Submission #6,925

2023-12-19 22:46:31

cpp17

Accepted 100/100

1.769s

199324 KiB

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define double long double

#define pii pair<int, int>

void bad() {
	cout << "NO" << '\n';
	exit(0);
}

signed main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
#ifdef CB
	freopen("in.txt", "r", stdin);
//	freopen("out.txt", "w", stdout);
#endif
	int N;
	cin >> N;
	vector<int> X(N), Y(N), Z(N);
	for (int i = 0; i < N; i++) {
		cin >> X[i];
	}
	for (int i = 0; i < N; i++) {
		cin >> Y[i];
	}
	for (int i = 0; i < N; i++) {
		cin >> Z[i];
	}
	map<tuple<int, int, int>, int> s;
	for (int i = 0; i < N; i++) {
		s[{X[i], Y[i], Z[i]}] = i;
	}
	map<pii, vector<int>> xy, yz, zx;
	for (int i = 0; i < N; i++) {
		xy[{X[i], Y[i]}].push_back(Z[i]);
		yz[{Y[i], Z[i]}].push_back(X[i]);
		zx[{Z[i], X[i]}].push_back(Y[i]);
	}
	for (auto& [p, v] : xy) {
		sort(v.begin(), v.end());
	}
	for (auto& [p, v] : yz) {
		sort(v.begin(), v.end());
	}
	for (auto& [p, v] : zx) {
		sort(v.begin(), v.end());
	}
	// same line
	for (int i = 0; i < N; i++) {
		vector<pair<vector<int>&, int>> a = {
			{xy[{X[i], Y[i]}], Z[i]},
			{yz[{Y[i], Z[i]}], X[i]},
			{zx[{Z[i], X[i]}], Y[i]},
		};
		for (auto [v, x] : a) {
			auto t = lower_bound(v.begin(), v.end(), x);
			if (t != v.begin()) {
				if (*prev(t) != *t - 1) {
					bad();
				}
			}
			if (next(t) != v.end()) {
				if (*next(t) != *t + 1) {
					bad();
				}
			}
		}
	}
	// same plane
	map<int, map<int, pii>> xp, yp, zp;
	for (int i = 0; i < N; i++) {
		xp[X[i]][Y[i]];
		yp[Y[i]][Z[i]];
		zp[Z[i]][X[i]];
	}
	for (auto& [x, m] : xp) {
		pii a = {INT_MAX, INT_MIN};
		for (auto t = m.begin(); t != m.end(); t++) {
			t->second = a;
			a.first = min(a.first, xy[{x, t->first}].front());
			a.second = max(a.second, xy[{x, t->first}].back());
		}
	}
	for (auto& [y, m] : yp) {
		pii a = {INT_MAX, INT_MIN};
		for (auto t = m.begin(); t != m.end(); t++) {
			t->second = a;
			a.first = min(a.first, yz[{y, t->first}].front());
			a.second = max(a.second, yz[{y, t->first}].back());
		}
	}
	for (auto& [z, m] : zp) {
		pii a = {INT_MAX, INT_MIN};
		for (auto t = m.begin(); t != m.end(); t++) {
			t->second = a;
			a.first = min(a.first, zx[{z, t->first}].front());
			a.second = max(a.second, zx[{z, t->first}].back());
		}
	}
	map<int, map<int, pii>> xs, ys, zs;
	for (int i = 0; i < N; i++) {
		xs[X[i]][Y[i]];
		ys[Y[i]][Z[i]];
		zs[Z[i]][X[i]];
	}
	for (auto& [x, m] : xs) {
		pii a = {INT_MAX, INT_MIN};
		for (auto t = m.rbegin(); t != m.rend(); t++) {
			t->second = a;
			a.first = min(a.first, xy[{x, t->first}].front());
			a.second = max(a.second, xy[{x, t->first}].back());
		}
	}
	for (auto& [y, m] : ys) {
		pii a = {INT_MAX, INT_MIN};
		for (auto t = m.rbegin(); t != m.rend(); t++) {
			t->second = a;
			a.first = min(a.first, yz[{y, t->first}].front());
			a.second = max(a.second, yz[{y, t->first}].back());
		}
	}
	for (auto& [z, m] : zs) {
		pii a = {INT_MAX, INT_MIN};
		for (auto t = m.rbegin(); t != m.rend(); t++) {
			t->second = a;
			a.first = min(a.first, zx[{z, t->first}].front());
			a.second = max(a.second, zx[{z, t->first}].back());
		}
	}
	for (int i = 0; i < N; i++) {
		if (xp[X[i]][Y[i]].first < Z[i]) {
			if (!s.count({X[i], Y[i] - 1, Z[i]}) && !s.count({X[i], Y[i], Z[i] - 1})) {
				bad();
			}
		}
		if (xp[X[i]][Y[i]].second > Z[i]) {
			if (!s.count({X[i], Y[i] - 1, Z[i]}) && !s.count({X[i], Y[i], Z[i] + 1})) {
				bad();
			}
		}
		if (xs[X[i]][Y[i]].first < Z[i]) {
			if (!s.count({X[i], Y[i] + 1, Z[i]}) && !s.count({X[i], Y[i], Z[i] - 1})) {
				bad();
			}
		}
		if (xs[X[i]][Y[i]].second > Z[i]) {
			if (!s.count({X[i], Y[i] + 1, Z[i]}) && !s.count({X[i], Y[i], Z[i] + 1})) {
				bad();
			}
		}
		if (yp[Y[i]][Z[i]].first < X[i]) {
			if (!s.count({X[i] - 1, Y[i], Z[i]}) && !s.count({X[i], Y[i], Z[i] - 1})) {
				bad();
			}
		}
		if (yp[Y[i]][Z[i]].second > X[i]) {
			if (!s.count({X[i] + 1, Y[i], Z[i]}) && !s.count({X[i], Y[i], Z[i] - 1})) {
				bad();
			}
		}
		if (ys[Y[i]][Z[i]].first < X[i]) {
			if (!s.count({X[i] - 1, Y[i], Z[i]}) && !s.count({X[i], Y[i], Z[i] + 1})) {
				bad();
			}
		}
		if (ys[Y[i]][Z[i]].second > X[i]) {
			if (!s.count({X[i] + 1, Y[i], Z[i]}) && !s.count({X[i], Y[i], Z[i] + 1})) {
				bad();
			}
		}
		if (zp[Z[i]][X[i]].first < Y[i]) {
			if (!s.count({X[i] - 1, Y[i], Z[i]}) && !s.count({X[i], Y[i] - 1, Z[i]})) {
				bad();
			}
		}
		if (zp[Z[i]][X[i]].second > Y[i]) {
			if (!s.count({X[i] - 1, Y[i], Z[i]}) && !s.count({X[i], Y[i] + 1, Z[i]})) {
				bad();
			}
		}
		if (zs[Z[i]][X[i]].first < Y[i]) {
			if (!s.count({X[i] + 1, Y[i], Z[i]}) && !s.count({X[i], Y[i] - 1, Z[i]})) {
				bad();
			}
		}
		if (zs[Z[i]][X[i]].second > Y[i]) {
			if (!s.count({X[i] + 1, Y[i], Z[i]}) && !s.count({X[i], Y[i] + 1, Z[i]})) {
				bad();
			}
		}
	}
	// check connectivity
	vector<int> v(N);
	auto dfs = [&](auto dfs, int i) {
		if (v[i]) {
			return;
		}
		v[i] = true;
		if (s.count({X[i] + 1, Y[i], Z[i]})) {
			dfs(dfs, s[{X[i] + 1, Y[i], Z[i]}]);
		}
		if (s.count({X[i] - 1, Y[i], Z[i]})) {
			dfs(dfs, s[{X[i] - 1, Y[i], Z[i]}]);
		}
		if (s.count({X[i], Y[i] + 1, Z[i]})) {
			dfs(dfs, s[{X[i], Y[i] + 1, Z[i]}]);
		}
		if (s.count({X[i], Y[i] - 1, Z[i]})) {
			dfs(dfs, s[{X[i], Y[i] - 1, Z[i]}]);
		}
		if (s.count({X[i], Y[i], Z[i] + 1})) {
			dfs(dfs, s[{X[i], Y[i], Z[i] + 1}]);
		}
		if (s.count({X[i], Y[i], Z[i] - 1})) {
			dfs(dfs, s[{X[i], Y[i], Z[i] - 1}]);
		}
	};
	dfs(dfs, 0);
	if (count(v.begin(), v.end(), true) != N) {
		bad();
	}
	cout << "YES" << '\n';
	return 0;
}

	Sum	Test	Verdict	Time	Memory
subtask1	0/0
		1	Accepted	3ms	1960 KiB
		2	Accepted	3ms	2188 KiB
		3	Accepted	3ms	2648 KiB
subtask2	18/18
		4	Accepted	3ms	2716 KiB
		5	Accepted	3ms	3036 KiB
		6	Accepted	3ms	3284 KiB
		7	Accepted	3ms	3280 KiB
		8	Accepted	3ms	3464 KiB
		9	Accepted	3ms	3572 KiB
		10	Accepted	3ms	3820 KiB
		11	Accepted	3ms	3760 KiB
		12	Accepted	3ms	3760 KiB
		13	Accepted	3ms	4052 KiB
subtask3	19/19
		14	Accepted	16ms	8916 KiB
		15	Accepted	3ms	4228 KiB
		16	Accepted	9ms	6192 KiB
		17	Accepted	10ms	6392 KiB
		18	Accepted	64ms	9412 KiB
		19	Accepted	61ms	9148 KiB
		20	Accepted	3ms	4260 KiB
		21	Accepted	7ms	5632 KiB
		22	Accepted	13ms	6532 KiB
		23	Accepted	12ms	6644 KiB
		24	Accepted	12ms	6608 KiB
		25	Accepted	61ms	9244 KiB
		26	Accepted	3ms	4264 KiB
subtask4	24/24
		27	Accepted	195ms	51212 KiB
		28	Accepted	17ms	8160 KiB
		29	Accepted	1.106s	107792 KiB
		30	Accepted	1.111s	115116 KiB
		31	Accepted	1.157s	107760 KiB
		32	Accepted	1.1s	108896 KiB
		33	Accepted	4ms	5552 KiB
		34	Accepted	219ms	51816 KiB
		35	Accepted	1.161s	102008 KiB
		36	Accepted	208ms	52028 KiB
		37	Accepted	1.243s	100988 KiB
		38	Accepted	465ms	77400 KiB
		39	Accepted	4ms	5380 KiB
subtask5	22/22
		40	Accepted	186ms	39560 KiB
		41	Accepted	4ms	5040 KiB
		42	Accepted	43ms	14344 KiB
		43	Accepted	150ms	34296 KiB
		44	Accepted	1.291s	71172 KiB
		45	Accepted	1.332s	72496 KiB
		46	Accepted	3ms	5032 KiB
		47	Accepted	3ms	4800 KiB
		48	Accepted	28ms	11256 KiB
		49	Accepted	140ms	31372 KiB
		50	Accepted	149ms	34404 KiB
		51	Accepted	162ms	34156 KiB
		52	Accepted	1.264s	73272 KiB
		53	Accepted	3ms	4780 KiB
subtask6	17/17
		54	Accepted	423ms	90884 KiB
		55	Accepted	1.769s	199324 KiB
		56	Accepted	175ms	36604 KiB
		57	Accepted	165ms	34872 KiB
		58	Accepted	158ms	35572 KiB
		59	Accepted	1.291s	72948 KiB
		60	Accepted	1.149s	159152 KiB
		61	Accepted	177ms	37316 KiB
		62	Accepted	163ms	35312 KiB
		63	Accepted	163ms	35304 KiB
		64	Accepted	1.279s	72204 KiB
		65	Accepted	1.286s	72592 KiB
		66	Accepted	221ms	71264 KiB