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Submission #1048816

# Submission time Handle Problem Language Result Execution time Memory
1048816 2024-08-08T09:38:27 Z vjudge1 Rectangles (IOI19_rect) C++17
100 / 100
 4176 ms 974228 KB 
#include "rect.h"
#include <bits/stdc++.h>
#define pb push_back
// #define endl ("\n")
#define all(aa) aa.begin(), aa.end()
typedef long long ll;
using namespace std;

struct DSU{
	int n, t;
	vector<int> p;
	DSU(int n, int t) : n(n), t(t), p(n) {
		for(int i = 0; i < n; i++) p[i] = i;
	}

	int find(int u){
		if(p[u] == u) return u;
		return p[u] = find(p[u]);
	}

	void merge(int u, int v){
		u = find(u);
		v = find(v);
		if(u == v) return;
		if(u > v) swap(u, v);
		if(t)
			p[u] = v;
		else
			p[v] = u;
	}
};

struct fenwick{
	int n;
	vector<int> fen;
	fenwick(int n) : n(n), fen(n){}

	void upd(int pos, int val){
		for(; pos < n; pos |= pos + 1)
			fen[pos] += val;
	}

	int query(int pos){
		int ret = 0;
		for(; pos >= 0; pos = (pos & (pos + 1)) - 1)
			ret += fen[pos];
		return ret;
	}

	int query(int ql, int qr){
		return query(qr) - query(ql - 1);
	}

};

ll count_rectangles(vector<vector<int>> a){
	int n = a.size(), m = a[0].size();
	ll ans = 0;

	vector<vector<pair<int, int>>> rows(n);
	for(int i = 0; i < n; i++){
		vector<pair<int, int>> vals;
		vector<int> act(m);
		DSU left(m, 0), right(m, 1);
		for(int j = 0; j < m; j++)
			vals.pb({a[i][j], j});
		sort(all(vals));
		vector<vector<int>> same_idx(m);
		int c = -1;
		for(int k = 0, lst = -1; k < m; k++){
			c += (lst != vals[k].first);
			same_idx[c].pb(vals[k].second);
			lst = vals[k].first;
		}
		same_idx.resize(c);

		for(int j = 0; j < c; j++){
			for(int ind : same_idx[j]){
				act[ind] = 1;
				if(ind && act[ind - 1])
					left.merge(ind - 1, ind), right.merge(ind - 1, ind);
				if(ind < m - 1 && act[ind + 1])
					left.merge(ind, ind + 1), right.merge(ind, ind + 1);
			}
			set<pair<int, int>> interval;
			for(int ind : same_idx[j])
				interval.insert({left.find(ind), right.find(ind)});
			for(auto [tl, tr] : interval)
				if(tl != 0 && tr != m - 1)
					rows[i].pb({tl, tr});
		}
	}

	vector<vector<vector<pair<int, int>>>> down_extend(n, vector<vector<pair<int, int>>>(m));
	vector<vector<int>> dp(m, vector<int>(m, -1));
	vector<vector<int>> dp2(m, vector<int>(m, -1));
	for(int i = n - 1; i >= 0; i--){
		for(auto [tl, tr] : rows[i]){
			int cev = (dp[tl][tr] == i + 1 ? dp2[tl][tr] + 1 : 1);
			down_extend[i][tl].pb({tr, cev});
			dp[tl][tr] = i;
			dp2[tl][tr] = cev;
		}
	}

	vector<vector<pair<int, int>>> cols(m);
	for(int i = 0; i < m; i++){
		vector<pair<int, int>> vals;
		vector<int> act(n);
		DSU up(n, 0), down(n, 1);
		for(int j = 0; j < n; j++)
			vals.pb({a[j][i], j});
		sort(all(vals));
		vector<vector<int>> same_idx(n);
		int c = -1;
		for(int k = 0, lst = - 1; k < n; k++){
			c += (vals[k].first != lst);
			same_idx[c].pb(vals[k].second);
			lst = vals[k].first;
		}
		same_idx.resize(c);

		for(int j = 0; j < c; j++){
			for(int ind : same_idx[j]){
				act[ind] = 1;
				if(ind && act[ind - 1])
					up.merge(ind - 1, ind), down.merge(ind - 1, ind);
				if(ind < n - 1 && act[ind + 1])
					up.merge(ind, ind + 1), down.merge(ind, ind + 1);
			}
			set<pair<int, int>> interval;
			for(int ind : same_idx[j])
				interval.insert({up.find(ind), down.find(ind)});
			for(auto [tl, tr] : interval)
				if(tl != 0 && tr != n - 1)
					cols[i].pb({tl, tr});
		}
	}

	vector<vector<vector<pair<int, int>>>> right_extend(n, vector<vector<pair<int, int>>>(m));
	vector<vector<int>> DP(n, vector<int>(n));
	vector<vector<int>> DP2(n, vector<int>(n));
	for(int i = m - 1; i >= 0; i--){
		for(auto [tl, tr] : cols[i]){
			int cev = (DP[tl][tr] == i + 1 ? DP2[tl][tr] + 1 : 1);
			right_extend[tl][i].pb({cev, tr});
			DP[tl][tr] = i;
			DP2[tl][tr] = cev;
		}
	}

	fenwick fen(n);
	for(int i = 0; i < n; i++) for(int j = 0; j < m; j++){
			sort(all(right_extend[i][j]));
			sort(all(down_extend[i][j])); reverse(all(down_extend[i][j]));
	}

	for(int i = 0; i < n; i++){
		for(int j = 0; j < m; j++){
			int c = right_extend[i][j].size() - 1;
			vector<int> rollback;
			for(auto [tr, ext] : down_extend[i][j]){
				while(c >= 0 && j + right_extend[i][j][c].first - 1 >= tr){
					fen.upd(right_extend[i][j][c].second , 1);
					rollback.pb(right_extend[i][j][c].second);
					c--;
				}
				ans += fen.query(i, i + ext - 1);
			}
			for(int x : rollback)
				fen.upd(x, -1);
		}
	}

	return ans;
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 452 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 544 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 452 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 544 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 3 ms 1384 KB Output is correct
23 Correct 2 ms 1372 KB Output is correct
24 Correct 2 ms 1372 KB Output is correct
25 Correct 2 ms 1112 KB Output is correct
26 Correct 3 ms 1116 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct
28 Correct 3 ms 1156 KB Output is correct
29 Correct 2 ms 1112 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 452 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 544 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 3 ms 1384 KB Output is correct
18 Correct 2 ms 1372 KB Output is correct
19 Correct 2 ms 1372 KB Output is correct
20 Correct 2 ms 1112 KB Output is correct
21 Correct 3 ms 1116 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 3 ms 1156 KB Output is correct
24 Correct 2 ms 1112 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 348 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 0 ms 348 KB Output is correct
30 Correct 14 ms 6744 KB Output is correct
31 Correct 14 ms 6744 KB Output is correct
32 Correct 14 ms 6848 KB Output is correct
33 Correct 10 ms 4480 KB Output is correct
34 Correct 19 ms 5468 KB Output is correct
35 Correct 19 ms 5872 KB Output is correct
36 Correct 18 ms 5468 KB Output is correct
37 Correct 17 ms 5468 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 452 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 544 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 3 ms 1384 KB Output is correct
18 Correct 2 ms 1372 KB Output is correct
19 Correct 2 ms 1372 KB Output is correct
20 Correct 2 ms 1112 KB Output is correct
21 Correct 3 ms 1116 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 3 ms 1156 KB Output is correct
24 Correct 2 ms 1112 KB Output is correct
25 Correct 14 ms 6744 KB Output is correct
26 Correct 14 ms 6744 KB Output is correct
27 Correct 14 ms 6848 KB Output is correct
28 Correct 10 ms 4480 KB Output is correct
29 Correct 19 ms 5468 KB Output is correct
30 Correct 19 ms 5872 KB Output is correct
31 Correct 18 ms 5468 KB Output is correct
32 Correct 17 ms 5468 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 1 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 150 ms 58000 KB Output is correct
39 Correct 140 ms 53140 KB Output is correct
40 Correct 128 ms 53220 KB Output is correct
41 Correct 120 ms 48264 KB Output is correct
42 Correct 175 ms 78672 KB Output is correct
43 Correct 173 ms 78588 KB Output is correct
44 Correct 175 ms 78928 KB Output is correct
45 Correct 164 ms 74320 KB Output is correct
46 Correct 129 ms 46164 KB Output is correct
47 Correct 162 ms 51416 KB Output is correct
48 Correct 294 ms 65364 KB Output is correct
49 Correct 291 ms 66576 KB Output is correct
50 Correct 113 ms 34660 KB Output is correct
51 Correct 126 ms 34508 KB Output is correct
52 Correct 247 ms 64116 KB Output is correct
53 Correct 246 ms 64772 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 50268 KB Output is correct
2 Correct 14 ms 36696 KB Output is correct
3 Correct 20 ms 49960 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 20 ms 50304 KB Output is correct
6 Correct 19 ms 50216 KB Output is correct
7 Correct 20 ms 50268 KB Output is correct
8 Correct 20 ms 50264 KB Output is correct
9 Correct 20 ms 50268 KB Output is correct
10 Correct 17 ms 49756 KB Output is correct
11 Correct 18 ms 50012 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 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 803 ms 279164 KB Output is correct
8 Correct 1720 ms 582048 KB Output is correct
9 Correct 1783 ms 584852 KB Output is correct
10 Correct 1745 ms 585024 KB Output is correct
11 Correct 312 ms 233760 KB Output is correct
12 Correct 574 ms 419672 KB Output is correct
13 Correct 585 ms 447040 KB Output is correct

Subtask #7
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 452 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 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 544 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 3 ms 1384 KB Output is correct
18 Correct 2 ms 1372 KB Output is correct
19 Correct 2 ms 1372 KB Output is correct
20 Correct 2 ms 1112 KB Output is correct
21 Correct 3 ms 1116 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 3 ms 1156 KB Output is correct
24 Correct 2 ms 1112 KB Output is correct
25 Correct 14 ms 6744 KB Output is correct
26 Correct 14 ms 6744 KB Output is correct
27 Correct 14 ms 6848 KB Output is correct
28 Correct 10 ms 4480 KB Output is correct
29 Correct 19 ms 5468 KB Output is correct
30 Correct 19 ms 5872 KB Output is correct
31 Correct 18 ms 5468 KB Output is correct
32 Correct 17 ms 5468 KB Output is correct
33 Correct 150 ms 58000 KB Output is correct
34 Correct 140 ms 53140 KB Output is correct
35 Correct 128 ms 53220 KB Output is correct
36 Correct 120 ms 48264 KB Output is correct
37 Correct 175 ms 78672 KB Output is correct
38 Correct 173 ms 78588 KB Output is correct
39 Correct 175 ms 78928 KB Output is correct
40 Correct 164 ms 74320 KB Output is correct
41 Correct 129 ms 46164 KB Output is correct
42 Correct 162 ms 51416 KB Output is correct
43 Correct 294 ms 65364 KB Output is correct
44 Correct 291 ms 66576 KB Output is correct
45 Correct 113 ms 34660 KB Output is correct
46 Correct 126 ms 34508 KB Output is correct
47 Correct 247 ms 64116 KB Output is correct
48 Correct 246 ms 64772 KB Output is correct
49 Correct 25 ms 50268 KB Output is correct
50 Correct 14 ms 36696 KB Output is correct
51 Correct 20 ms 49960 KB Output is correct
52 Correct 0 ms 348 KB Output is correct
53 Correct 20 ms 50304 KB Output is correct
54 Correct 19 ms 50216 KB Output is correct
55 Correct 20 ms 50268 KB Output is correct
56 Correct 20 ms 50264 KB Output is correct
57 Correct 20 ms 50268 KB Output is correct
58 Correct 17 ms 49756 KB Output is correct
59 Correct 18 ms 50012 KB Output is correct
60 Correct 0 ms 348 KB Output is correct
61 Correct 803 ms 279164 KB Output is correct
62 Correct 1720 ms 582048 KB Output is correct
63 Correct 1783 ms 584852 KB Output is correct
64 Correct 1745 ms 585024 KB Output is correct
65 Correct 312 ms 233760 KB Output is correct
66 Correct 574 ms 419672 KB Output is correct
67 Correct 585 ms 447040 KB Output is correct
68 Correct 0 ms 348 KB Output is correct
69 Correct 0 ms 348 KB Output is correct
70 Correct 0 ms 348 KB Output is correct
71 Correct 1 ms 348 KB Output is correct
72 Correct 0 ms 348 KB Output is correct
73 Correct 2023 ms 722044 KB Output is correct
74 Correct 1786 ms 654952 KB Output is correct
75 Correct 1672 ms 655044 KB Output is correct
76 Correct 1665 ms 588008 KB Output is correct
77 Correct 2680 ms 974228 KB Output is correct
78 Correct 2294 ms 491940 KB Output is correct
79 Correct 2474 ms 520944 KB Output is correct
80 Correct 4176 ms 799860 KB Output is correct
81 Correct 2275 ms 501600 KB Output is correct
82 Correct 3114 ms 648036 KB Output is correct
83 Correct 3950 ms 815972 KB Output is correct
84 Correct 2144 ms 482352 KB Output is correct
85 Correct 3791 ms 793524 KB Output is correct
86 Correct 3626 ms 770792 KB Output is correct
87 Correct 1425 ms 597072 KB Output is correct
88 Correct 2543 ms 973700 KB Output is correct
89 Correct 2600 ms 950616 KB Output is correct
90 Correct 2686 ms 950340 KB Output is correct