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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
#408232#6421. Degree of Spanning TreeNelofus#AC ✓162ms14184kbC++203.7kb2024-05-09 21:31:162024-05-09 21:31:17

Judging History

你现在查看的是最新测评结果

  • [2024-05-09 21:31:17]
  • 评测
  • 测评结果:AC
  • 用时:162ms
  • 内存:14184kb
  • [2024-05-09 21:31:16]
  • 提交

answer

// Code by Heratino & Nelofus
// Narcissus & どうか安寧な記憶を

#include <bits/stdc++.h>
using i64 = long long;

//{{{星光闪耀
template<typename Ta, typename Tb>
inline void chkmax(Ta &a, const Tb &b) {if (a < b)	a = b;}
template<typename Ta, typename Tb>
inline void chkmin(Ta &a, const Tb &b) {if (a > b)	a = b;}
char buf[1 << 20], *P1, *P2;
inline char gc() {
	if (P1 == P2)
		P2 = (P1 = buf) + fread(buf, 1, 1 << 20, stdin);
	return P1 == P2 ? EOF : *P1++;
}
template<typename T>
inline void read(T &ans) {
	ans = 0;
	T w = 1;
	char c = gc();
	while (!isdigit(c)) {
		if (c == '-')	w = -1;
		c = gc();
	}
	while (isdigit(c)) {
		ans = (ans << 3) + (ans << 1) + (c ^ 48);
		c = gc();
	}
	ans *= w;
}
template<typename T, typename ...Ts>
void read(T &a, Ts&... other) {
	read(a);
	read(other...);
}
//}}}

constexpr int N = 2e5 + 10;

std::pair<int, int> E[N];
bool isAnswer[N];
int deg[N];
std::vector<int> G[N];
int n, m;

inline int get(int u, int x) {return u ^ E[x].first ^ E[x].second;}

struct DSU_ {
	int fa[N], siz[N];
	void init(int _n) {
		for (int i = 1; i <= _n; i++)
			fa[i] = i, siz[i] = 1;
	}
	inline int find(int x) {
		return x == fa[x] ? x : fa[x] = find(fa[x]);
	}
	inline bool merge(int u, int v) {
		u = find(u), v = find(v);
		if (u == v)
			return false;
		if (siz[u] < siz[v])
			siz[v] += siz[u], fa[u] = v;
		else
			siz[u] += siz[v], fa[v] = u;
		return true;
	}
} DSU;

int tot = 0;

void clear() {
	tot = 0;
	DSU.init(n);
	memset(isAnswer + 1, 0, m * sizeof(bool));
	memset(deg + 1, 0, n * sizeof(int));
	for (int i = 1; i <= n; i++)
		G[i].clear();
}

void dfs(int u, int fa) {
	for (const int &i : G[u]) {
		int v = get(u, i);
		if (v == fa)
			continue;
		DSU.fa[v] = DSU.fa[u];
		dfs(v, u);
	}
}

void solve() {
	read(n, m);
	clear();

	for (int i = 1; i <= m; i++) {
		int u, v;
		read(u, v);
		if (u == v)
			continue;
		if (u > v)
			std::swap(u, v);
		E[++tot] = std::make_pair(u, v);
	}

	std::sort(E + 1, E + 1 + tot);
	m = std::unique(E + 1, E + 1 + tot) - E - 1;

	for (int i = 1; i <= m; i++) {
		const auto &[u, v] = E[i];
		if (DSU.merge(u, v)) {
			G[u].push_back(i);
			G[v].push_back(i);
			isAnswer[i] = true;
			deg[u]++, deg[v]++;
		}
	}
	int rt = 0;
	for (int i = 1; i <= n; i++)
		if (deg[i] > n / 2)
			rt = i;
	if (!rt) {
		std::cout << "Yes\n";
		for (int i = 1; i <= m; i++) {
			const auto &[u, v] = E[i];
			if (isAnswer[i])
				std::cout << u << ' ' << v << '\n';
		}
		return ;
	}

	DSU.init(n);
	for (const int &i : G[rt]) {
		dfs(get(rt, i), rt);
	}
	for (int i = 1; i <= m; i++) {
		if (isAnswer[i]) {
			continue;
		}
		auto [u, v] = E[i];
		if (u == rt || v == rt || DSU.find(u) == DSU.find(v))
			continue;
		int sonu = DSU.find(u);
		int sonv = DSU.find(v);
		deg[rt]--, deg[u]++, deg[v]++, deg[sonu]--;
		if (deg[u] > n / 2 || deg[v] > n / 2) {
			std::swap(u, v);
			std::swap(sonu, sonv);
			deg[sonu]--, deg[sonv]++;
		}
		if (deg[u] > n / 2 || deg[v] > n / 2) {
			deg[u]--, deg[v]--, deg[sonu]++, deg[rt]++;
			continue;
		}
		DSU.fa[sonu] = DSU.fa[sonv];
		isAnswer[i] = true;
		auto pr = std::make_pair(std::min(rt, sonu), std::max(rt, sonu));
		int t = std::lower_bound(E + 1, E + 1 + m, pr) - E;

		assert(E[t] == pr);

		isAnswer[t] = false;
		if (deg[rt] <= n / 2)
			break;
	}
	if (deg[rt] <= n / 2) {
		std::cout << "Yes\n";
		for (int i = 1; i <= m; i++) {
			if (isAnswer[i])
				std::cout << E[i].first << ' ' << E[i].second << '\n';
		}
	} else {
		std::cout << "No\n";
	}
}

int main() {
#ifdef HeratinoNelofus
	freopen("input.txt", "r", stdin);
#endif

	int T;
	read(T);
	while (T--) {
		solve();
	}
	return 0;
}

詳細信息

Test #1:

score: 100
Accepted
time: 0ms
memory: 5636kb

input:

2
6 9
1 2
1 3
1 4
2 3
2 4
3 4
4 5
4 6
4 6
3 4
1 3
2 3
3 3
1 2

output:

Yes
1 2
1 3
1 4
4 5
4 6
No

result:

ok 2 cases

Test #2:

score: 0
Accepted
time: 100ms
memory: 9552kb

input:

11140
10 15
9 6
5 7
6 5
2 3
7 5
7 5
3 10
9 7
5 5
9 1
7 5
2 8
7 5
4 3
6 2
9 19
3 7
3 9
2 8
2 8
3 6
5 1
1 8
8 9
8 3
4 8
5 5
3 1
4 3
1 3
8 6
1 3
7 4
4 3
8 8
12 20
10 2
5 5
2 4
3 3
3 3
5 11
9 2
5 5
7 12
11 3
3 3
3 5
5 3
3 1
4 6
7 11
6 8
4 5
6 12
6 5
8 18
4 2
4 3
2 4
2 4
4 3
4 8
2 2
6 7
2 4
6 2
1 4
8 7
4...

output:

Yes
1 9
2 3
2 6
2 8
3 4
3 10
5 6
5 7
6 9
Yes
1 3
1 5
1 8
2 8
3 6
3 7
3 9
4 7
Yes
1 3
2 4
2 9
2 10
3 5
3 11
4 5
4 6
6 8
6 12
7 11
Yes
1 4
2 4
2 6
2 7
3 4
3 5
4 8
Yes
1 2
1 5
2 3
2 9
3 4
5 6
5 7
7 8
Yes
1 4
1 6
1 7
1 9
2 3
2 5
2 6
2 10
8 10
Yes
1 3
1 7
2 3
2 4
2 6
3 5
Yes
1 4
1 6
1 10
1 11
1 12
1 13
2...

result:

ok 11140 cases

Test #3:

score: 0
Accepted
time: 149ms
memory: 14044kb

input:

5
100000 197799
37555 22723
91160 32701
6451 4416
43186 26432
9750 82955
28292 33907
91534 78442
17771 67061
40351 28116
21494 23114
34672 66640
72636 95093
13033 6538
53698 87837
79541 71230
53985 63500
84753 5378
67971 56748
90951 20169
4465 97293
18331 53564
41043 95738
48579 96439
90865 7526
391...

output:

Yes
1 1295
1 34457
1 45338
1 51912
1 79669
1 97056
2 23589
2 58889
3 6936
3 29964
3 44515
3 51002
3 80631
4 19083
4 35140
4 42887
4 92524
5 54719
5 57297
5 81078
5 95985
6 484
6 5405
6 86612
6 87773
7 65534
7 98458
8 4586
8 30625
8 32122
8 35804
8 48558
8 87681
9 6925
9 69470
9 79888
9 92777
10 6204...

result:

ok 5 cases

Test #4:

score: 0
Accepted
time: 93ms
memory: 14184kb

input:

5
100000 100000
98195 31806
98195 70169
92153 98195
98195 46320
94369 56771
94369 49988
74295 98195
33796 98195
89903 94369
98195 1814
82388 98195
10189 94369
98195 6267
29845 98195
22425 94369
6241 98195
98195 33204
66516 98195
94369 71364
26277 94369
94369 94722
94369 25349
14629 98195
9329 98195
...

output:

Yes
1 98195
2 98195
3 98195
4 94369
5 94369
6 98195
7 94369
8 98195
9 94369
10 98195
11 98195
12 94369
13 98195
14 94369
15 94369
16 94369
17 98195
18 98195
19 98195
20 94369
21 94369
22 94369
23 94369
24 94369
25 94369
26 94369
27 94369
28 94369
29 98195
30 94369
31 94369
32 98195
33 98195
34 94369...

result:

ok 5 cases

Test #5:

score: 0
Accepted
time: 162ms
memory: 14152kb

input:

5
100000 149998
50735 5447
50735 24875
15119 49666
50735 30352
44756 49555
26546 32695
98445 50735
71657 50735
92212 50735
50735 19382
30935 50735
43688 46767
54630 54562
31371 50735
48877 50735
78593 76833
74317 37258
50735 48236
67116 50735
36579 50735
37536 44353
50735 46602
35088 29568
86657 507...

output:

Yes
1 35019
1 50735
2 15015
2 50735
3 50735
3 60958
4 40777
4 50735
5 50200
5 50735
6 22341
6 50735
7 50735
7 89814
8 2615
8 50735
9 50735
9 63844
10 25168
10 50735
11 1279
11 50735
12 27968
12 50735
13 36941
13 50735
14 50735
14 90189
15 50735
15 52058
16 41994
16 50735
17 11154
17 50735
18 50735
1...

result:

ok 5 cases

Test #6:

score: 0
Accepted
time: 83ms
memory: 13724kb

input:

11102
14 14
9 10
10 14
9 11
10 2
9 14
9 5
10 13
9 8
4 9
3 10
10 1
12 10
10 6
9 7
6 6
3 2
3 5
2 6
1 6
3 4
3 6
5 5
3 2
2 1
4 5
2 5
5 3
8 8
5 6
4 6
8 6
8 4
6 1
8 3
2 8
7 8
12 12
8 12
12 2
4 12
9 12
12 3
1 12
1 8
6 8
11 8
7 8
8 10
12 5
15 15
9 15
6 15
13 8
15 3
8 11
15 12
8 2
15 4
8 10
15 8
15 14
8 4
7 ...

output:

Yes
1 10
2 10
3 10
4 9
5 9
6 10
7 9
8 9
9 10
9 11
9 14
10 12
10 13
Yes
1 6
2 3
2 6
3 4
3 5
Yes
1 2
2 3
3 5
4 5
Yes
1 6
2 8
3 8
4 6
4 8
5 6
7 8
Yes
1 8
1 12
2 12
3 12
4 12
5 12
6 8
7 8
8 10
8 11
9 12
Yes
1 15
2 8
3 15
4 8
4 15
5 8
6 15
7 8
8 10
8 11
8 13
9 15
12 15
14 15
Yes
1 9
2 3
3 6
3 7
3 10
3 11...

result:

ok 11102 cases

Test #7:

score: 0
Accepted
time: 117ms
memory: 14092kb

input:

11102
14 19
9 3
3 6
8 3
2 14
7 3
11 3
13 9
3 14
3 5
2 3
7 4
1 10
13 3
4 3
3 1
3 10
12 8
11 6
3 12
11 15
9 11
10 7
1 2
9 6
11 2
11 10
8 11
11 5
3 8
11 4
11 3
11 7
1 11
5 4
6 11
5 6
1 2
4 3
3 5
1 3
5 4
3 2
12 16
8 11
12 10
12 3
5 7
12 5
1 12
9 4
12 2
6 12
12 8
10 1
12 11
7 12
12 9
3 2
4 12
6 7
3 1
6 3...

output:

Yes
1 3
1 10
2 3
2 14
3 5
3 7
3 11
3 12
3 13
4 7
6 11
8 12
9 13
Yes
1 2
1 11
3 8
3 11
4 5
4 11
6 9
6 11
7 10
7 11
Yes
1 2
1 3
3 5
4 5
Yes
1 10
1 12
2 3
2 12
4 9
4 12
5 7
5 12
6 12
8 11
8 12
Yes
1 3
1 5
2 3
3 6
4 6
Yes
1 4
1 5
1 6
2 5
3 4
Yes
1 2
1 6
3 6
3 10
4 6
4 11
5 6
5 7
6 9
8 9
Yes
1 4
1 5
2 5
...

result:

ok 11102 cases

Test #8:

score: 0
Accepted
time: 59ms
memory: 6652kb

input:

100000
5 7
2 5
1 4
2 1
1 3
5 1
4 2
2 3
5 7
2 4
4 3
2 1
4 5
2 5
1 4
3 2
5 7
5 1
4 2
4 5
4 3
4 1
3 1
2 1
5 7
4 1
4 3
3 5
2 5
4 5
2 4
1 5
5 7
5 2
2 1
5 4
2 4
4 3
3 2
1 4
5 7
2 4
5 1
1 3
2 1
2 3
4 1
2 5
5 7
5 4
4 2
5 2
3 5
4 1
5 1
4 3
5 7
1 5
2 3
2 5
2 4
3 5
4 5
1 2
5 7
1 3
5 2
2 4
1 2
5 3
2 3
4 3
5 7
3...

output:

Yes
1 4
1 5
2 3
2 4
Yes
1 2
1 4
2 5
3 4
Yes
1 3
1 5
2 4
3 4
Yes
1 4
1 5
2 5
3 4
Yes
1 2
1 4
2 5
3 4
Yes
1 4
1 5
2 3
2 4
Yes
1 4
1 5
2 5
3 4
Yes
1 2
1 5
2 4
3 5
Yes
1 3
2 4
2 5
3 4
Yes
1 3
1 4
2 5
3 5
Yes
1 2
1 5
2 4
3 5
Yes
1 2
1 5
2 4
3 5
Yes
1 3
1 5
2 5
3 4
Yes
1 4
1 5
2 5
3 4
Yes
1 3
1 5
2 4
3 4
...

result:

ok 100000 cases

Test #9:

score: 0
Accepted
time: 36ms
memory: 6728kb

input:

1000
5 970
3 1
4 3
3 1
1 3
2 3
2 3
3 2
2 3
2 3
2 3
3 2
3 2
3 1
2 3
3 2
3 2
2 3
2 3
3 2
3 2
2 3
3 2
2 3
2 3
3 5
2 3
2 3
2 3
3 2
3 2
5 3
2 3
3 2
2 3
3 2
3 2
3 1
3 2
3 5
3 2
2 1
2 3
3 5
2 3
2 3
5 3
3 2
3 1
3 2
3 2
1 3
4 3
3 1
4 3
5 3
3 2
3 4
2 3
3 5
2 3
3 1
3 2
2 3
4 3
2 3
2 3
1 3
3 1
2 3
3 2
3 2
2 3
2...

output:

Yes
1 3
2 4
2 5
3 4
Yes
1 3
1 5
2 5
3 4
Yes
1 4
1 5
2 5
3 4
Yes
1 4
1 5
2 5
3 4
Yes
1 3
1 5
2 5
3 4
Yes
1 4
1 5
2 3
2 4
Yes
1 3
1 5
2 4
3 4
Yes
1 3
1 5
2 4
3 4
Yes
1 3
1 4
2 4
3 5
Yes
1 4
1 5
2 3
2 4
Yes
1 3
1 4
2 4
3 5
Yes
1 4
1 5
2 5
3 4
Yes
1 2
1 4
2 5
3 4
Yes
1 2
1 5
2 4
3 5
Yes
1 4
1 5
2 3
2 4
...

result:

ok 1000 cases

Test #10:

score: 0
Accepted
time: 51ms
memory: 6656kb

input:

100000
5 5
5 1
1 3
3 5
2 3
4 1
5 5
3 1
3 4
1 5
5 2
5 3
5 5
2 5
1 2
4 5
4 3
2 4
5 5
1 2
4 3
2 4
4 1
5 1
5 5
5 2
3 2
1 4
1 2
3 1
5 5
2 5
1 3
4 5
1 2
5 1
5 5
1 5
5 2
4 5
1 4
3 4
5 5
4 2
1 2
1 4
5 1
3 4
5 5
1 3
5 2
5 4
5 1
1 4
5 5
2 3
4 5
2 4
3 4
1 3
5 5
1 4
4 5
2 5
3 4
5 3
5 5
4 1
4 5
4 3
3 2
1 3
5 5
3...

output:

Yes
1 4
1 5
2 3
3 5
Yes
1 3
1 5
2 5
3 4
Yes
1 2
2 5
3 4
4 5
Yes
1 2
1 5
2 4
3 4
Yes
1 3
1 4
2 3
2 5
Yes
1 2
1 3
2 5
4 5
Yes
1 4
1 5
2 5
3 4
Yes
1 2
1 5
2 4
3 4
Yes
1 3
1 4
2 5
4 5
Yes
1 3
2 3
2 4
4 5
Yes
1 4
2 5
3 4
3 5
Yes
1 3
1 4
2 3
4 5
Yes
1 4
1 5
2 3
2 5
Yes
1 2
1 5
2 4
3 5
Yes
1 2
1 5
3 4
3 5
...

result:

ok 100000 cases