cap > 0 && level[e.to] < 0) {
                level[e.to] = level[v] + 1;
                que.push(e.to);
            }
        }
    }
}

int dfs(int v,int t,int f) {
    if (v == t)return f;
    for (int &i = iter[v]; i < G[v].size(); i++) {
        edge &e = G[v][i];
        if (e.cap > 0 && level[v] < level[e.to]) {
            int d = dfs(e.to, t, min(f, e.cap));
            if (d > 0) {
                e.cap -= d;
                G[e.to][e.rev].cap += d;
                return d;
            }
        }
    }
    return 0;
}

int max_flow(int s,int t) {
    int flow = 0;
    for (; ;) {
        bfs(s);
        if (level[t] < 0)return flow;
        memset(iter, 0, sizeof(iter));
        int f;
        while ((f = dfs(s, t, INF)) > 0) {
            flow += f;
        }
    }
}

string ss[30];
int n,m;
//int dx[4]={0,1,0,-1},dy[4]={1,0,-1,0};

int Hash(int x,int y) {
    return x * m + y;
}

int S=1234;
int T=1313;

bool vis[MAX_V];

void AddEdges(int W,int I,int N) {
    if (!vis[W])
        add_edge(S, W, 1);
    add_edge(W, I, 1);
    add_edge(I + n * m + 5, N, 1);
    if (!vis[N])
        add_edge(N, T, 1);
    vis[W] = vis[N] = 1;
}

int main() {
    cin.sync_with_stdio(false);
    cin >> n >> m;
    for (int i = 0; i < n; i++)
        cin >> ss[i];
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) {
            if (ss[i][j] != 'I')continue;
            add_edge(Hash(i, j), Hash(i, j) + n * m+5, 1);
            int u, v;
            u = j - 1;
            v = j + 1;
            if (u >= 0 && v < m) {
                if (ss[i][u] == 'N' && ss[i][v] == 'W')swap(u, v);
                if (ss[i][u] == 'W' && ss[i][v] == 'N')
                    AddEdges(Hash(i, u), Hash(i, j), Hash(i, v));
            }
            u = i - 1;
            v = i + 1;
            if (u >= 0 && v < n) {
                if (ss[u][j] == 'N' && ss[v][j] == 'W')swap(u, v);
                if (ss[u][j] == 'W' && ss[v][j] == 'N')
                    AddEdges(Hash(u, j), Hash(i, j), Hash(v, j));
            }
            u = j - 1;
            v = i - 1;
            if (u >= 0 && v >= 0) {
                if (ss[i][u] == 'N' && ss[v][j] == 'W')
                    AddEdges(Hash(v, j), Hash(i, j), Hash(i, u));
                if (ss[i][u] == 'W' && ss[v][j] == 'N')
                    AddEdges(Hash(i, u), Hash(i, j), Hash(v, j));
            }
            u = i - 1;
            v = j + 1;
            if (u >= 0 && v < m) {
                if (ss[u][j] == 'N' && ss[i][v] == 'W')
                    AddEdges(Hash(i, v), Hash(i, j), Hash(u, j));
                if (ss[u][j] == 'W' && ss[i][v] == 'N')
                    AddEdges(Hash(u, j), Hash(i, j), Hash(i, v));
            }
            u = j + 1;
            v = i + 1;
            if (u < m && v < n) {
                if (ss[i][u] == 'N' && ss[v][j] == 'W')
                    AddEdges(Hash(v, j), Hash(i, j), Hash(i, u));
                if (ss[i][u] == 'W' && ss[v][j] == 'N')
                    AddEdges(Hash(i, u), Hash(i, j), Hash(v, j));
            }
            u = i + 1;
            v = j - 1;
            if (u < n && v >= 0) {
                if (ss[u][j] == 'N' && ss[i][v] == 'W')
                    AddEdges(Hash(i, v), Hash(i, j), Hash(u, j));
                if (ss[u][j] == 'W' && ss[i][v] == 'N')
                    AddEdges(Hash(u, j), Hash(i, j), Hash(i, v));
            }
        }
    int f = max_flow(S, T);
    cout << f << endl;
    return 0;
}