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답안 #727882

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
727882 2023-04-21T14:10:53 Z SanguineChameleon 육각형 영역 (APIO21_hexagon) C++17
20 / 100
 2000 ms 67920 KB 
#include "hexagon.h"
#include <bits/stdc++.h>
using namespace std;

#ifdef KAMIRULEZ
	const bool local = true;
	const int subtask = 6;
#else
	const bool local = false;
	const int subtask = -1;
#endif

const long long mod = 1e9 + 7;
const long long one_half = (mod + 1) / 2;
const long long one_third = (mod + 1) / 3;
const int dx[7] = {0, 0, 1, 1, 0, -1, -1};
const int dy[7] = {0, 1, 1, 0, -1, -1, 0};

struct point {
	long long x, y;

	point() {};

	point(long long _x, long long _y): x(_x), y(_y) {};

	point operator*(long long d) {
		return point(x * d, y * d);
	}

	point operator+(point p2) {
		return point(x + p2.x, y + p2.y);
	}

	long long operator^(point p2) {
		return x * p2.y - y * p2.x;
	}
};

point dv[7] = {point(0, 0), point(0, 1), point(1, 1), point(1, 0), point(0, -1), point(-1, -1), point(-1, 0)};

ostream& operator<<(ostream &out, point p) {
	out << "(" << p.x << "," << p.y << ")";
	return out;
}

struct line {
	int type, dir, len;
	point p1, p2;
	int id;

	line() {};

	line(int _type, int _dir, point _p1, point _p2, int _id): type(_type), dir(_dir), p1(_p1), p2(_p2), id(_id) {
		len = p2.x - p1.x + 1;
	};

	long long calc() {
		long long Ly = p1.y;
		long long Ry = p1.y + (dir == 1 ? 0 : len - 1);
		if (type == 1) {
			Ly = 1 - Ly;
			Ry = 1 - Ry;
		}
		return (Ly + Ry) % mod * len % mod * one_half % mod;
	}

	long long eval_x(long long x) {
		if (dir == 1) {
			return p1.y;
		}
		else {
			return p1.y + (x - p1.x);
		}
	}

	void shorten(long long left_x, long long right_x) {
		long long v1 = eval_x(left_x);
		long long v2 = eval_x(right_x);
		p1 = point(left_x, v1);
		p2 = point(right_x, v2);
	}
};

ostream& operator<<(ostream &out, line L) {
	if (L.type == 1) {
		out << "(bottom,";
	}
	else {
		out << "(top,";
	}
	out << L.p1 << "," << L.p2 << ")";
	return out;
}

bool operator<(line L1, line L2) {
	int max_x = max(L1.p1.x, L2.p1.x);
	int v1 = L1.eval_x(max_x);
	int v2 = L2.eval_x(max_x);
	if (v1 != v2) {
		return v1 < v2;
	}
	else {
		return L1.type < L2.type;
	}
};

struct column {
	long long x, left_y, right_y, min_dist, left_min, right_min;

	column() {};

	column(long long _x, long long _left_y, long long _right_y): x(_x), left_y(_left_y), right_y(_right_y) {};

	column(long long _x, long long _left_y, long long _right_y, long long _min_dist, long long _left_min, long long _right_min): x(_x), left_y(_left_y), right_y(_right_y), min_dist(_min_dist), left_min(_left_min), right_min(_right_min) {};

	long long calc(long long A, long long B) {
		long long left_len = (left_min - left_y) % mod;
		long long mid_len = (right_min - left_min + 1) % mod;
		long long right_len = (right_y - right_min) % mod;
		long long A_sum = (right_y - left_y + 1) % mod;
		long long B_sum = (min_dist * mid_len % mod + (min_dist + 1 + min_dist + left_len) * left_len % mod * one_half % mod + (min_dist + 1 + min_dist + right_len) * right_len % mod * one_half % mod) % mod;
		return (A_sum * A + B_sum * B) % mod;
	}
};

ostream& operator<<(ostream &out, column Col) {
	out << "(" << Col.x << ",(" << Col.left_y << "," << Col.right_y << "),min=" << Col.min_dist << ",(" << Col.left_min << "," << Col.right_min << "))";
	return out;
}

struct comp {
	line bottom, top;
	int left_x, right_x, len;
	column left_col, right_col;
	long long sum;

	comp() {};

	comp(line _bottom, line _top, int _left_x, int _right_x): bottom(_bottom), top(_top), left_x(_left_x), right_x(_right_x) {
		bottom.shorten(left_x, right_x);
		top.shorten(left_x, right_x);
		len = right_x - left_x + 1;
	}

	long long calc() {
		long long Ly = top.p1.y - bottom.p1.y + 1;
		long long Ry = top.p2.y - bottom.p2.y + 1;
		return (Ly + Ry) % mod * len % mod * one_half % mod;
	}
};

ostream& operator<<(ostream &out, comp C) {
	out << "(" << C.bottom << "," << C.top << ",(" << C.left_x << "," << C.right_x << "))";
	return out;
}

column move_right_one(column Col1, column Col2) {
	if (Col2.left_y > Col1.right_min + 1) {
		Col2.min_dist = Col2.left_y - (Col1.right_min + 1) + (Col1.min_dist + 1);
		Col2.left_min = Col2.left_y;
		Col2.right_min = Col2.left_y;
		return Col2;
	}
	if (Col2.right_y < Col1.left_min) {
		Col2.min_dist = Col1.left_min - Col2.right_y + (Col1.min_dist + 1);
		Col2.left_min = Col2.right_y;
		Col2.right_min = Col2.right_y;
		return Col2;
	}
	Col2.min_dist = Col1.min_dist + 1;
	Col2.left_min = max(Col2.left_y, Col1.left_min);
	Col2.right_min = min(Col2.right_y, Col1.right_min + 1);
	return Col2;
}

column move_left_one(column Col1, column Col2) {
	if (Col2.left_y > Col1.right_min) {
		Col2.min_dist = Col2.left_y - Col1.right_min + (Col1.min_dist + 1);
		Col2.left_min = Col2.left_y;
		Col2.right_min = Col2.left_y;
		return Col2;
	}
	if (Col2.right_y < Col1.left_min - 1) {
		Col2.min_dist = (Col1.left_min - 1) - Col2.right_y + (Col1.min_dist + 1);
		Col2.left_min = Col2.right_y;
		Col2.right_min = Col2.right_y;
		return Col2;
	}
	Col2.min_dist = Col1.min_dist + 1;
	Col2.left_min = max(Col2.left_y, Col1.left_min - 1);
	Col2.right_min = min(Col2.right_y, Col1.right_min);
	return Col2;
}

pair<long long, column> move_right(column Col, line bottom, line top, long long left_x, long long right_x, long long A, long long B) {
	column cur = Col;
	long long res = cur.calc(A, B);
	for (int x = left_x + 1; x <= right_x; x++) {
		column nxt = move_right_one(cur, column(x, bottom.eval_x(x), top.eval_x(x)));
		res += nxt.calc(A, B);
		res %= mod;
		cur = nxt;
	}
	return make_pair(res, cur);
}

pair<long long, column> move_left(column Col, line bottom, line top, long long right_x, long long left_x, long long A, long long B) {
	column cur = Col;
	long long res = cur.calc(A, B);
	for (int x = right_x - 1; x >= left_x; x--) {
		column nxt = move_left_one(cur, column(x, bottom.eval_x(x), top.eval_x(x)));
		res += nxt.calc(A, B);
		res %= mod;
		cur = nxt;
	}
	return make_pair(res, cur);
}

vector<comp> comps;
vector<vector<int>> adj;

void dfs(int u, int par, long long A, long long B) {
	for (auto v: adj[u]) {
		if (v == par) {
			continue;
		}
		if (comps[u].right_x + 1 == comps[v].left_x) {
			comps[v].left_col = move_right_one(comps[u].right_col, column(comps[v].left_x, comps[v].bottom.p1.y, comps[v].top.p1.y));
			auto p_right = move_right(comps[v].left_col, comps[v].bottom, comps[v].top, comps[v].left_x, comps[v].right_x, A, B);
			comps[v].sum = p_right.first;
			comps[v].right_col = p_right.second;
		}
		else {
			comps[v].right_col = move_left_one(comps[u].left_col, column(comps[v].right_x, comps[v].bottom.p2.y, comps[v].top.p2.y));
			auto p_left = move_left(comps[v].right_col, comps[v].bottom, comps[v].top, comps[v].right_x, comps[v].left_x, A, B);
			comps[v].sum = p_left.first;
			comps[v].left_col = p_left.second;
		}
		dfs(v, u, A, B);
	}
}

int draw_territory(int N, int A, int B, vector<int> D, vector<int> L) {
	if (N == 3 && (!local || subtask == 1 || subtask == 2)) {
		int len = L[0] + 1;
		long long A_sum = 1LL * len * (len + 1) % mod * one_half % mod;
		long long B_sum = 1LL * len * (len - 1) % mod * one_half % mod + (len - 1) * len % mod * (len * 2 - 1) % mod * one_half % mod * one_third % mod;
		return (A_sum * A + B_sum * B) % mod;
	}
	long long L_sum = 0;
	for (int i = 0; i < N; i++) {
		L_sum += L[i];
	}
	if (L_sum <= 2000 && (!local || subtask == 3)) {
		vector<vector<bool>> border(4069, vector<bool>(4069, false));
		vector<vector<int>> dist(4069, vector<int>(4069, -1));
		int cx = 0;
		int cy = 0;
		for (int i = 0; i < N; i++) {
			for (int j = 0; j < L[i]; j++) {
				cx += dx[D[i]];
				cy += dy[D[i]];
				border[cx + 2023][cy + 2023] = true;
			}
		}
		deque<pair<int, int>> q = {{0, 0}};
		dist[0][0] = -2;
		while (!q.empty()) {
			cx = q.front().first;
			cy = q.front().second;
			q.pop_front();
			for (int d = 1; d <= 6; d++) {
				int nx = cx + dx[d];
				int ny = cy + dy[d];
				if (0 <= nx && nx < 4069 && 0 <= ny && ny < 4069 && !border[nx][ny] && dist[nx][ny] == -1) {
					dist[nx][ny] = -2;
					q.push_back({nx, ny});
				}
			}
		}
		q.push_back({2023, 2023});
		dist[2023][2023] = 0;
		long long res = 0;
		while (!q.empty()) {
			cx = q.front().first;
			cy = q.front().second;
			res += 1LL * B * dist[cx][cy] + A;
			res %= mod;
			q.pop_front();
			for (int d = 1; d <= 6; d++) {
				int nx = cx + dx[d];
				int ny = cy + dy[d];
				if (0 <= nx && nx < 4069 && 0 <= ny && ny < 4069 && dist[nx][ny] == -1) {
					dist[nx][ny] = dist[cx][cy] + 1;
					q.push_back({nx, ny});
				}
			}
		}
		return res;
	}
	long long area = 0;
	point cur = point(0, 0);
	vector<point> poly(N);
	for (int i = 0; i < N; i++) {
		poly[i] = cur;
		cur = cur + (dv[D[i]] * L[i]);
	}
	for (int i = 0; i < N; i++) {
		area += poly[i] ^ poly[(i + 1) % N];
	}
	if (area < 0) {
		reverse(D.begin(), D.end());
		for (int i = 0; i < N; i++) {
			if (D[i] <= 3) {
				D[i] += 3;
			}
			else {
				D[i] -= 3;
			}
		}
		reverse(L.begin(), L.end());
		cur = point(0, 0);
		for (int i = 0; i < N; i++) {
			poly[i] = cur;
			cur = cur + (dv[D[i]] * L[i]);
		}
	}
	vector<line> lines;
	vector<int> prv_x;
	for (int i = 0; i < N; i++) {
		point prv = poly[(i + (N - 1)) % N];
		point cur = poly[i];
		point nxt1 = poly[(i + 1) % N];
		point nxt2 = poly[(i + 2) % N];
		if (cur.x < nxt1.x) {
			point p1 = cur;
			point p2 = nxt1;
			int dir = (cur.y == nxt1.y ? 1 : 2);
			if (prv.x < cur.x) {
				if (dir == 1) {
					p1 = p1 + point(1, 0);
				}
				else {
					p1 = p1 + point(1, 1);
				}
			}
			if (prv.x == cur.x && prv.y < cur.y) {
				if (dir == 1) {
					p1 = p1 + point(1, 0);
				}
				else {
					p1 = p1 + point(1, 1);
				}
			}
			if (nxt1.x == nxt2.x && nxt1.y > nxt2.y) {
				if (dir == 1) {
					p2 = p2 + point(-1, 0);
				}
				else {
					p2 = p2 + point(-1, -1);
				}
			}
			if (p1.x <= p2.x) {
				lines.emplace_back(1, dir, p1, p2, lines.size());
				prv_x.push_back(p1.x);
			}
		}
		if (cur.x > nxt1.x) {
			point p1 = nxt1;
			point p2 = cur;
			int dir = (cur.y == nxt1.y ? 1 : 2);
			if (prv.x > cur.x) {
				if (dir == 1) {
					p2 = p2 + point(-1, 0);
				}
				else {
					p2 = p2 + point(-1, -1);
				}
			}
			if (prv.x == cur.x && prv.y > cur.y) {
				if (dir == 1) {
					p2 = p2 + point(-1, 0);
				}
				else {
					p2 = p2 + point(-1, -1);
				}
			}
			if (nxt1.x == nxt2.x && nxt1.y < nxt2.y) {
				if (dir == 1) {
					p1 = p1 + point(1, 0);
				}
				else {
					p1 = p1 + point(1, 1);
				}
			}
			if (p1.x <= p2.x) {
				lines.emplace_back(2, dir, p1, p2, lines.size());
				prv_x.push_back(p1.x);
			}
		}
	}
	vector<pair<int, pair<int, int>>> events;
	for (int i = 0; i < (int)lines.size(); i++) {
		events.push_back(make_pair(lines[i].p1.x - 1, make_pair(2, i)));
		events.push_back(make_pair(lines[i].p1.x, make_pair(0, i)));
		events.push_back(make_pair(lines[i].p2.x, make_pair(1, i)));
	}
	sort(events.begin(), events.end());
	set<line, less<>> S;
	for (auto e: events) {
		int cur_x = e.first;
		int type = e.second.first;
		line L = lines[e.second.second];
		auto it = (type == 0 ? S.insert(L).first : S.lower_bound(L));
		if (type == 1) {
			if (it->type == 1 && next(it) != S.end()) {
				auto bottom = it;
				auto top = next(it);
				if (prv_x[bottom->id] <= cur_x && prv_x[top->id] <= cur_x) {
					comps.emplace_back(*bottom, *top, prv_x[bottom->id], cur_x);
					prv_x[bottom->id] = cur_x + 1;
					prv_x[top->id] = cur_x + 1;
				}
			}
			if (it->type == 2 && it != S.begin()) {
				auto bottom = prev(it);
				auto top = it;
				if (prv_x[bottom->id] <= cur_x && prv_x[top->id] <= cur_x) {
					comps.emplace_back(*bottom, *top, prv_x[bottom->id], cur_x);
					prv_x[bottom->id] = cur_x + 1;
					prv_x[top->id] = cur_x + 1;
				}
			}
			S.erase(it);
		}
		if (type == 2) {
			if (it != S.end() && it != S.begin()) {
				auto bottom = prev(it);
				auto top = it;
				if (bottom->type == 1 && top->type == 2) {
					if (prv_x[bottom->id] <= cur_x && prv_x[top->id] <= cur_x) {
						comps.emplace_back(*bottom, *top, prv_x[bottom->id], cur_x);
						prv_x[bottom->id] = cur_x + 1;
						prv_x[top->id] = cur_x + 1;
					}
				}
			}
		}
	}
	adj.resize(comps.size());
	events.clear();
	for (int i = 0; i < (int)comps.size(); i++) {
		events.push_back(make_pair(comps[i].right_x + 1, make_pair(comps[i].bottom.p2.y, i)));
		events.push_back(make_pair(comps[i].left_x, make_pair(comps[i].bottom.p1.y, -i - 1)));
	}
	sort(events.begin(), events.end());
	int lid = -1;
	int rid = -1;
	int edge_cnt = 0;
	for (auto e: events) {
		if (e.second.second >= 0) {
			lid = e.second.second;
		}
		else {
			rid = -e.second.second - 1;
		}
		if (lid >= 0 && rid >= 0 && comps[lid].right_x + 1 == comps[rid].left_x && max(comps[lid].bottom.p2.y, comps[rid].bottom.p1.y) - 1 <= min(comps[lid].top.p2.y, comps[rid].top.p1.y)) {
			adj[lid].push_back(rid);
			adj[rid].push_back(lid);
			edge_cnt++;
		}
	}
	assert(edge_cnt + 1 == (int)comps.size());
	if (B == 0 && (!local || subtask == 4 || subtask == 5)) {
		long long res = 0;
		for (auto C: comps) {
			res += C.calc();
			res %= mod;
		}
		if (res < 0) {
			res += mod;
		}
		res = res * A % mod;
		return res;
	}
	int root = -1;
	for (int i = 0; i < (int)comps.size(); i++) {
		auto C = comps[i];
		if (C.left_x <= 0 && 0 <= C.right_x) {
			int left_y = C.bottom.eval_x(0);
			int right_y = C.top.eval_x(0);
			if (left_y <= 0 && 0 <= right_y) {
				column mid_col(0, left_y, right_y, 0, 0, 0);
				auto p_left = move_left(mid_col, C.bottom, C.top, 0, C.left_x, A, B);
				auto p_right = move_right(mid_col, C.bottom, C.top, 0, C.right_x, A, B);
				comps[i].left_col = p_left.second;
				comps[i].right_col = p_right.second;
				comps[i].sum = (p_left.first + p_right.first + mod - mid_col.calc(A, B)) % mod;
				root = i;
				break;
			}
		}
	}
	dfs(root, -1, A, B);
	long long res = 0;
	for (auto C: comps) {
		res += C.sum;
		res %= mod;
	}
	return res;
}

Subtask #1
3.0 / 3.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct

Subtask #2
6.0 / 6.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 296 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 212 KB Output is correct

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 654 ms 67568 KB Output is correct
2 Correct 816 ms 67564 KB Output is correct
3 Correct 672 ms 67580 KB Output is correct
4 Correct 853 ms 67572 KB Output is correct
5 Correct 660 ms 67640 KB Output is correct
6 Correct 692 ms 67916 KB Output is correct
7 Correct 659 ms 67920 KB Output is correct
8 Correct 637 ms 67664 KB Output is correct
9 Correct 641 ms 67772 KB Output is correct
10 Correct 664 ms 67556 KB Output is correct
11 Correct 656 ms 67536 KB Output is correct
12 Correct 654 ms 67692 KB Output is correct
13 Correct 619 ms 67536 KB Output is correct
14 Correct 636 ms 67668 KB Output is correct
15 Correct 652 ms 67684 KB Output is correct
16 Correct 738 ms 67572 KB Output is correct
17 Correct 729 ms 67532 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct

Subtask #4
0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 9 ms 3304 KB Output is correct
3 Correct 2 ms 1032 KB Output is correct
4 Correct 2 ms 596 KB Output is correct
5 Correct 5 ms 1804 KB Output is correct
6 Correct 9 ms 3204 KB Output is correct
7 Runtime error 36 ms 16304 KB Execution killed with signal 6
8 Halted 0 ms 0 KB -

Subtask #5
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 9 ms 3200 KB Output is correct
5 Correct 2 ms 1076 KB Output is correct
6 Correct 2 ms 596 KB Output is correct
7 Correct 6 ms 1804 KB Output is correct
8 Correct 9 ms 3332 KB Output is correct
9 Runtime error 34 ms 16400 KB Execution killed with signal 6
10 Halted 0 ms 0 KB -

Subtask #6
0 / 19.0

# 결과 실행 시간 메모리 Grader output
1 Correct 692 ms 67800 KB Output is correct
2 Correct 653 ms 67520 KB Output is correct
3 Correct 677 ms 67504 KB Output is correct
4 Correct 705 ms 67568 KB Output is correct
5 Correct 759 ms 67712 KB Output is correct
6 Correct 665 ms 67792 KB Output is correct
7 Correct 677 ms 67552 KB Output is correct
8 Correct 724 ms 67548 KB Output is correct
9 Correct 758 ms 67536 KB Output is correct
10 Correct 702 ms 67676 KB Output is correct
11 Correct 693 ms 67680 KB Output is correct
12 Correct 656 ms 67680 KB Output is correct
13 Correct 644 ms 67916 KB Output is correct
14 Correct 646 ms 67556 KB Output is correct
15 Correct 655 ms 67576 KB Output is correct
16 Correct 667 ms 67568 KB Output is correct
17 Correct 658 ms 67572 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 7 ms 3304 KB Output is correct
20 Correct 2 ms 1032 KB Output is correct
21 Correct 1 ms 596 KB Output is correct
22 Correct 5 ms 1804 KB Output is correct
23 Correct 8 ms 3204 KB Output is correct
24 Runtime error 32 ms 16308 KB Execution killed with signal 6
25 Halted 0 ms 0 KB -

Subtask #7
0 / 18.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Execution timed out 2088 ms 212 KB Time limit exceeded
6 Halted 0 ms 0 KB -

Subtask #8
0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 621 ms 67696 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 624 ms 67488 KB Output is correct
7 Correct 629 ms 67676 KB Output is correct
8 Correct 622 ms 67668 KB Output is correct
9 Correct 641 ms 67536 KB Output is correct
10 Correct 646 ms 67572 KB Output is correct
11 Correct 686 ms 67564 KB Output is correct
12 Correct 652 ms 67540 KB Output is correct
13 Correct 651 ms 67652 KB Output is correct
14 Correct 661 ms 67532 KB Output is correct
15 Correct 631 ms 67532 KB Output is correct
16 Correct 625 ms 67560 KB Output is correct
17 Correct 650 ms 67524 KB Output is correct
18 Correct 637 ms 67576 KB Output is correct
19 Correct 637 ms 67532 KB Output is correct
20 Correct 652 ms 67564 KB Output is correct
21 Correct 636 ms 67672 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 7 ms 3304 KB Output is correct
24 Correct 2 ms 1032 KB Output is correct
25 Correct 1 ms 560 KB Output is correct
26 Correct 5 ms 1804 KB Output is correct
27 Correct 9 ms 3204 KB Output is correct
28 Runtime error 34 ms 16320 KB Execution killed with signal 6
29 Halted 0 ms 0 KB -