Submission #1039912

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1039912	2024-07-31T12:09:34 Z	ymm	Capital City (JOI20_capital_city)	C++17	100 / 100	721 ms	263212 KB

capital_city

#include <bits/stdc++.h>
#define Loop(x,l,r) for (ll x = (l); x < (ll)(r); ++x)
#define LoopR(x,l,r) for (ll x = (r)-1; x >= (ll)(l); --x)
typedef long long ll;
typedef std::pair<int, int> pii;
typedef std::pair<ll , ll > pll;
using namespace std;

const int N = 200'010;
const int lg = 20;

struct snode;
struct gnode;

struct gnode {
	gnode *par;
	gnode *anc[lg];
	vector<gnode *> adj;
	gnode *hchild, *hroot, *hleaf;
	snode *sroot;
	int st, ft, ht;
	int col;

	int sz() { return ft - st; }
	int hsz() { return hleaf->ht - hroot->ht + 1; }
} graph[N];

struct snode {
	vector<snode *> adj;
	vector<snode *> adjt;
	int weight;
	int vis;

	static void add_edge(snode *v, snode *u) {
		v->adj.push_back(u);
		u->adjt.push_back(v);
	}
} pool[(1<<28) / sizeof(gnode)];

vector<snode *> all_snodes;

snode *new_snode()
{
	static int p = 0;
	all_snodes.push_back(&pool[p]);
	return &pool[p++];
}

void dfsg1(gnode *v, gnode *p, int &t, int h)
{
	v->par = p;
	v->st = t++;
	v->ht = h;

	v->anc[0] = v->par? v->par: v;
	Loop (i,0,lg-1)
		v->anc[i + 1] = v->anc[i]->anc[i];

	for (auto u : v->adj)
		if (u != p)
			dfsg1(u, v, t, h + 1);
	v->ft = t++;
	for (auto u : v->adj) {
		if (u == p)
			continue;
		if (v->hchild == 0 || v->hchild->sz() < u->sz())
			v->hchild = u;
	}
}

gnode *lca(gnode *v, gnode *u)
{
	if (v->ht < u->ht)
		swap(v, u);
	int diff = v->ht - u->ht;
	Loop (i,0,lg)
		if ((diff >> i) & 1)
			v = v->anc[i];
	if (v == u)
		return v;
	LoopR (i,0,lg) {
		if (v->anc[i] != u->anc[i]) {
			v = v->anc[i];
			u = u->anc[i];
		}
	}
	return v->anc[0];
}

gnode gn[N];
snode col_snode[N];
int n, k;

void init_col_snode()
{
	Loop (i,0,k) {
		col_snode[i].weight = 1;
		all_snodes.push_back(&col_snode[i]);
	}
}

snode *make_seg(snode **ptr, int l, int r)
{
	if (r - l == 1)
		return ptr[l];
	snode *sn = new_snode();
	snode::add_edge(sn, make_seg(ptr, l, (l + r)/2));
	snode::add_edge(sn, make_seg(ptr, (l + r)/2, r));
	return sn;
}

snode *make_seg(gnode *u, gnode *d)
{
	vector<snode *> vec(d->ht - u->ht + 1);
	gnode *v = d;
	Loop (i,0,vec.size()) {
		vec.end()[-i-1] = &col_snode[v->col];
		v = v->par;
	}
	return make_seg(vec.data() - u->ht, u->ht, d->ht + 1);
}

template<typename Fn>
void seg_apply(snode *v, Fn fn, int l, int r, int b, int e)
{
	if (l <= b && e <= r) {
		fn(v);
		return;
	}
	if (r <= b || e <= l)
		return;
	seg_apply(v->adj[0], fn, l, r, b, (b+e)/2);
	seg_apply(v->adj[1], fn, l, r, (b+e)/2, e);
}

template<typename Fn>
void seg_apply(gnode *v, Fn fn, int l, int r)
{
	//cerr << v - graph << ' ' << l << ' ' << r << '\n';
	seg_apply(v->sroot, fn, l, r, v->ht, v->hleaf->ht + 1);
}

void dfsg2(gnode *v, gnode *p, gnode *hroot)
{
	for (gnode *u : v->adj) {
		if (u == p)
			continue;
		dfsg2(u, v, u == v->hchild? hroot: u);
	}
	v->hleaf = v->hchild? v->hchild->hleaf: v;
	v->hroot = hroot;
	if (v == hroot)
		v->sroot = make_seg(v, v->hleaf);
}

template<typename Fn>
void path_apply(gnode *u, gnode *d, Fn fn)
{
	while (d->hroot->ht > u->ht) {
		gnode *h = d->hroot;
		seg_apply(h, fn, h->ht, d->ht + 1);
		d = h->par;
	}
	gnode *h = d->hroot;
	assert(h == u->hroot);
	seg_apply(h, fn, u->ht, d->ht + 1);
}

void path_add_col_to(gnode *u, gnode *d, snode *col_node)
{
	//cerr << col_node - col_snode << " => " << u - graph << " --- " << d - graph << '\n';
	path_apply(u, d, [=](snode *sn) {
		//cerr << col_node - col_snode << " -> " << sn - col_snode << '\n';
		snode::add_edge(col_node, sn);
	});
	// while (d && d->ht >= u->ht) {
	// 	snode::add_edge(col_node, &col_snode[d->col]);
	// 	//cerr << col_node - col_snode << " -> " << d->col << '\n';
	// 	d = d->par;
	// }
}

void scc_dfs1(snode *v, vector<snode *> &vec)
{
	v->vis = 1;
	for (snode *u : v->adj) {
		if (!u->vis)
			scc_dfs1(u, vec);
	}
	vec.push_back(v);
}

int scc_dfs2(snode *v, int viscol)
{
	v->vis = viscol;
	int ans = v->weight;
	for (snode *u : v->adjt) {
		if (u->vis == -1)
			ans += scc_dfs2(u, viscol);
	}
	return ans;
}

int scc_solve()
{
	vector<snode *> vec;
	for (snode *sn : all_snodes)
		sn->vis = 0;
	for (snode *sn : all_snodes) {
		if (!sn->vis)
			scc_dfs1(sn, vec);
	}
	reverse(vec.begin(), vec.end());
	for (snode *sn : all_snodes)
		sn->vis = -1;
	vector<int> scc_weight;
	for (snode *sn : vec) {
		if (sn->vis != -1)
			continue;
		int x = scc_dfs2(sn, scc_weight.size());
		scc_weight.push_back(x);
	}
	vector<bool> scc_ok(scc_weight.size(), true);
	//Loop (i,0,k)
	//	cerr << i << ": " << col_snode[i].vis << '\n';
	for (snode *v : all_snodes) for (snode *u : v->adj) {
		if (v->vis != u->vis)
			scc_ok[v->vis] = false;
	}
	int ans = INT_MAX;
	Loop (i,0,scc_weight.size()) {
		if (!scc_ok[i])
			continue;
		assert(scc_weight[i]);
		ans = min(ans, scc_weight[i]);
	}
	return ans;
}

vector<gnode *> gnodes_of_col[N];

void make_virtuals()
{
	auto cmp = [](gnode *v, gnode *u) { return v->st < u->st; };
	Loop (col,0,k) {
		vector<gnode *> vec = gnodes_of_col[col];
		sort(vec.begin(), vec.end(), cmp);
		if (vec.empty())
			continue;

		int cnt = vec.size();
		Loop (i,0,cnt-1)
			vec.push_back(lca(vec[i], vec[i + 1]));
		sort(vec.begin(), vec.end(), cmp);

		vector<gnode *> st;
		for (gnode *v : vec) {
			while (st.size() && st.back()->ft <= v->st)
				st.pop_back();
			if (st.size())
				path_add_col_to(st.back(), v, &col_snode[col]);
			st.push_back(v);
		}
	}
}

int main()
{
	cin.tie(0) -> sync_with_stdio(false);
	cin >> n >> k;
	Loop (i,0,n-1) {
		int v, u;
		cin >> v >> u;
		--v; --u;
		graph[v].adj.push_back(&graph[u]);
		graph[u].adj.push_back(&graph[v]);
	}
	Loop (i,0,n) {
		gnode *v = &graph[i];
		cin >> v->col;
		v->col--;
		gnodes_of_col[v->col].push_back(v);
	}
	init_col_snode();
	int dummy = 0;
	dfsg1(&graph[0], nullptr, dummy, 0);
	dfsg2(&graph[0], nullptr, &graph[0]);
	make_virtuals();
	int ans = scc_solve();
	cout << ans-1 << '\n';
}

Subtask #1
1.0 / 1.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	60 ms	171088 KB	Output is correct
2	Correct	53 ms	171088 KB	Output is correct
3	Correct	50 ms	171164 KB	Output is correct
4	Correct	51 ms	171088 KB	Output is correct
5	Correct	53 ms	171092 KB	Output is correct
6	Correct	62 ms	171092 KB	Output is correct
7	Correct	50 ms	171092 KB	Output is correct
8	Correct	55 ms	171092 KB	Output is correct
9	Correct	52 ms	171088 KB	Output is correct
10	Correct	52 ms	171092 KB	Output is correct

Subtask #2
10.0 / 10.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	60 ms	171088 KB	Output is correct
2	Correct	53 ms	171088 KB	Output is correct
3	Correct	50 ms	171164 KB	Output is correct
4	Correct	51 ms	171088 KB	Output is correct
5	Correct	53 ms	171092 KB	Output is correct
6	Correct	62 ms	171092 KB	Output is correct
7	Correct	50 ms	171092 KB	Output is correct
8	Correct	55 ms	171092 KB	Output is correct
9	Correct	52 ms	171088 KB	Output is correct
10	Correct	52 ms	171092 KB	Output is correct
11	Correct	55 ms	171612 KB	Output is correct
12	Correct	54 ms	171576 KB	Output is correct
13	Correct	53 ms	171604 KB	Output is correct
14	Correct	58 ms	171604 KB	Output is correct
15	Correct	53 ms	171604 KB	Output is correct
16	Correct	53 ms	171780 KB	Output is correct
17	Correct	52 ms	171600 KB	Output is correct
18	Correct	52 ms	171600 KB	Output is correct
19	Correct	52 ms	171604 KB	Output is correct
20	Correct	55 ms	171600 KB	Output is correct
21	Correct	58 ms	171600 KB	Output is correct
22	Correct	60 ms	171856 KB	Output is correct
23	Correct	54 ms	171856 KB	Output is correct
24	Correct	53 ms	171604 KB	Output is correct
25	Correct	57 ms	171856 KB	Output is correct
26	Correct	56 ms	171860 KB	Output is correct
27	Correct	55 ms	171684 KB	Output is correct
28	Correct	53 ms	171608 KB	Output is correct
29	Correct	51 ms	171604 KB	Output is correct
30	Correct	53 ms	171600 KB	Output is correct

Subtask #3
30.0 / 30.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	721 ms	263212 KB	Output is correct
2	Correct	324 ms	262432 KB	Output is correct
3	Correct	701 ms	263132 KB	Output is correct
4	Correct	320 ms	262364 KB	Output is correct
5	Correct	671 ms	258360 KB	Output is correct
6	Correct	314 ms	262300 KB	Output is correct
7	Correct	667 ms	256084 KB	Output is correct
8	Correct	314 ms	255512 KB	Output is correct
9	Correct	487 ms	226208 KB	Output is correct
10	Correct	453 ms	224176 KB	Output is correct
11	Correct	450 ms	226720 KB	Output is correct
12	Correct	451 ms	229648 KB	Output is correct
13	Correct	514 ms	225288 KB	Output is correct
14	Correct	455 ms	229364 KB	Output is correct
15	Correct	475 ms	231180 KB	Output is correct
16	Correct	459 ms	224872 KB	Output is correct
17	Correct	459 ms	226368 KB	Output is correct
18	Correct	465 ms	224968 KB	Output is correct
19	Correct	504 ms	230272 KB	Output is correct
20	Correct	448 ms	228764 KB	Output is correct
21	Correct	53 ms	171092 KB	Output is correct

Subtask #4
59.0 / 59.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	60 ms	171088 KB	Output is correct
2	Correct	53 ms	171088 KB	Output is correct
3	Correct	50 ms	171164 KB	Output is correct
4	Correct	51 ms	171088 KB	Output is correct
5	Correct	53 ms	171092 KB	Output is correct
6	Correct	62 ms	171092 KB	Output is correct
7	Correct	50 ms	171092 KB	Output is correct
8	Correct	55 ms	171092 KB	Output is correct
9	Correct	52 ms	171088 KB	Output is correct
10	Correct	52 ms	171092 KB	Output is correct
11	Correct	55 ms	171612 KB	Output is correct
12	Correct	54 ms	171576 KB	Output is correct
13	Correct	53 ms	171604 KB	Output is correct
14	Correct	58 ms	171604 KB	Output is correct
15	Correct	53 ms	171604 KB	Output is correct
16	Correct	53 ms	171780 KB	Output is correct
17	Correct	52 ms	171600 KB	Output is correct
18	Correct	52 ms	171600 KB	Output is correct
19	Correct	52 ms	171604 KB	Output is correct
20	Correct	55 ms	171600 KB	Output is correct
21	Correct	58 ms	171600 KB	Output is correct
22	Correct	60 ms	171856 KB	Output is correct
23	Correct	54 ms	171856 KB	Output is correct
24	Correct	53 ms	171604 KB	Output is correct
25	Correct	57 ms	171856 KB	Output is correct
26	Correct	56 ms	171860 KB	Output is correct
27	Correct	55 ms	171684 KB	Output is correct
28	Correct	53 ms	171608 KB	Output is correct
29	Correct	51 ms	171604 KB	Output is correct
30	Correct	53 ms	171600 KB	Output is correct
31	Correct	721 ms	263212 KB	Output is correct
32	Correct	324 ms	262432 KB	Output is correct
33	Correct	701 ms	263132 KB	Output is correct
34	Correct	320 ms	262364 KB	Output is correct
35	Correct	671 ms	258360 KB	Output is correct
36	Correct	314 ms	262300 KB	Output is correct
37	Correct	667 ms	256084 KB	Output is correct
38	Correct	314 ms	255512 KB	Output is correct
39	Correct	487 ms	226208 KB	Output is correct
40	Correct	453 ms	224176 KB	Output is correct
41	Correct	450 ms	226720 KB	Output is correct
42	Correct	451 ms	229648 KB	Output is correct
43	Correct	514 ms	225288 KB	Output is correct
44	Correct	455 ms	229364 KB	Output is correct
45	Correct	475 ms	231180 KB	Output is correct
46	Correct	459 ms	224872 KB	Output is correct
47	Correct	459 ms	226368 KB	Output is correct
48	Correct	465 ms	224968 KB	Output is correct
49	Correct	504 ms	230272 KB	Output is correct
50	Correct	448 ms	228764 KB	Output is correct
51	Correct	53 ms	171092 KB	Output is correct
52	Correct	483 ms	227784 KB	Output is correct
53	Correct	495 ms	227776 KB	Output is correct
54	Correct	487 ms	228132 KB	Output is correct
55	Correct	483 ms	228244 KB	Output is correct
56	Correct	484 ms	227528 KB	Output is correct
57	Correct	493 ms	227564 KB	Output is correct
58	Correct	484 ms	220192 KB	Output is correct
59	Correct	464 ms	219332 KB	Output is correct
60	Correct	580 ms	231744 KB	Output is correct
61	Correct	584 ms	235964 KB	Output is correct
62	Correct	322 ms	262300 KB	Output is correct
63	Correct	316 ms	262300 KB	Output is correct
64	Correct	293 ms	257648 KB	Output is correct
65	Correct	323 ms	262300 KB	Output is correct
66	Correct	364 ms	231312 KB	Output is correct
67	Correct	348 ms	222012 KB	Output is correct
68	Correct	344 ms	229040 KB	Output is correct
69	Correct	355 ms	228976 KB	Output is correct
70	Correct	381 ms	228940 KB	Output is correct
71	Correct	382 ms	229016 KB	Output is correct
72	Correct	383 ms	229036 KB	Output is correct
73	Correct	385 ms	230052 KB	Output is correct
74	Correct	404 ms	229556 KB	Output is correct
75	Correct	355 ms	230588 KB	Output is correct
76	Correct	440 ms	212500 KB	Output is correct
77	Correct	465 ms	211264 KB	Output is correct
78	Correct	537 ms	225800 KB	Output is correct
79	Correct	467 ms	224960 KB	Output is correct
80	Correct	445 ms	228120 KB	Output is correct
81	Correct	484 ms	226724 KB	Output is correct
82	Correct	455 ms	228288 KB	Output is correct
83	Correct	445 ms	224744 KB	Output is correct
84	Correct	530 ms	231296 KB	Output is correct
85	Correct	484 ms	227844 KB	Output is correct
86	Correct	452 ms	225140 KB	Output is correct
87	Correct	454 ms	225024 KB	Output is correct
88	Correct	493 ms	226852 KB	Output is correct
89	Correct	467 ms	220720 KB	Output is correct
90	Correct	458 ms	219936 KB	Output is correct
91	Correct	438 ms	221832 KB	Output is correct
92	Correct	481 ms	224172 KB	Output is correct
93	Correct	471 ms	221224 KB	Output is correct
94	Correct	462 ms	220984 KB	Output is correct
95	Correct	448 ms	221744 KB	Output is correct
96	Correct	478 ms	224616 KB	Output is correct
97	Correct	531 ms	224312 KB	Output is correct

Submission #1039912

Compilation message

Subtask #1 1.0 / 1.0

Subtask #2 10.0 / 10.0

Subtask #3 30.0 / 30.0

Subtask #4 59.0 / 59.0

Subtask #1
1.0 / 1.0

Subtask #2
10.0 / 10.0

Subtask #3
30.0 / 30.0

Subtask #4
59.0 / 59.0