python/TangDou/AcWing_TiGao/T3/MinialSpanningTree/1144.cpp

#include <bits/stdc++.h>
using namespace std;
const int N = 1000 * 1000 + 10;
const int M = 2 * N;
int n, m;

// 二维转一维的办法,坐标从(1,1)开始
inline int get(int x, int y) {
    // m为列宽
    return (x - 1) * m + y;
}
struct Edge {
    int a, b, w;
    const bool operator<(const Edge &t) const {
        return w < t.w;
    }
} e[M];
int el;

// 并查集
int p[N];
int find(int x) {
    if (p[x] != x) p[x] = find(p[x]);
    return p[x];
}
// 先连1的边，再连2的边
void create_edges() {
    for (int i = 1; i <= (n - 1) * m; i++)
        e[el++] = {i, i + m, 1}; // i~i+m是一条纵向边

    for (int i = 1; i <= n * m; i++) {
        if (i % m == 0) continue; // 最后一列放过
        e[el++] = {i, i + 1, 2};
    }
    // 因为加进去就是按边权由小到大录入的，所以不用再排序了
}
int main() {
    cin >> n >> m;
    // 建边
    create_edges();

    // 并查集初始化
    for (int i = 1; i <= n * m; i++) p[i] = i;

    int x1, y1, x2, y2;
    // 利用二维转一维办法，将(x,y)映射成节点编号
    // 某些点之间已经有连线了=> 标识这些点已在并查集中
    while (cin >> x1 >> y1 >> x2 >> y2) {
        int a = get(x1, y1), b = get(x2, y2);
        p[find(a)] = find(b);
    }

    int res = 0; // 用Kruskal算法即可
    for (int i = 0; i < el; i++) {
        int a = find(e[i].a), b = find(e[i].b), w = e[i].w;
        if (a != b) p[a] = b, res += w;
    }
    printf("%d\n", res);
    return 0;
}