题解【洛谷P2323】 [HNOI2006]公路修建问题

题面

题解

跑两遍\(Kruskal\)，第一次找出\(k\)条一级公路，第二次找出\(n - k - 1\)条二级公路，直接计算\(MST\)的权值之和即可。

代码

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <cctype>
#define gI gi
#define itn int
#define File(x) freopen(x".in","r",stdin);freopen(x".out","w",stdout)

using namespace std;

inline int gi()
{
    int f = 1, x = 0; char c = getchar();
    while (c < '0' || c > '9') {if (c == '-') f = -1; c = getchar();}
    while (c >= '0' && c <= '9') {x = x * 10 + c - '0'; c = getchar();}
    return f * x;
}

int n, m, fa[20003], k, vis[20003];
struct OIer
{
	int a, b, c1, c2, id;
} d[20003];
struct STO_Tham
{
	int Id, Tham;
} ans[20003];

int getf(int u)
{
	if (fa[u] == u) return u;
	return fa[u] = getf(fa[u]);
}

int maxx = 900000000, maxy, tot;

inline bool cmp(OIer x, OIer y) {return x.c1 < y.c1;}

inline bool cmp1(OIer x, OIer y) {return x.c2 < y.c2;}

inline bool OrzTham(STO_Tham x, STO_Tham y) {return x.Id < y.Id;}

int main()
{
	//File("P2323");
	n = gi(), k = gi(), m = gi(); --m;
	for (int i = 1; i <= m; i+=1)
	{
		d[i].a = gi(), d[i].b = gi(), d[i].c1 = gi(), d[i].c2 = gi(), d[i].id = i;
	}
	for (int i = 1; i <= n; i+=1) fa[i] = i;
	sort(d + 1, d + 1 + m, cmp);
	for (int i = 1; i <= m; i+=1)
	{
		int u = getf(d[i].a), v = getf(d[i].b);
		if (u != v)
		{
			fa[u] = v;
			ans[++tot].Id = d[i].id, ans[tot].Tham = 1;
			maxy = max(maxy, d[i].c1);
			if (tot == k) break;
		}
	}
	sort(d + 1, d + 1 + m, cmp1);
	for (int i = 1; i <= m; i+=1)
	{
		int u = getf(d[i].a), v = getf(d[i].b);
		if (u != v)
		{
			fa[u] = v;
			ans[++tot].Id = d[i].id, ans[tot].Tham = 2;
			maxy = max(maxy, d[i].c2);
			if (tot == n - 1) break;
		}
	}
	sort(ans + 1, ans + 1 + tot, OrzTham);
	printf("%d\n", maxy);
	for (int i = 1; i < n; i+=1) printf("%d %d\n", ans[i].Id, ans[i].Tham);
	return 0;
}