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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#518827#1067. TOLLVectorLi100 0ms3644kbC++175.5kb2024-08-14 12:39:342024-08-14 12:39:34

Judging History

你现在查看的是测评时间为 2024-08-14 12:39:34 的历史记录

  • [2024-11-07 12:41:18]
  • 管理员手动重测本题所有提交记录
  • 测评结果:16
  • 用时:1ms
  • 内存:5828kb
  • [2024-08-14 12:39:34]
  • 评测
  • 测评结果:100
  • 用时:0ms
  • 内存:3644kb
  • [2024-08-14 12:39:34]
  • 提交

answer

#include <bits/stdc++.h>
#define long long long

using namespace std;

struct union_find {
	vector<int> s, p;

	union_find(int n = 0) : s(n, 1), p(n) {
		iota(p.begin(), p.end(), 0);
	}

	int find(int u) {
		if (p[u] != u) {
			p[u] = find(p[u]);
		}
		return p[u];
	}

	bool merge(int u, int v) {
		u = find(u);
		v = find(v);
		if (u == v) {
			return false;
		}
		if (s[u] < s[v]) {
			swap(u, v);
		}
		p[v] = u;
		s[u] = s[u] + s[v];
		return true;
	}

	bool same(int u, int v) {
		return find(u) == find(v);
	}

	int size(int u) {
		u = find(u);
		return s[u];
	}
};

/*
思维不难,但是一定一定要思路清晰。

1. 看到 k <= 20,想一想 bitmasks,如果想到了,不难想出一种简单的暴力:
我们枚举每一条需要选的边,然后强制把它加到树上(当然,如果出现环直接 pass)
再跑最小生成树,用边去限定我们那些没有确定边权的边(用了一个经典的结论),
时间复杂度为 2^k * mlogn,可以拿到约 56 分。

2. 我们发现,这整个过程中,总有一些边会加入到最小生成树,这也很好理解。
我们一共就 k 条可以选择的边,这些边能连起来的连通块就 k + 1 个,而图
一共有 n 个连通块,很显然一定是会有很多很多边需要连起来的。所以,我们
直接将所有 k 条边加入,然后再跑一边最小生成树,这个时候选择的边是一定
会一直选下去的。

3. 很自然的,我们缩一下点(这个使用并查集可以维护),我们现在就剩下了 k + 1
个点,再把剩余的那些原边跑一边最小生成树,这样子,我们就确保了多余的边只有
k 条,再算上原来的 k 条边,一共是 k * 2 条,瞎搞都可以。
*/

const int N = (int) 1E5;
const int M = (int) 3E5;
const int K = 20 + 20;
const int A = numeric_limits<int>::max();

int n, m, k;

bool t1[M];
array<int, 3> e1[M];
array<int, 2> e2[K];
array<int, 3> e3[K];
vector<int> e4[K + 1];

int a[N];
long e[K + 1];

void Kruskal1() {
	union_find s(n);
	for (int i = 0; i < k; i++) {
		int u = e2[i][0], v = e2[i][1];
		s.merge(u, v);
	}
	for (int i = 0; i < m; i++) {
		int u = e1[i][1], v = e1[i][2];
		t1[i] = s.merge(u, v);
	}
}

int root;

void Kruskal2() {
	union_find s1(n);
	for (int i = 0; i < m; i++) {
		int u = e1[i][1], v = e1[i][2];
		if (t1[i] == true) {
			s1.merge(u, v);
		}
	}
	int c = 0;
	vector<int> p(n, -1);
	for (int i = 0; i < n; i++) {
		if (s1.find(i) == i) {
			p[i] = c;
			c = c + 1;
		}
	}
	assert(c == k + 1);
	for (int i = 0; i < k; i++) {
		int u = e2[i][0], v = e2[i][1];
		u = p[s1.find(u)];
		v = p[s1.find(v)];
		e2[i] = {u, v};
	}
	int t = 0;
	union_find s2(k + 1);
	for (int i = 0; i < m; i++) {
		int u = e1[i][1], v = e1[i][2], w = e1[i][0];
		if (t1[i] == false) {
			int x = p[s1.find(u)];
			int y = p[s1.find(v)];
			if (s2.merge(x, y)) {
				e3[t] = {w, x, y};
				t = t + 1;
			}
		}
	}
	assert(t == k);
	for (int i = 0; i < n; i++) {
		int u = p[s1.find(i)];
		e[u] = e[u] + a[i];
	}
	root = p[s1.find(0)];
}

int p[K + 1], d[K + 1];
int g[K + 1];
long t[K + 1];

void DFS(int u) {
	t[u] = e[u];
	for (auto v : e4[u]) {
		if (v != p[u]) {
			p[v] = u;
			d[v] = d[u] + 1;
			DFS(v);
			t[u] = t[u] + t[v];
		}
	}
}

void check(int u, int v, int w) {
	while (u != v) {
		if (d[u] > d[v]) {
			swap(u, v);
		}
		g[v] = min(g[v], w);
		v = p[v];
	}
}

void solve() {
	cin >> n >> m >> k;
	for (int i = 0; i < m; i++) {
		int u, v, w;
		cin >> u >> v >> w;
		u = u - 1, v = v - 1;
		e1[i] = {w, u, v};
	}
	for (int i = 0; i < k; i++) {
		int u, v;
		cin >> u >> v;
		u = u - 1, v = v - 1;
		e2[i] = {u, v};
	}
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}

	sort(e1, e1 + m);
	Kruskal1();
	Kruskal2();

	// for (int i = 0; i < k; i++) {
	// 	cout << e2[i][0] << " " << e2[i][1] << "\n";
	// }
	// for (int i = 0; i < k; i++) {
	// 	cout << e3[i][1] << " " << e3[i][2] << " " << e3[i][0] << "\n";
	// }
	// return;

	long c = 0;
	for (int S = 0; S < (1 << k); S++) {
		union_find s(k + 1);
		bool f = true;
		for (int i = 0; i < k; i++) {
			if (S >> i & 1) {
				int u = e2[i][0], v = e2[i][1];
				if (not s.merge(u, v)) {
					f = false;
					break;
				}
			}
		}
		if (not f) {
			continue;
		}

		vector<bool> t3(k);
		for (int i = 0; i < k; i++) {
			int u = e3[i][1], v = e3[i][2];
			t3[i] = s.merge(u, v);
		}

		for (int i = 0; i < k + 1; i++) {
			e4[i] = vector<int>();
		}
		for (int i = 0; i < k; i++) {
			if (S >> i & 1) {
				int u = e2[i][0], v = e2[i][1];
				e4[u].push_back(v);
				e4[v].push_back(u);
			}
		}
		for (int i = 0; i < k; i++) {
			if (t3[i] == true) {
				int u = e3[i][1], v = e3[i][2];
				e4[u].push_back(v);
				e4[v].push_back(u);
			}
		}

		p[root] = -1;
		d[root] = 0;
		DFS(root);
		// g[i] 表示节点 i 到节点 i 的父节点的边权最大是多少,初始的,为 MAX 即可
		fill(g, g + k + 1, A);
		for (int i = 0; i < k; i++) {
			if (t3[i] == false) {
				int u = e3[i][1], v = e3[i][2], w = e3[i][0];
				check(u, v, w);
			}
		}

		long b = 0;
		for (int i = 0; i < k; i++) {
			if (S >> i & 1) {
				int u = e2[i][0], v = e2[i][1];
				int x = d[u] > d[v] ? u : v;
				b = b + t[x] * g[x];
			}
		}

		c = max(c, b);
	}
	cout << c << "\n";
}

int32_t main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int t;
	t = 1;
	for (int i = 0; i < t; i++) {
		solve();
	}
	return 0;
}

详细

Subtask #1:

score: 100
Accepted

Test #1:

score: 100
Accepted
time: 0ms
memory: 3584kb

input:

10 20 1
9 10 378587
3 10 283693
10 1 276961
8 1 828871
6 3 814717
3 5 701468
4 8 116841
7 5 859891
2 5 973550
9 2 460881
6 5 260184
8 9 895822
3 8 864166
10 4 746770
6 9 818592
7 1 748443
6 2 308698
6 7 170433
6 1 854347
2 10 641070
8 2
739814 240233 280283 628215 946109 596323 536584 590185 294679 ...

output:

909864568000

result:

ok single line: '909864568000'

Test #2:

score: 100
Accepted
time: 0ms
memory: 3644kb

input:

8 20 1
7 2 707898
6 4 739797
6 1 921019
7 3 739954
2 6 26438
5 4 242350
8 5 147225
7 6 53026
2 5 18161
5 1 319852
8 1 928770
6 5 291033
6 8 870601
3 5 596483
4 8 769617
1 4 516480
3 8 960359
2 3 672639
7 8 951165
3 4 911419
7 5
485318 528016 310567 880656 812984 803814 654959 289193

output:

34729855934

result:

ok single line: '34729855934'

Subtask #2:

score: 0
Runtime Error

Dependency #1:

100%
Accepted

Test #3:

score: 100
Accepted
time: 0ms
memory: 3640kb

input:

26 50 10
10 16 402572
16 17 883196
13 26 698082
5 16 96211
11 16 642512
16 22 44910
5 2 928962
3 24 834337
2 12 56104
18 1 851938
4 14 441768
6 21 793020
25 7 341805
7 22 664203
25 19 671175
8 7 362800
7 6 377915
21 20 975066
8 4 264657
4 26 445906
9 26 821755
18 9 285249
3 17 120207
11 15 816139
23...

output:

26876914464865

result:

ok single line: '26876914464865'

Test #4:

score: 0
Runtime Error

input:

30 50 10
24 16 369496
5 2 882195
24 23 579700
24 1 795457
7 10 903779
13 21 98625
27 24 857438
2 26 795121
21 15 117380
10 6 168591
12 2 439190
4 3 631680
18 24 785210
2 16 558732
22 26 215162
4 2 399966
15 2 203973
1 30 206852
12 10 263496
28 29 122008
6 19 593874
1 28 729019
11 14 346091
11 13 859...

output:


result:


Subtask #3:

score: 0
Skipped

Dependency #1:

100%
Accepted

Dependency #2:

0%

Subtask #4:

score: 0
Skipped

Dependency #1:

100%
Accepted

Dependency #2:

0%

Subtask #5:

score: 0
Skipped

Dependency #1:

100%
Accepted

Dependency #2:

0%

Subtask #6:

score: 0
Skipped

Dependency #1:

100%
Accepted

Dependency #2:

0%