oj.uz

답안 #601896

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
601896 2022-07-22T12:00:43 Z model_code Giraffes (JOI22_giraffes) C++17
100 / 100
 2868 ms 2052 KB 
/*
	100-POINT SOLUTION FOR "GIRAFFES" (JOI 2022 OPEN CONTEST)
	- Solution: Speeding up dynamic programming with sweepline algorithm using segment tree
	- Time Complexty: O(N log N * (N - answer)) (= O(N^1.5 log N) for average case)
*/

#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

class segtree {
private:
	int sz;
	std::vector<int> val;
public:
	static const int INF = 2012345678;
	segtree() : sz(0), val(std::vector<int>()) {};
	segtree(int n) {
		sz = 1;
		while (sz < n) {
			sz *= 2;
		}
		val = std::vector<int>(sz * 2, INF);
	}
	void reset() {
		for (int i = 0; i < sz * 2; i++) {
			val[i] = INF;
		}
	}
	void upgrade(int pos, int x) {
		pos += sz;
		val[pos] = std::min(val[pos], x);
		while (pos > 1) {
			pos >>= 1;
			val[pos] = std::min(val[pos * 2], val[pos * 2 + 1]);
		}
	}
	int rangemin(int l, int r) {
		l += sz;
		r += sz;
		int answer = INF;
		while (l != r) {
			if ((l & 1) == 1) answer = std::min(answer, val[l++]);
			if ((r & 1) == 1) answer = std::min(answer, val[--r]);
			l >>= 1;
			r >>= 1;
		}
		return answer;
	}
};

class square {
public:
	int x, y, l;
	square() : x(0), y(0), l(0) {};
	square(int x_, int y_, int l_) : x(x_), y(y_), l(l_) {};
};

int solve(int N, const vector<int>& P) {
	// dp[i][j]: smallest size of square of "answer = t" with point (j, P[j]) at direction i
	const int INF = 1012345678;
	vector<vector<int> > dp(4, vector<int>(N, 0));
	int t = 1;
	
	// step #0. preparation
	vector<int> pa(N), pb(N);
	for (int i = 0; i < N; i++) {
		pa[i] = i;
		pb[i] = i;
	}
	sort(pa.begin(), pa.end(), [&](int i, int j) { return i - P[i] < j - P[j]; });
	sort(pb.begin(), pb.end(), [&](int i, int j) { return i + P[i] < j + P[j]; });
	
	while (true) {
		// step #1. enumerate all squares
		vector<square> sq;
		for (int i = 0; i < 4; i++) {
			for (int j = 0; j < N; j++) {
				if (dp[i][j] != INF) {
					int x = j - (i & 2 ? dp[i][j] : 0);
					int y = P[j] - (i & 1 ? dp[i][j] : 0);
					sq.push_back(square(x, y, dp[i][j]));
				}
			}
		}
		int S = sq.size();
		
		// step #2. preparation
		dp = vector<vector<int> >(4, vector<int>(N, INF));
		vector<square> sqa = sq;
		sort(sqa.begin(), sqa.end(), [](const square& s1, const square& s2) { return s1.x - s1.y < s2.x - s2.y; });
		vector<square> sqb = sq;
		sort(sqb.begin(), sqb.end(), [](const square& s1, const square& s2) { return s1.x + s1.y + s1.l < s2.x + s2.y + s2.l; });
		segtree seg1(N);
		segtree seg2(N);
		int posp, possq;
		
		// step #3. sweepline by increasing x-y
		seg1.reset();
		seg2.reset();
		posp = 0;
		possq = 0;
		while (posp != N || possq != S) {
			int px = pa[posp];
			int py = P[pa[posp]];
			int v1 = (posp != N ? px - py : INF);
			int v2 = (possq != S ? sqa[possq].x - sqa[possq].y : INF);
			if (v1 >= v2) {
				seg1.upgrade(sqa[possq].x, sqa[possq].y + sqa[possq].l);
				seg2.upgrade(sqa[possq].y + sqa[possq].l, -sqa[possq].x);
				possq += 1;
			}
			else {
				dp[0][px] = min(dp[0][px], seg1.rangemin(px + 1, N) - py);
				dp[3][px] = min(dp[3][px], px - (-seg2.rangemin(0, py)));
				posp += 1;
			}
		}
		
		// step #4. sweepline by decreasing x-y
		seg1.reset();
		seg2.reset();
		posp = N - 1;
		possq = S - 1;
		while (posp != -1 || possq != -1) {
			int px = pa[posp];
			int py = P[pa[posp]];
			int v1 = (posp != -1 ? px - py : -INF);
			int v2 = (possq != -1 ? sqa[possq].x - sqa[possq].y : -INF);
			if (v1 <= v2) {
				seg1.upgrade(sqa[possq].y, sqa[possq].x + sqa[possq].l);
				seg2.upgrade(sqa[possq].x + sqa[possq].l, -sqa[possq].y);
				possq -= 1;
			}
			else {
				dp[0][px] = min(dp[0][px], seg1.rangemin(py + 1, N) - px);
				dp[3][px] = min(dp[3][px], py - (-seg2.rangemin(0, px)));
				posp -= 1;
			}
		}
		
		// step #5. sweepline by increasing x+y
		seg1.reset();
		seg2.reset();
		posp = 0;
		possq = 0;
		while (posp != N || possq != S) {
			int px = pb[posp];
			int py = P[pb[posp]];
			int v1 = (posp != N ? px + py : INF);
			int v2 = (possq != S ? sqb[possq].x + sqb[possq].y + sqb[possq].l : INF);
			if (v1 >= v2) {
				seg1.upgrade(sqb[possq].x, -sqb[possq].y);
				seg2.upgrade(sqb[possq].y, -sqb[possq].x);
				possq += 1;
			}
			else {
				dp[1][px] = min(dp[1][px], py - (-seg1.rangemin(px + 1, N)));
				dp[2][px] = min(dp[2][px], px - (-seg2.rangemin(py + 1, N)));
				posp += 1;
			}
		}
		
		// step #6. sweepline by decreasing x+y
		seg1.reset();
		seg2.reset();
		posp = N - 1;
		possq = S - 1;
		while (posp != -1 || possq != -1) {
			int px = pb[posp];
			int py = P[pb[posp]];
			int v1 = (posp != -1 ? px + py : -INF);
			int v2 = (possq != -1 ? sqb[possq].x + sqb[possq].y + sqb[possq].l : -INF);
			if (v1 <= v2) {
				seg1.upgrade(sqb[possq].y + sqb[possq].l, sqb[possq].x + sqb[possq].l);
				seg2.upgrade(sqb[possq].x + sqb[possq].l, sqb[possq].y + sqb[possq].l);
				possq -= 1;
			}
			else {
				dp[1][px] = min(dp[1][px], seg1.rangemin(0, py) - px);
				dp[2][px] = min(dp[2][px], seg2.rangemin(0, px) - py);
				posp -= 1;
			}
		}
		
		// step #7. final cleanup
		for (int i = 0; i < 4; i++) {
			for (int j = 0; j < N; j++) {
				int xlim = (i & 2 ? j : (N - 1) - j);
				int ylim = (i & 1 ? P[j] : (N - 1) - P[j]);
				if (dp[i][j] > min(xlim, ylim)) {
					dp[i][j] = INF;
				}
			}
		}
		if (dp == vector<vector<int> >(4, vector<int>(N, INF))) {
			break;
		}
		t += 1;
	}
	return N - t;
}

int main() {
	int N;
	cin >> N;
	vector<int> P(N);
	for (int i = 0; i < N; i++) {
		cin >> P[i];
		P[i] -= 1;
	}
	int answer = solve(N, P);
	cout << answer << endl;
	return 0;
}

Subtask #1
10.0 / 10.0

# 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 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 2 ms 292 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 300 KB Output is correct
10 Correct 1 ms 212 KB Output is correct

Subtask #2
22.0 / 22.0

# 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 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 2 ms 292 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 300 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 216 KB Output is correct
17 Correct 1 ms 300 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 300 KB Output is correct
20 Correct 1 ms 212 KB Output is correct

Subtask #3
27.0 / 27.0

# 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 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 2 ms 292 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 300 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 216 KB Output is correct
17 Correct 1 ms 300 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 300 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 2 ms 212 KB Output is correct
23 Correct 6 ms 348 KB Output is correct
24 Correct 7 ms 340 KB Output is correct
25 Correct 10 ms 340 KB Output is correct
26 Correct 10 ms 376 KB Output is correct
27 Correct 11 ms 296 KB Output is correct
28 Correct 12 ms 296 KB Output is correct
29 Correct 11 ms 340 KB Output is correct
30 Correct 11 ms 340 KB Output is correct

Subtask #4
41.0 / 41.0

# 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 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 2 ms 292 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 300 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 216 KB Output is correct
17 Correct 1 ms 300 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 300 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 212 KB Output is correct
22 Correct 2 ms 212 KB Output is correct
23 Correct 6 ms 348 KB Output is correct
24 Correct 7 ms 340 KB Output is correct
25 Correct 10 ms 340 KB Output is correct
26 Correct 10 ms 376 KB Output is correct
27 Correct 11 ms 296 KB Output is correct
28 Correct 12 ms 296 KB Output is correct
29 Correct 11 ms 340 KB Output is correct
30 Correct 11 ms 340 KB Output is correct
31 Correct 383 ms 788 KB Output is correct
32 Correct 1471 ms 1500 KB Output is correct
33 Correct 2451 ms 2008 KB Output is correct
34 Correct 2363 ms 1992 KB Output is correct
35 Correct 2360 ms 1948 KB Output is correct
36 Correct 2570 ms 1956 KB Output is correct
37 Correct 2348 ms 2052 KB Output is correct
38 Correct 2423 ms 2024 KB Output is correct
39 Correct 2868 ms 1988 KB Output is correct
40 Correct 2631 ms 2020 KB Output is correct