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Submission #1001094

# Submission time Handle Problem Language Result Execution time Memory
1001094 2024-06-18T14:28:41 Z vuavisao September (APIO24_september) C++17
100 / 100
 248 ms 47304 KB 
#include "september.h"
 
#include <vector>

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
 
const int N = 100'000 + 10;
const int INF = 1'000'000'000;

struct FenWick {
	int n_node = 0;
	vector<int> tree;

	void resize(int n) { n_node = n; vector<int>().swap(tree); tree.resize(n_node + 10, 0); }
	FenWick() {};
	FenWick(int n) { this->resize(n); };

	void Update(int idx, int val) {
		for ( ; idx <= n_node; idx += (idx & - idx)) tree[idx] += val;
		return;
	}

	int Query(int idx) {
		int res = 0;
		for ( ; idx > 0; idx -= (idx & - idx)) res += tree[idx];
		return res;
	}

	int Sum_to(int l, int r) {
		if (l > r) return 0;
		return Query(r) - Query(l - 1);
	}

	int kth(int val) {
		int res = 0, s = 0;
		for (int mask = 30; mask >= 0; -- mask) {
			int nxt = res | (1 << mask);
			if (nxt < n_node && s + tree[nxt] < val) {
				res = nxt;
				s += tree[nxt];
			}
		}
		++ res; return res;
	}
};

struct FenWickMax {
	int n_node = 0;
	vector<int> tree;

	void resize(int n) { n_node = n; vector<int>().swap(tree); tree.resize(n_node + 10, -INF); }
	FenWickMax() {};
	FenWickMax(int n) { this->resize(n); };

	void Update(int idx, int val) {
		for ( ; idx > 0; idx -= (idx & - idx)) tree[idx] = max(tree[idx], val);
		return;
	}

	int Query(int idx) {
		int res = -INF;
		for ( ; idx <= n_node; idx += (idx & - idx)) res = max(res, tree[idx]);
		return res;
	}
};

int n, m;
int parent[N];
vector<int> g[N];
int perRem[10][N];

int need[10][N];

namespace Order {
	int indexing[N];

	void dfs(int u, int res[]) {
		int idx = indexing[u];
		res[idx] = idx;
		for (const auto& v : g[u]) {
			dfs(v, res);
			res[idx] = max(res[idx], res[indexing[v]]);
		}
	}
	
	void solve(int perRem[], int res[]) {
		for (int i = 1; i < n; ++ i) {
			indexing[perRem[i]] = i;
		}
		indexing[1] = 0;
		dfs(1, res);
	}
}

namespace One {
	bool check() {
		return (m == 1);
	}

	vector<int> open[N];
	int dp[N];

	int solve() {
		for (int i = 0; i <= n + 1; ++ i) {
			vector<int>().swap(open[i]);
			dp[i] = -INF;
		}
		for (int i = 1; i < n; ++ i) {
			open[need[1][i]].push_back(i);
		}
		dp[0] = 0;
		FenWick bit(n);
		for (int i = 1; i < n; ++ i) bit.Update(i, 1);

		FenWickMax bitMax(n);
		for (int i = 1; i < n; ++ i) {
			for (const auto& idx : open[i]) bit.Update(idx, -1);
			bitMax.Update(i, dp[i - 1]);
			int cnt = bit.Query(i);
			int last = bit.kth(cnt) + (cnt != 0);
			if (last <= i) {
				dp[i] = bitMax.Query(last) + 1;
			}
		}
		return dp[n - 1];
	}
}

namespace Brute_force {
	bool check() {
		return (n <= 1'000);
	}

	unsigned seed = chrono::system_clock::now().time_since_epoch().count();
	mt19937_64 rng(seed); 

	ll Rand(ll a, ll b = 1ll * INF * INF) {
		return a + rng() % (b - a + 1);
	}

	bool can[1'010][1'010];
	ll base[N];
	ll Hash[10][N];

	vector<int> open[N];

	int exist[N];
	int dp[N];

	int solve() {
		srand(time(nullptr));
		for (int i = 0; i <= n + 1; ++ i) {
			dp[i] = -INF;
			exist[i] = 0;
			vector<int>().swap(open[i]);
		}
		for (int i = 0; i <= n + 1; ++ i) {
			for (int j = 0; j <= n + 1; ++ j) {
				can[i][j] = false;
			}
		}
		for (int i = 1; i <= n; ++ i) base[i] = Rand(1);
		for (int i = 1; i <= m; ++ i) {
			for (int j = 1; j < n; ++ j) {
				Hash[i][j] = base[perRem[i][j]];
				open[need[i][j]].push_back(j);
			}
		}
		for (int i = 1; i < n; ++ i) {
			ll xorHash[6];
			memset(xorHash, 0, sizeof(xorHash));
			for (int j = i; j < n; ++ j) {
				for (int k = 1; k <= m; ++ k) {
					xorHash[k] ^= Hash[k][j];
				}
				if (*min_element(xorHash + 1, xorHash + 1 + m) == *max_element(xorHash + 1, xorHash + 1 + m)) {
					can[i][j] = true;
				}
			}
		}
		dp[0] = 0;
		for (int i = 1; i < n; ++ i) {
			for (const auto& idx : open[i]) ++ exist[idx];
			for (int j = i; j >= 1; -- j) {
				if (exist[j] < m) break;
				if (can[j][i]) {
					// cout << j << ' ' << i << ' ' << dp[i] << ' ' << dp[j - 1] << '\n';
					dp[i] = max(dp[i], dp[j - 1] + 1);
				}
			}
		}
		return dp[n - 1];
	}
}

namespace Full {
	int L[N], R[N];
	int pred[N];
	vector<int> position[N];
	int indexing[N];

	vector<int> open[N];
	int exist[N];

	FenWickMax bitMax[N];
	int dp[N];

	int solve() {
		for (int i = 0; i <= n + 1; ++ i) {
			position[i].clear();
			pred[i] = 0;
			L[i] = n + 1;
			R[i] = 0;

			dp[i] = -INF;
			exist[i] = 0;
			vector<int>().swap(open[i]);
		}
		for (int i = 1; i <= m; ++ i) {
			for (int j = 1; j < n; ++ j) {
				int u = perRem[i][j];
				L[u] = min(L[u], j);
				R[u] = max(R[u], j);

				open[need[i][j]].push_back(j);
			}
		}

		for (int u = 2; u <= n; ++ u) {
			++ pred[L[u]];
			-- pred[R[u]];
		}
		for (int i = 1; i < n; ++ i) {
			pred[i] += pred[i - 1];
			position[pred[i - 1]].push_back(i - 1);
			indexing[i - 1] = position[pred[i - 1]].size();
		}
		
		FenWick bit(n);
		for (int i = 1; i < n; ++ i) bit.Update(i, m);

		for (int i = 0; i < n; ++ i) {
			if (position[i].empty()) continue;
			bitMax[i].resize(position[i].size());
		}
		dp[0] = 0;
		
		for (int i = 1; i < n; ++ i) {
			for (const auto& idx : open[i]) {
				bit.Update(idx, -1);
				if (++ exist[idx] == m) {
					int newIndex = idx - 1;
					assert(newIndex < i);
					int group = pred[newIndex];
					bitMax[group].Update(indexing[newIndex], dp[newIndex]);
				}
			}
			int group = pred[i];
			if (position[group].empty()) continue;
			
			int cnt = bit.Query(i);
			int last = bit.kth(cnt) - (cnt == 0);
			auto ptr = lower_bound(position[group].begin(), position[group].end(), last);
			if (ptr != position[group].end()) {
				int idx = position[group][ptr - position[group].begin()];
				dp[i] = bitMax[group].Query(indexing[idx]) + 1;
			}
		}
		return dp[n - 1];
	}
}
 
int solve(int N, int M, std::vector<int> F, std::vector<std::vector<int>> S) {
	n = N; m = M;
	for (int i = 0; i <= n + 1; ++ i) g[i].clear();
	for (int v = 2; v <= n; ++ v) {
		int u = F[v - 1] + 1;
		g[u].push_back(v);
		parent[v] = u;
	}
	for (int i = 0; i < m; ++ i) {
		for (int j = 0; j < n - 1; ++ j) {
			perRem[i + 1][j + 1] = S[i][j] + 1;
		}
	}

	for (int i = 1; i <= m; ++ i) {
		Order::solve(perRem[i], need[i]);
	}
	
	if (One::check()) {
		return One::solve();
	}
	if (Brute_force::check()) {
		return Brute_force::solve();
	}
	return Full::solve();
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 24156 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 4 ms 24160 KB Output is correct
4 Correct 5 ms 24156 KB Output is correct
5 Correct 4 ms 24156 KB Output is correct
6 Correct 5 ms 24156 KB Output is correct
7 Correct 4 ms 24180 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 24156 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 4 ms 24160 KB Output is correct
4 Correct 5 ms 24156 KB Output is correct
5 Correct 4 ms 24156 KB Output is correct
6 Correct 5 ms 24156 KB Output is correct
7 Correct 4 ms 24180 KB Output is correct
8 Correct 5 ms 26204 KB Output is correct
9 Correct 5 ms 30300 KB Output is correct
10 Correct 4 ms 22136 KB Output is correct
11 Correct 4 ms 24156 KB Output is correct
12 Correct 5 ms 24156 KB Output is correct
13 Correct 5 ms 32348 KB Output is correct
14 Correct 5 ms 34396 KB Output is correct

Subtask #3
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 24160 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 5 ms 24152 KB Output is correct

Subtask #4
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 24156 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 4 ms 24160 KB Output is correct
4 Correct 5 ms 24156 KB Output is correct
5 Correct 4 ms 24156 KB Output is correct
6 Correct 5 ms 24156 KB Output is correct
7 Correct 4 ms 24180 KB Output is correct
8 Correct 5 ms 24160 KB Output is correct
9 Correct 4 ms 24156 KB Output is correct
10 Correct 5 ms 24152 KB Output is correct
11 Correct 7 ms 24164 KB Output is correct
12 Correct 5 ms 24152 KB Output is correct
13 Correct 5 ms 24156 KB Output is correct
14 Correct 5 ms 24156 KB Output is correct
15 Correct 5 ms 24156 KB Output is correct
16 Correct 5 ms 22108 KB Output is correct
17 Correct 5 ms 24184 KB Output is correct

Subtask #5
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 24160 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 5 ms 24152 KB Output is correct
4 Correct 14 ms 22620 KB Output is correct
5 Correct 14 ms 22872 KB Output is correct
6 Correct 13 ms 25180 KB Output is correct

Subtask #6
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 24156 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 4 ms 24160 KB Output is correct
4 Correct 5 ms 24156 KB Output is correct
5 Correct 4 ms 24156 KB Output is correct
6 Correct 5 ms 24156 KB Output is correct
7 Correct 4 ms 24180 KB Output is correct
8 Correct 5 ms 26204 KB Output is correct
9 Correct 5 ms 30300 KB Output is correct
10 Correct 4 ms 22136 KB Output is correct
11 Correct 4 ms 24156 KB Output is correct
12 Correct 5 ms 24156 KB Output is correct
13 Correct 5 ms 32348 KB Output is correct
14 Correct 5 ms 34396 KB Output is correct
15 Correct 5 ms 24160 KB Output is correct
16 Correct 4 ms 24156 KB Output is correct
17 Correct 5 ms 24152 KB Output is correct
18 Correct 7 ms 24164 KB Output is correct
19 Correct 5 ms 24152 KB Output is correct
20 Correct 5 ms 24156 KB Output is correct
21 Correct 5 ms 24156 KB Output is correct
22 Correct 5 ms 24156 KB Output is correct
23 Correct 5 ms 22108 KB Output is correct
24 Correct 5 ms 24184 KB Output is correct
25 Correct 14 ms 22620 KB Output is correct
26 Correct 14 ms 22872 KB Output is correct
27 Correct 13 ms 25180 KB Output is correct
28 Correct 14 ms 23132 KB Output is correct
29 Correct 14 ms 34636 KB Output is correct
30 Correct 15 ms 34396 KB Output is correct
31 Correct 13 ms 34396 KB Output is correct
32 Correct 13 ms 23132 KB Output is correct
33 Correct 13 ms 34392 KB Output is correct
34 Correct 14 ms 20828 KB Output is correct

Subtask #7
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 24160 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 5 ms 24152 KB Output is correct
4 Correct 208 ms 38640 KB Output is correct
5 Correct 228 ms 39020 KB Output is correct
6 Correct 222 ms 39968 KB Output is correct

Subtask #8
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 24156 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 4 ms 24160 KB Output is correct
4 Correct 5 ms 24156 KB Output is correct
5 Correct 4 ms 24156 KB Output is correct
6 Correct 5 ms 24156 KB Output is correct
7 Correct 4 ms 24180 KB Output is correct
8 Correct 5 ms 24160 KB Output is correct
9 Correct 4 ms 24156 KB Output is correct
10 Correct 5 ms 24152 KB Output is correct
11 Correct 7 ms 24164 KB Output is correct
12 Correct 5 ms 24152 KB Output is correct
13 Correct 5 ms 24156 KB Output is correct
14 Correct 5 ms 24156 KB Output is correct
15 Correct 5 ms 24156 KB Output is correct
16 Correct 5 ms 22108 KB Output is correct
17 Correct 5 ms 24184 KB Output is correct
18 Correct 208 ms 38640 KB Output is correct
19 Correct 228 ms 39020 KB Output is correct
20 Correct 222 ms 39968 KB Output is correct
21 Correct 248 ms 33972 KB Output is correct
22 Correct 237 ms 35060 KB Output is correct
23 Correct 222 ms 34196 KB Output is correct
24 Correct 210 ms 30308 KB Output is correct
25 Correct 240 ms 29432 KB Output is correct
26 Correct 245 ms 29660 KB Output is correct
27 Correct 230 ms 33364 KB Output is correct

Subtask #9
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 24160 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 5 ms 24152 KB Output is correct
4 Correct 14 ms 22620 KB Output is correct
5 Correct 14 ms 22872 KB Output is correct
6 Correct 13 ms 25180 KB Output is correct
7 Correct 208 ms 38640 KB Output is correct
8 Correct 228 ms 39020 KB Output is correct
9 Correct 222 ms 39968 KB Output is correct
10 Correct 204 ms 47304 KB Output is correct
11 Correct 188 ms 44232 KB Output is correct
12 Correct 196 ms 43332 KB Output is correct

Subtask #10
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 24156 KB Output is correct
2 Correct 4 ms 24156 KB Output is correct
3 Correct 4 ms 24160 KB Output is correct
4 Correct 5 ms 24156 KB Output is correct
5 Correct 4 ms 24156 KB Output is correct
6 Correct 5 ms 24156 KB Output is correct
7 Correct 4 ms 24180 KB Output is correct
8 Correct 5 ms 26204 KB Output is correct
9 Correct 5 ms 30300 KB Output is correct
10 Correct 4 ms 22136 KB Output is correct
11 Correct 4 ms 24156 KB Output is correct
12 Correct 5 ms 24156 KB Output is correct
13 Correct 5 ms 32348 KB Output is correct
14 Correct 5 ms 34396 KB Output is correct
15 Correct 5 ms 24160 KB Output is correct
16 Correct 4 ms 24156 KB Output is correct
17 Correct 5 ms 24152 KB Output is correct
18 Correct 7 ms 24164 KB Output is correct
19 Correct 5 ms 24152 KB Output is correct
20 Correct 5 ms 24156 KB Output is correct
21 Correct 5 ms 24156 KB Output is correct
22 Correct 5 ms 24156 KB Output is correct
23 Correct 5 ms 22108 KB Output is correct
24 Correct 5 ms 24184 KB Output is correct
25 Correct 14 ms 22620 KB Output is correct
26 Correct 14 ms 22872 KB Output is correct
27 Correct 13 ms 25180 KB Output is correct
28 Correct 14 ms 23132 KB Output is correct
29 Correct 14 ms 34636 KB Output is correct
30 Correct 15 ms 34396 KB Output is correct
31 Correct 13 ms 34396 KB Output is correct
32 Correct 13 ms 23132 KB Output is correct
33 Correct 13 ms 34392 KB Output is correct
34 Correct 14 ms 20828 KB Output is correct
35 Correct 208 ms 38640 KB Output is correct
36 Correct 228 ms 39020 KB Output is correct
37 Correct 222 ms 39968 KB Output is correct
38 Correct 248 ms 33972 KB Output is correct
39 Correct 237 ms 35060 KB Output is correct
40 Correct 222 ms 34196 KB Output is correct
41 Correct 210 ms 30308 KB Output is correct
42 Correct 240 ms 29432 KB Output is correct
43 Correct 245 ms 29660 KB Output is correct
44 Correct 230 ms 33364 KB Output is correct
45 Correct 204 ms 47304 KB Output is correct
46 Correct 188 ms 44232 KB Output is correct
47 Correct 196 ms 43332 KB Output is correct
48 Correct 202 ms 37064 KB Output is correct
49 Correct 229 ms 38728 KB Output is correct
50 Correct 197 ms 38972 KB Output is correct
51 Correct 194 ms 37836 KB Output is correct
52 Correct 212 ms 36900 KB Output is correct
53 Correct 199 ms 36812 KB Output is correct
54 Correct 202 ms 37924 KB Output is correct