oj.uz

Submission #1089752

# Submission time Handle Problem Language Result Execution time Memory
1089752 2024-09-17T05:40:50 Z ymm Dancing Elephants (IOI11_elephants) C++17
100 / 100
 2062 ms 23608 KB 
#include "elephants.h"
#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;

int L;

struct Part {
	vector<int> Ps;
	vector<pii> ans;

	void calc_ans() {
		ans.resize(Ps.size());
		if (ans.empty())
			return;
		ans.back() = {1, Ps.back() + L};
		size_t ptr = ans.size();
		LoopR (i,0,(ll)ans.size()-1) {
			while (Ps[ptr-1] - Ps[i] >= L)
				--ptr;
			ans[i].first = ptr == ans.size()? 1: ans[ptr].first + 1;
			ans[i].second = ptr == ans.size()? Ps[i] + L: ans[ptr].second;
		}
	}

	// vec must be sorted
	// O(vec.size())
	Part(const vector<int> &vec) {
		Ps = vec;
		calc_ans();
	}

	auto lower_bound(int x) {
		// implement caching mechanism if needed
		return std::lower_bound(Ps.begin(), Ps.end(), x);
	}

	// O(log(Ps.size()))
	pii get(int p) {
		auto it = lower_bound(p);
		if (it == Ps.end())
			return {0, p};
		return ans[it - Ps.begin()];
	}

	// O(Ps.size())
	void put(int x) {
		auto it = lower_bound(x);
		Ps.insert(it, x);
		calc_ans();
	}

	// O(Ps.size())
	void remove(int x) {
		auto it = lower_bound(x);
		assert(it != Ps.end() && *it == x);
		Ps.erase(it);
		calc_ans();
	}
};

struct PartList {
	vector<Part> parts;
	vector<int> bounds;
	map<int, int> pos_cnt;
	static constexpr int S = 1024;

	// O(nlog(n))
	void init(const vector<int> &vec) {
		pos_cnt.clear();
		for (int x : vec)
			pos_cnt[x]++;
		vector<int> Ps;
		for (auto [x, _] : pos_cnt)
			Ps.push_back(x);
		repart(Ps);
	}

	// Ps must be sorted
	// O(Ps.size())
	void repart(const vector<int> &Ps) {
		bounds.clear();
		parts.clear();
		for (size_t i = 0; i < Ps.size(); i += S) {
			size_t j = min(i + S, Ps.size());
			if (j != Ps.size())
				bounds.push_back(Ps[j]);
			parts.emplace_back(vector(Ps.begin() + i, Ps.begin() + j));
		}
	}

	// O(n)
	void repart() {
		vector<int> vec;
		for (auto &p : parts)
			vec.insert(vec.end(), p.Ps.begin(), p.Ps.end());
		repart(vec);
	}

	// O(log(n) + S) + amortized O(n/S)
	void move(int x, int y) {
		auto &cntx = pos_cnt[x];
		auto &cnty = pos_cnt[y];
		if (!--cntx) {
			int i = upper_bound(bounds.begin(), bounds.end(), x) - bounds.begin();
			parts[i].remove(x);
		}
		if (!cnty++) {
			int i = upper_bound(bounds.begin(), bounds.end(), y) - bounds.begin();
			parts[i].put(y);
			if (parts[i].Ps.size() > 2*S)
				repart();
		}
	}

	// O(n/S * log(S))
	int calc() {
		int ans = 0;
		int pnt = 0;
		for (auto &p : parts) {
			auto [x, y] = p.get(pnt);
			//cerr << "Ps = ";
			//for (auto x : p.Ps)
			//	cerr << x << ", ";
			//cerr << "\npnt = " << pnt << ", x = " << x << ", y = " << y << '\n';
			ans += x;
			pnt = y;
		}
		return ans;
	}
};

const int N = 150'010;
PartList part_list;
int pos[N];
int n;

void init(int n_, int L_, int X[])
{
	n = n_;
	L = L_ + 1;
	Loop (i,0,n)
		pos[i] = X[i];
	part_list.init(vector(pos, pos + n));
}

int update(int i, int y)
{
	part_list.move(pos[i], y);
	pos[i] = y;
	return part_list.calc();
}

// move = O(log(n) + S) + amortized O(n/S)
// calc = O(n/S * log(S))
// q log(n) + qS + nq/S + nq/S log(S)
// qS + nq/S log(S)
// S^2 / log(S) = n
// S = 1280

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct

Subtask #2
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct

Subtask #3
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 206 ms 4836 KB Output is correct
8 Correct 223 ms 5204 KB Output is correct
9 Correct 206 ms 6096 KB Output is correct
10 Correct 200 ms 8180 KB Output is correct
11 Correct 210 ms 8004 KB Output is correct
12 Correct 513 ms 7936 KB Output is correct
13 Correct 214 ms 7952 KB Output is correct

Subtask #4
47.0 / 47.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 206 ms 4836 KB Output is correct
8 Correct 223 ms 5204 KB Output is correct
9 Correct 206 ms 6096 KB Output is correct
10 Correct 200 ms 8180 KB Output is correct
11 Correct 210 ms 8004 KB Output is correct
12 Correct 513 ms 7936 KB Output is correct
13 Correct 214 ms 7952 KB Output is correct
14 Correct 122 ms 5204 KB Output is correct
15 Correct 338 ms 6996 KB Output is correct
16 Correct 805 ms 8824 KB Output is correct
17 Correct 786 ms 10564 KB Output is correct
18 Correct 936 ms 10552 KB Output is correct
19 Correct 343 ms 11172 KB Output is correct
20 Correct 861 ms 10904 KB Output is correct
21 Correct 845 ms 10996 KB Output is correct
22 Correct 295 ms 11024 KB Output is correct

Subtask #5
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 206 ms 4836 KB Output is correct
8 Correct 223 ms 5204 KB Output is correct
9 Correct 206 ms 6096 KB Output is correct
10 Correct 200 ms 8180 KB Output is correct
11 Correct 210 ms 8004 KB Output is correct
12 Correct 513 ms 7936 KB Output is correct
13 Correct 214 ms 7952 KB Output is correct
14 Correct 122 ms 5204 KB Output is correct
15 Correct 338 ms 6996 KB Output is correct
16 Correct 805 ms 8824 KB Output is correct
17 Correct 786 ms 10564 KB Output is correct
18 Correct 936 ms 10552 KB Output is correct
19 Correct 343 ms 11172 KB Output is correct
20 Correct 861 ms 10904 KB Output is correct
21 Correct 845 ms 10996 KB Output is correct
22 Correct 295 ms 11024 KB Output is correct
23 Correct 1458 ms 19428 KB Output is correct
24 Correct 1301 ms 18716 KB Output is correct
25 Correct 794 ms 17692 KB Output is correct
26 Correct 907 ms 23568 KB Output is correct
27 Correct 1142 ms 23608 KB Output is correct
28 Correct 1113 ms 8680 KB Output is correct
29 Correct 1066 ms 8272 KB Output is correct
30 Correct 1070 ms 8832 KB Output is correct
31 Correct 1059 ms 8324 KB Output is correct
32 Correct 855 ms 23388 KB Output is correct
33 Correct 386 ms 15644 KB Output is correct
34 Correct 843 ms 23388 KB Output is correct
35 Correct 337 ms 16248 KB Output is correct
36 Correct 40 ms 6376 KB Output is correct
37 Correct 366 ms 15724 KB Output is correct
38 Correct 798 ms 22888 KB Output is correct
39 Correct 911 ms 23340 KB Output is correct
40 Correct 846 ms 22944 KB Output is correct
41 Correct 2020 ms 22896 KB Output is correct
42 Correct 2062 ms 22368 KB Output is correct