oj.uz

Submission #1089751

# Submission time Handle Problem Language Result Execution time Memory
1089751 2024-09-17T05:39:57 Z ymm Dancing Elephants (IOI11_elephants) C++17
100 / 100
 2457 ms 25608 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 = 1280;

	// 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 0 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 0 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 1 ms 344 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct

Subtask #3
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 1 ms 344 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 260 ms 4912 KB Output is correct
8 Correct 263 ms 5308 KB Output is correct
9 Correct 254 ms 6716 KB Output is correct
10 Correct 202 ms 8460 KB Output is correct
11 Correct 239 ms 8412 KB Output is correct
12 Correct 619 ms 8256 KB Output is correct
13 Correct 205 ms 8156 KB Output is correct

Subtask #4
47.0 / 47.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 1 ms 344 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 260 ms 4912 KB Output is correct
8 Correct 263 ms 5308 KB Output is correct
9 Correct 254 ms 6716 KB Output is correct
10 Correct 202 ms 8460 KB Output is correct
11 Correct 239 ms 8412 KB Output is correct
12 Correct 619 ms 8256 KB Output is correct
13 Correct 205 ms 8156 KB Output is correct
14 Correct 158 ms 5420 KB Output is correct
15 Correct 374 ms 7252 KB Output is correct
16 Correct 992 ms 9532 KB Output is correct
17 Correct 946 ms 11168 KB Output is correct
18 Correct 1097 ms 11420 KB Output is correct
19 Correct 363 ms 11772 KB Output is correct
20 Correct 1044 ms 12264 KB Output is correct
21 Correct 984 ms 11980 KB Output is correct
22 Correct 337 ms 11192 KB Output is correct

Subtask #5
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 1 ms 344 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 260 ms 4912 KB Output is correct
8 Correct 263 ms 5308 KB Output is correct
9 Correct 254 ms 6716 KB Output is correct
10 Correct 202 ms 8460 KB Output is correct
11 Correct 239 ms 8412 KB Output is correct
12 Correct 619 ms 8256 KB Output is correct
13 Correct 205 ms 8156 KB Output is correct
14 Correct 158 ms 5420 KB Output is correct
15 Correct 374 ms 7252 KB Output is correct
16 Correct 992 ms 9532 KB Output is correct
17 Correct 946 ms 11168 KB Output is correct
18 Correct 1097 ms 11420 KB Output is correct
19 Correct 363 ms 11772 KB Output is correct
20 Correct 1044 ms 12264 KB Output is correct
21 Correct 984 ms 11980 KB Output is correct
22 Correct 337 ms 11192 KB Output is correct
23 Correct 1614 ms 21536 KB Output is correct
24 Correct 1426 ms 20860 KB Output is correct
25 Correct 843 ms 19808 KB Output is correct
26 Correct 1042 ms 25608 KB Output is correct
27 Correct 1150 ms 25372 KB Output is correct
28 Correct 1658 ms 10012 KB Output is correct
29 Correct 1621 ms 9292 KB Output is correct
30 Correct 1615 ms 9800 KB Output is correct
31 Correct 1599 ms 9296 KB Output is correct
32 Correct 835 ms 24864 KB Output is correct
33 Correct 445 ms 17112 KB Output is correct
34 Correct 730 ms 25116 KB Output is correct
35 Correct 332 ms 18340 KB Output is correct
36 Correct 45 ms 8272 KB Output is correct
37 Correct 388 ms 18120 KB Output is correct
38 Correct 781 ms 24096 KB Output is correct
39 Correct 901 ms 25016 KB Output is correct
40 Correct 818 ms 24092 KB Output is correct
41 Correct 2348 ms 23884 KB Output is correct
42 Correct 2457 ms 25372 KB Output is correct