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Submission #500576

# Submission time Handle Problem Language Result Execution time Memory
500576 2021-12-31T12:31:34 Z InternetPerson10 Rectangles (IOI19_rect) C++17
100 / 100
 3469 ms 443128 KB 
#include "rect.h"
#include <bits/stdc++.h>
 
using namespace std;
 
const int SMALL = -2;
const int BIG = 1234567890;
 
struct ordered_set { // This is actually just a fenwick tree
    vector<int> nums;
    int size = 4096;
    int ct = 0;
    ordered_set() {
        nums.resize(size+1);
    }
    void insert(int n) {
        ct++;
        n++;
        while(n <= size) {
            nums[n]++;
            n += (n & (-n));
        }
    }
    void erase(int n) {
        ct--;
        n++;
        while(n <= size) {
            nums[n]--;
            n += (n & (-n));
        }
    }
    int count(int n) {
        int ans = 0;
        while(n) {
            ans += nums[n];
            n -= (n & (-n));
        }
        return ct - ans;
    }
};
 
long long count_rectangles(vector<vector<int>> a) {
    // Idea: consider "good" segments, where the ones to the left and to the right are bigger
    // It turns out there are O(n) such subsegments in a segment with n elements
    // Thus, in a "good" rectangle, each row and column must be a good segment
    // Fix the upper left corner of a rectangle, consider some particular segment
    //  which starts at this square, WLOG it is horizontal
    // The number of rectangles that "use" this segment is equal to the number of
    //  vertical segments that all have the same length, which cover the same width
    // You can do this with like, sweep line
    int n = a.size();
    int m = a[0].size();
    if(min(n, m) <= 2) return 0;
    vector<vector<vector<pair<int, int>>>> ps(n);
    vector<pair<int, int>> v;
    for(int i = 0; i < n; i++) {
        ps[i].resize(m);
        v.push_back({BIG, -1});
        for(int j = 0; j < m; j++) {
            while(v.back().first < a[i][j]) {
                if(j - v.back().second > 1) ps[i][v.back().second+1].push_back({1, j-1});
                while(v.size() >= 2) {
                    if(v.back().first == v[v.size()-2].first) v.pop_back();
                    else break;
                }
                v.pop_back();
            }
            if(j - v.back().second > 1 && v.size() > 1) ps[i][v.back().second+1].push_back({1, j-1});
            v.push_back({a[i][j], j});
        }
        vector<pair<int, int>>().swap(v);
    }
    for(int i = 0; i < m; i++) {
        v.push_back({BIG, -1});
        for(int j = 0; j < n; j++) {
            while(v.back().first < a[j][i]) {
                if(j - v.back().second > 1) ps[v.back().second+1][i].push_back({-1, j-1});
                while(v.size() >= 2) {
                    if(v.back().first == v[v.size()-2].first) v.pop_back();
                    else break;
                }
                v.pop_back();
            }
            if(j - v.back().second > 1 && v.size() > 1) ps[v.back().second+1][i].push_back({-1, j-1});
            v.push_back({a[j][i], j});
        }
        vector<pair<int, int>>().swap(v);
    }
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < m; j++) {
            for(auto &p : ps[i][j]) {
                swap(p.first, p.second);
                // cout << i << ' ' << j << ' ' << p.first << ' ' << p.second << '\n';
            }
            sort(ps[i][j].begin(), ps[i][j].end());
        }
    }
    for(int i = n-2; i > 0; i--) {
        for(int j = m-2; j > 0; j--) {
            for(auto &p : ps[i][j]) {
                if(p.second > 0) { // strokes horizontal
                    pair<int, int> pe = {p.first, 0};
                    auto it = lower_bound(ps[i+1][j].begin(), ps[i+1][j].end(), pe);
                    if(it != ps[i+1][j].end()) {
                        auto pa = (*it);
                        // cout << pa.first << ' ' << pa.second << '\n';
                        if(pa.first == p.first && pa.second > 0) {
                            p.second += pa.second;
                        }
                    }
                }
                else { // strokes vertical
                    pair<int, int> pe = {p.first, -BIG};
                    auto it = lower_bound(ps[i][j+1].begin(), ps[i][j+1].end(), pe);
                    if(it != ps[i][j+1].end()) {
                        auto pa = (*it);
                        if(pa.first == p.first && pa.second < 0) {
                            p.second += pa.second;
                        }
                    }
                }
            }
        }
    }
    long long ans = 0;
    ordered_set s;
    for(int i = 1; i < n-1; i++) {
        for(int j = 1; j < m-1; j++) {
            vector<pair<pair<int, int>, int>> pts;
            for(auto p : ps[i][j]) {
                // cout << i << ' ' << j << ' ' << p.first << ' ' << p.second << '\n';
                if(p.second > 0) pts.push_back({{i-1+p.second, -p.first}, 1});
                else pts.push_back({{p.first, -j+1+p.second}, -1});
            }
            sort(pts.begin(), pts.end());
            for(auto p : pts) {
                // cout << p.first.first << ' ' << p.first.second << ' ' << p.second << '\n';
                if(p.second == 1) {
                    ans += s.count(abs(p.first.second));
                }
                else {
                    s.insert(abs(p.first.second));
                }
            }
            for(auto p : pts) {
                if(p.second == -1) {
                    s.erase(abs(p.first.second));
                }
            }
            // cout << ans << '\n';
        }
    }
    return ans;
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 292 KB Output is correct
14 Correct 0 ms 288 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 0 ms 288 KB Output is correct
18 Correct 0 ms 288 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 0 ms 204 KB Output is correct
21 Correct 0 ms 204 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 292 KB Output is correct
14 Correct 0 ms 288 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 0 ms 288 KB Output is correct
18 Correct 0 ms 288 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 0 ms 204 KB Output is correct
21 Correct 0 ms 204 KB Output is correct
22 Correct 2 ms 716 KB Output is correct
23 Correct 2 ms 748 KB Output is correct
24 Correct 2 ms 716 KB Output is correct
25 Correct 2 ms 588 KB Output is correct
26 Correct 3 ms 680 KB Output is correct
27 Correct 3 ms 680 KB Output is correct
28 Correct 3 ms 716 KB Output is correct
29 Correct 1 ms 460 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 292 KB Output is correct
14 Correct 0 ms 288 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 2 ms 716 KB Output is correct
18 Correct 2 ms 748 KB Output is correct
19 Correct 2 ms 716 KB Output is correct
20 Correct 2 ms 588 KB Output is correct
21 Correct 3 ms 680 KB Output is correct
22 Correct 3 ms 680 KB Output is correct
23 Correct 3 ms 716 KB Output is correct
24 Correct 1 ms 460 KB Output is correct
25 Correct 0 ms 288 KB Output is correct
26 Correct 0 ms 288 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 0 ms 204 KB Output is correct
29 Correct 0 ms 204 KB Output is correct
30 Correct 16 ms 2980 KB Output is correct
31 Correct 12 ms 2940 KB Output is correct
32 Correct 12 ms 2988 KB Output is correct
33 Correct 9 ms 2244 KB Output is correct
34 Correct 17 ms 2904 KB Output is correct
35 Correct 16 ms 2984 KB Output is correct
36 Correct 16 ms 2884 KB Output is correct
37 Correct 17 ms 2840 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 292 KB Output is correct
14 Correct 0 ms 288 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 2 ms 716 KB Output is correct
18 Correct 2 ms 748 KB Output is correct
19 Correct 2 ms 716 KB Output is correct
20 Correct 2 ms 588 KB Output is correct
21 Correct 3 ms 680 KB Output is correct
22 Correct 3 ms 680 KB Output is correct
23 Correct 3 ms 716 KB Output is correct
24 Correct 1 ms 460 KB Output is correct
25 Correct 16 ms 2980 KB Output is correct
26 Correct 12 ms 2940 KB Output is correct
27 Correct 12 ms 2988 KB Output is correct
28 Correct 9 ms 2244 KB Output is correct
29 Correct 17 ms 2904 KB Output is correct
30 Correct 16 ms 2984 KB Output is correct
31 Correct 16 ms 2884 KB Output is correct
32 Correct 17 ms 2840 KB Output is correct
33 Correct 0 ms 288 KB Output is correct
34 Correct 0 ms 288 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 0 ms 204 KB Output is correct
37 Correct 0 ms 204 KB Output is correct
38 Correct 105 ms 31624 KB Output is correct
39 Correct 98 ms 26712 KB Output is correct
40 Correct 78 ms 26784 KB Output is correct
41 Correct 86 ms 22100 KB Output is correct
42 Correct 151 ms 31532 KB Output is correct
43 Correct 155 ms 31560 KB Output is correct
44 Correct 152 ms 31524 KB Output is correct
45 Correct 172 ms 29480 KB Output is correct
46 Correct 90 ms 21712 KB Output is correct
47 Correct 115 ms 23740 KB Output is correct
48 Correct 216 ms 31172 KB Output is correct
49 Correct 234 ms 31644 KB Output is correct
50 Correct 114 ms 15924 KB Output is correct
51 Correct 106 ms 15960 KB Output is correct
52 Correct 221 ms 30068 KB Output is correct
53 Correct 225 ms 30516 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 716 KB Output is correct
2 Correct 1 ms 588 KB Output is correct
3 Correct 1 ms 460 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 3 ms 588 KB Output is correct
6 Correct 3 ms 588 KB Output is correct
7 Correct 3 ms 588 KB Output is correct
8 Correct 2 ms 588 KB Output is correct
9 Correct 2 ms 588 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 288 KB Output is correct
2 Correct 0 ms 288 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 524 ms 125260 KB Output is correct
8 Correct 1216 ms 269796 KB Output is correct
9 Correct 1139 ms 270776 KB Output is correct
10 Correct 1141 ms 271172 KB Output is correct
11 Correct 162 ms 97620 KB Output is correct
12 Correct 324 ms 184684 KB Output is correct
13 Correct 371 ms 196804 KB Output is correct

Subtask #7
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 292 KB Output is correct
14 Correct 0 ms 288 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 2 ms 716 KB Output is correct
18 Correct 2 ms 748 KB Output is correct
19 Correct 2 ms 716 KB Output is correct
20 Correct 2 ms 588 KB Output is correct
21 Correct 3 ms 680 KB Output is correct
22 Correct 3 ms 680 KB Output is correct
23 Correct 3 ms 716 KB Output is correct
24 Correct 1 ms 460 KB Output is correct
25 Correct 16 ms 2980 KB Output is correct
26 Correct 12 ms 2940 KB Output is correct
27 Correct 12 ms 2988 KB Output is correct
28 Correct 9 ms 2244 KB Output is correct
29 Correct 17 ms 2904 KB Output is correct
30 Correct 16 ms 2984 KB Output is correct
31 Correct 16 ms 2884 KB Output is correct
32 Correct 17 ms 2840 KB Output is correct
33 Correct 105 ms 31624 KB Output is correct
34 Correct 98 ms 26712 KB Output is correct
35 Correct 78 ms 26784 KB Output is correct
36 Correct 86 ms 22100 KB Output is correct
37 Correct 151 ms 31532 KB Output is correct
38 Correct 155 ms 31560 KB Output is correct
39 Correct 152 ms 31524 KB Output is correct
40 Correct 172 ms 29480 KB Output is correct
41 Correct 90 ms 21712 KB Output is correct
42 Correct 115 ms 23740 KB Output is correct
43 Correct 216 ms 31172 KB Output is correct
44 Correct 234 ms 31644 KB Output is correct
45 Correct 114 ms 15924 KB Output is correct
46 Correct 106 ms 15960 KB Output is correct
47 Correct 221 ms 30068 KB Output is correct
48 Correct 225 ms 30516 KB Output is correct
49 Correct 2 ms 716 KB Output is correct
50 Correct 1 ms 588 KB Output is correct
51 Correct 1 ms 460 KB Output is correct
52 Correct 0 ms 204 KB Output is correct
53 Correct 3 ms 588 KB Output is correct
54 Correct 3 ms 588 KB Output is correct
55 Correct 3 ms 588 KB Output is correct
56 Correct 2 ms 588 KB Output is correct
57 Correct 2 ms 588 KB Output is correct
58 Correct 1 ms 332 KB Output is correct
59 Correct 1 ms 332 KB Output is correct
60 Correct 0 ms 204 KB Output is correct
61 Correct 524 ms 125260 KB Output is correct
62 Correct 1216 ms 269796 KB Output is correct
63 Correct 1139 ms 270776 KB Output is correct
64 Correct 1141 ms 271172 KB Output is correct
65 Correct 162 ms 97620 KB Output is correct
66 Correct 324 ms 184684 KB Output is correct
67 Correct 371 ms 196804 KB Output is correct
68 Correct 0 ms 288 KB Output is correct
69 Correct 0 ms 288 KB Output is correct
70 Correct 1 ms 332 KB Output is correct
71 Correct 0 ms 204 KB Output is correct
72 Correct 0 ms 204 KB Output is correct
73 Correct 1937 ms 392336 KB Output is correct
74 Correct 1620 ms 324984 KB Output is correct
75 Correct 997 ms 325156 KB Output is correct
76 Correct 1226 ms 265284 KB Output is correct
77 Correct 2156 ms 392312 KB Output is correct
78 Correct 2003 ms 237008 KB Output is correct
79 Correct 2027 ms 250152 KB Output is correct
80 Correct 3283 ms 393548 KB Output is correct
81 Correct 2175 ms 265936 KB Output is correct
82 Correct 2675 ms 354548 KB Output is correct
83 Correct 3469 ms 443128 KB Output is correct
84 Correct 1897 ms 249268 KB Output is correct
85 Correct 3309 ms 429152 KB Output is correct
86 Correct 3323 ms 416468 KB Output is correct
87 Correct 1511 ms 264120 KB Output is correct
88 Correct 2382 ms 438436 KB Output is correct
89 Correct 2333 ms 438004 KB Output is correct
90 Correct 2286 ms 438484 KB Output is correct