oj.uz

Submission #1089753

# Submission time Handle Problem Language Result Execution time Memory
1089753 2024-09-17T05:41:57 Z ymm Dancing Elephants (IOI11_elephants) C++17
100 / 100
 1742 ms 23500 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 = 768;

	// 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 348 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 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Correct 1 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 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 176 ms 4540 KB Output is correct
8 Correct 180 ms 5132 KB Output is correct
9 Correct 186 ms 6456 KB Output is correct
10 Correct 163 ms 8304 KB Output is correct
11 Correct 216 ms 8328 KB Output is correct
12 Correct 409 ms 8240 KB Output is correct
13 Correct 176 ms 8192 KB Output is correct

Subtask #4
47.0 / 47.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 176 ms 4540 KB Output is correct
8 Correct 180 ms 5132 KB Output is correct
9 Correct 186 ms 6456 KB Output is correct
10 Correct 163 ms 8304 KB Output is correct
11 Correct 216 ms 8328 KB Output is correct
12 Correct 409 ms 8240 KB Output is correct
13 Correct 176 ms 8192 KB Output is correct
14 Correct 118 ms 5196 KB Output is correct
15 Correct 268 ms 7248 KB Output is correct
16 Correct 645 ms 8764 KB Output is correct
17 Correct 642 ms 10332 KB Output is correct
18 Correct 761 ms 10564 KB Output is correct
19 Correct 288 ms 11420 KB Output is correct
20 Correct 725 ms 10744 KB Output is correct
21 Correct 678 ms 10972 KB Output is correct
22 Correct 256 ms 11164 KB Output is correct

Subtask #5
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 176 ms 4540 KB Output is correct
8 Correct 180 ms 5132 KB Output is correct
9 Correct 186 ms 6456 KB Output is correct
10 Correct 163 ms 8304 KB Output is correct
11 Correct 216 ms 8328 KB Output is correct
12 Correct 409 ms 8240 KB Output is correct
13 Correct 176 ms 8192 KB Output is correct
14 Correct 118 ms 5196 KB Output is correct
15 Correct 268 ms 7248 KB Output is correct
16 Correct 645 ms 8764 KB Output is correct
17 Correct 642 ms 10332 KB Output is correct
18 Correct 761 ms 10564 KB Output is correct
19 Correct 288 ms 11420 KB Output is correct
20 Correct 725 ms 10744 KB Output is correct
21 Correct 678 ms 10972 KB Output is correct
22 Correct 256 ms 11164 KB Output is correct
23 Correct 1236 ms 19364 KB Output is correct
24 Correct 1161 ms 18720 KB Output is correct
25 Correct 686 ms 17688 KB Output is correct
26 Correct 888 ms 23452 KB Output is correct
27 Correct 1004 ms 23500 KB Output is correct
28 Correct 909 ms 8724 KB Output is correct
29 Correct 885 ms 8272 KB Output is correct
30 Correct 933 ms 8836 KB Output is correct
31 Correct 814 ms 8272 KB Output is correct
32 Correct 780 ms 23272 KB Output is correct
33 Correct 373 ms 15768 KB Output is correct
34 Correct 699 ms 23316 KB Output is correct
35 Correct 316 ms 15992 KB Output is correct
36 Correct 48 ms 6740 KB Output is correct
37 Correct 393 ms 16076 KB Output is correct
38 Correct 725 ms 22924 KB Output is correct
39 Correct 818 ms 23356 KB Output is correct
40 Correct 753 ms 22852 KB Output is correct
41 Correct 1705 ms 22096 KB Output is correct
42 Correct 1742 ms 22620 KB Output is correct