棋盘覆盖

AcWing-372-棋盘覆盖

分析

见《进阶指南》第426页。

实现

#include <iostream>
#include <cstring>
using namespace std;

const int N = 110, M = 10010;
struct edge {
    int to, next;
};
edge e[4 * M];
int idx, head[M];
int n, m;
int a[N][N];
int ln, rn;
bool mark[M];
int match[M];

void add_edge (int u, int v) {
    e[idx].to = v;
    e[idx].next = head[u];
    head[u] = idx ++;
}
bool dfs (int cur) {
    for (int i = head[cur]; i != -1; i = e[i].next) {
        int to = e[i].to;
        if (mark[to] == true) continue;
        mark[to] = true;
        if (match[to] == 0 || dfs(match[to]) == true) {
            match[to] = cur;
            return true;
        }
    }
    return false;
}

int main () {
    memset(head, -1, sizeof(head));
    cin >> n >> m;
    for (int i = 1, x, y; i <= m; ++ i) {
        cin >> x >> y;
        a[x][y] = -1;
    }

    for (int i = 1; i <= n; ++ i)
        for (int j = 1; j <= n; ++ j)
            if ((i + j) % 2 == 0 && a[i][j] != -1)
                a[i][j] = ++ ln;
    for (int i = 1; i <= n; ++ i)
        for (int j = 1; j <= n; ++ j)
            if ((i + j) % 2 == 1 && a[i][j] != -1)
                a[i][j] = ln + (++ rn);
    for (int i = 1; i <= n; ++ i) {
        for (int j = 1; j <= n; ++ j) {
            if (a[i][j] == -1) continue;
            if (j + 1 <= n && a[i][j + 1] != -1) {
                add_edge(a[i][j], a[i][j + 1]);
                add_edge(a[i][j + 1], a[i][j]);
            }
            if (i + 1 <= n && a[i + 1][j] != -1) {
                add_edge(a[i][j], a[i + 1][j]);
                add_edge(a[i + 1][j], a[i][j]);
            }
        }
    }
    int res = 0;
    for (int i = 1; i <= ln; ++ i) {
        memset(mark, 0, sizeof(mark));
        if (dfs(i) == true) ++ res;
    }
    cout << res << endl;
    return 0;
}