Luogu P4055 [JSOI2009]游戏

题目描述

Solution

后手为先手选择起点,问后手是否必胜

显然只要这张二分图没有完美匹配,就一定存在不必须点

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#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <cmath>
#include <iomanip>
#define maxn 10010
#define maxm 110
#define INF 1000000000
using namespace std;

int dx[] = { 0, 0, -1, 1 };
int dy[] = { 1, -1, 0, 0 };

int n, m;

inline int id(int x, int y) { return (x - 1) * m + y; }
inline pair<int, int> Id(int v) {
int x = v / m + 1, y = v % m;
if (y == 0) y += m, --x;
return { x, y };
}

int g[maxm][maxn];

char c[maxm];

struct Edge {
int to, next, w;
} e[1000000]; int c1, head[maxn];
inline void add_edge(int u, int v, int w) {
e[c1].to = v; e[c1].w = w;
e[c1].next = head[u]; head[u] = c1++;
}

inline void Add_edge(int u, int v, int w) {
add_edge(u, v, w); add_edge(v, u, 0);
}

int dep[maxn], s, t;
bool bfs() {
fill(dep, dep + maxn, 0); dep[s] = 1;
queue<int> Q; Q.push(s);
while (!Q.empty()) {
int u = Q.front(); Q.pop();
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to, w = e[i].w;
if (w > 0 && !dep[v]) {
dep[v] = dep[u] + 1;
Q.push(v); if (v == t) return 1;
}
}
}
return 0;
}

int dfs(int u, int _w) {
if (u == t || !_w) return _w;
int s = 0;
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to, w = e[i].w;
if (w > 0 && dep[v] == dep[u] + 1) {
int di = dfs(v, min(_w - s, w));
e[i].w -= di; e[i ^ 1].w += di;
s += di; if (s == _w) break;
}
}
if (s < _w) dep[u] = 0;
return s;
}

int mf;
void dinic() {
while (bfs()) mf += dfs(s, INF);
}

vector<pair<int, int>> ans; bool vis[maxn];
void Dfs(int u, int f) {
vis[u] = 1; pair<int, int> t = Id(u);
if (t.first + t.second & 1 ^ f && u > 0 && u < n * m + 1) ans.push_back(t);
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to, w = e[i].w;
if (w == f && !vis[v]) Dfs(v, f);
}
}

int main() { fill(head, head + maxn, -1);
ios::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);

cin >> n >> m; s = 0; t = n * m + 1;
for (int i = 1; i <= n; ++i) {
cin >> c + 1;
for (int j = 1; j <= m; ++j)
if (c[j] == '.') g[i][j] = 1;
} int sum = 0;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= m; ++j) {
if (!g[i][j]) continue; ++sum;
if (i + j & 1) { Add_edge(id(i, j), t, 1); continue; }
Add_edge(s, id(i, j), 1);
for (int k = 0; k < 4; ++k) {
int x = i + dx[k], y = j + dy[k];
if (x < 1 || x > n || y < 1 || y > m || !g[x][y]) continue;
Add_edge(id(i, j), id(x, y), 1);
}
}
dinic();
if (mf == sum) return cout << "LOSE\n", 0;
cout << "WIN\n";
Dfs(s, 1); Dfs(t, 0); sort(ans.begin(), ans.end());
for (auto u : ans) cout << u.first << " " << u.second << "\n";
return 0;
}