Luogu5021 [NOIP2018]赛道修建

题目蓝链

Description

给你一棵树，树上每条边都有一个边权。你要在上面选出\(m\)条没有重复边的路径，使得选出的最短路径尽量的长

Solution

最短的最长，这显然就是二分答案

然后就直接在树上贪心就可以了，对于每一个点把它的字树尽可能多的两两匹配，最后如果有匹配不了的就与当前点连向父亲的边连起来，这个匹配可以用\(set\)去实现

Code

#include <bits/stdc++.h>

using namespace std;

#define fst first
#define snd second
#define squ(x) ((LL)(x) * (x))
#define debug(...) fprintf(stderr, __VA_ARGS__)

typedef long long LL;
typedef pair<int, int> pii;

inline int read() {
	int sum = 0, fg = 1; char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') fg = -1;
	for (; isdigit(c); c = getchar()) sum = (sum << 3) + (sum << 1) + (c ^ 0x30);
	return fg * sum;
}

typedef set<pii>::iterator It;

const int maxn = 5e4 + 10;

int n, m, cnt, ans, Begin[maxn], Next[maxn << 1], To[maxn << 1], w[maxn << 1], e ;

void Add(int x, int y, int z) { To[++e] = y, Next[e] = Begin[x], Begin[x] = e, w[e] = z; }

int S[maxn], len[maxn];
bool v[maxn];
set<pii> Set;

void dfs(int now, int f) {

	for (int i = Begin[now]; i + 1; i = Next[i]) {
		int son = To[i];
		if (son == f) continue;
		dfs(son, now);
	}

	Set.clear(), S[0] = 0;
	for (int i = Begin[now]; i + 1; i = Next[i]) {
		int son = To[i];
		if (son == f) continue;
		S[++S[0]] = len[son] + w[i];
	}

	sort(S + 1, S + S[0] + 1);
	It lst = Set.begin();
	for (int i = 1; i <= S[0]; i++) {
		if (S[i] >= ans) { ++cnt, v[i] = 1; continue; }
		lst = Set.insert(lst, (pii){S[i], i}), v[i] = 0;
	}

	for (int i = 1; i <= S[0]; i++) {
		if (v[i]) continue;
		It pos = Set.lower_bound((pii){ans - S[i], 0});
		if (pos == Set.end() || (*pos) == (pii){S[i], i}) continue;
		v[i] = 1, v[pos->snd] = 1, ++cnt;
		Set.erase((pii){S[i], i}), Set.erase(pos);
	}

	len[now] = 0;
	for (int i = S[0]; i >= 1; i--)
		if (!v[i]) {
			len[now] = S[i];
			break;
		}
}

bool check(int mid) {
	ans = mid, cnt = 0;
	dfs(1, 0);
	return cnt >= m;
}

int main() {
	freopen("track.in", "r", stdin);
	freopen("track.out", "w", stdout);

	e = -1, memset(Begin, -1, sizeof Begin);
	n = read(), m = read();
	for (int i = 1; i < n; i++) {
		int x = read(), y = read(), z = read();
		Add(x, y, z), Add(y, x, z);
	}

	int l = 1, r = 5e8;
	while (l <= r) {
		int mid = (l + r) >> 1;
		if (check(mid)) l = mid + 1;
		else r = mid - 1;
	}

	cout << r << endl;

	return 0;
}

Summary

这道题一定要注意\(set\)的使用方法 考场上写挂了

要先用一个数组把\(set\)里的元素存起来，然后去遍历这个数组。在\(set\)中删除一个元素的时候，直接对这个元素的编号打一个\(vis\)标记就可以了