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답안 #500581

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
500581 2021-12-31T12:58:21 Z InternetPerson10 Rectangles (IOI19_rect) C++17
100 / 100
 3315 ms 402600 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

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 292 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 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 0 ms 204 KB Output is correct
8 Correct 1 ms 396 KB Output is correct
9 Correct 1 ms 268 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 204 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 288 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 0 ms 284 KB Output is correct
18 Correct 0 ms 204 KB Output is correct
19 Correct 0 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

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 292 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 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 0 ms 204 KB Output is correct
8 Correct 1 ms 396 KB Output is correct
9 Correct 1 ms 268 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 204 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 288 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 0 ms 284 KB Output is correct
18 Correct 0 ms 204 KB Output is correct
19 Correct 0 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 680 KB Output is correct
23 Correct 2 ms 684 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 664 KB Output is correct
27 Correct 3 ms 596 KB Output is correct
28 Correct 3 ms 716 KB Output is correct
29 Correct 2 ms 456 KB Output is correct

Subtask #3
12.0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 292 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 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 0 ms 204 KB Output is correct
8 Correct 1 ms 396 KB Output is correct
9 Correct 1 ms 268 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 204 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 288 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 2 ms 680 KB Output is correct
18 Correct 2 ms 684 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 664 KB Output is correct
22 Correct 3 ms 596 KB Output is correct
23 Correct 3 ms 716 KB Output is correct
24 Correct 2 ms 456 KB Output is correct
25 Correct 0 ms 284 KB Output is correct
26 Correct 0 ms 204 KB Output is correct
27 Correct 0 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 11 ms 2980 KB Output is correct
31 Correct 11 ms 2968 KB Output is correct
32 Correct 11 ms 3112 KB Output is correct
33 Correct 9 ms 2252 KB Output is correct
34 Correct 16 ms 2904 KB Output is correct
35 Correct 16 ms 3036 KB Output is correct
36 Correct 15 ms 2856 KB Output is correct
37 Correct 15 ms 2892 KB Output is correct

Subtask #4
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 292 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 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 0 ms 204 KB Output is correct
8 Correct 1 ms 396 KB Output is correct
9 Correct 1 ms 268 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 204 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 288 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 2 ms 680 KB Output is correct
18 Correct 2 ms 684 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 664 KB Output is correct
22 Correct 3 ms 596 KB Output is correct
23 Correct 3 ms 716 KB Output is correct
24 Correct 2 ms 456 KB Output is correct
25 Correct 11 ms 2980 KB Output is correct
26 Correct 11 ms 2968 KB Output is correct
27 Correct 11 ms 3112 KB Output is correct
28 Correct 9 ms 2252 KB Output is correct
29 Correct 16 ms 2904 KB Output is correct
30 Correct 16 ms 3036 KB Output is correct
31 Correct 15 ms 2856 KB Output is correct
32 Correct 15 ms 2892 KB Output is correct
33 Correct 0 ms 284 KB Output is correct
34 Correct 0 ms 204 KB Output is correct
35 Correct 0 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 104 ms 33944 KB Output is correct
39 Correct 93 ms 28112 KB Output is correct
40 Correct 80 ms 28084 KB Output is correct
41 Correct 88 ms 23484 KB Output is correct
42 Correct 156 ms 33032 KB Output is correct
43 Correct 153 ms 33092 KB Output is correct
44 Correct 163 ms 33280 KB Output is correct
45 Correct 151 ms 31296 KB Output is correct
46 Correct 82 ms 22320 KB Output is correct
47 Correct 111 ms 24484 KB Output is correct
48 Correct 219 ms 32620 KB Output is correct
49 Correct 225 ms 33576 KB Output is correct
50 Correct 108 ms 17276 KB Output is correct
51 Correct 108 ms 17224 KB Output is correct
52 Correct 209 ms 31428 KB Output is correct
53 Correct 216 ms 32372 KB Output is correct

Subtask #5
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 716 KB Output is correct
2 Correct 1 ms 716 KB Output is correct
3 Correct 1 ms 588 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 2 ms 716 KB Output is correct
6 Correct 2 ms 716 KB Output is correct
7 Correct 2 ms 716 KB Output is correct
8 Correct 2 ms 716 KB Output is correct
9 Correct 2 ms 636 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

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 284 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 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 292 KB Output is correct
7 Correct 503 ms 127404 KB Output is correct
8 Correct 1168 ms 272196 KB Output is correct
9 Correct 1177 ms 274540 KB Output is correct
10 Correct 1137 ms 276780 KB Output is correct
11 Correct 170 ms 103008 KB Output is correct
12 Correct 312 ms 190916 KB Output is correct
13 Correct 341 ms 203120 KB Output is correct

Subtask #7
28.0 / 28.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 292 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 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 0 ms 204 KB Output is correct
8 Correct 1 ms 396 KB Output is correct
9 Correct 1 ms 268 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 204 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 288 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 2 ms 680 KB Output is correct
18 Correct 2 ms 684 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 664 KB Output is correct
22 Correct 3 ms 596 KB Output is correct
23 Correct 3 ms 716 KB Output is correct
24 Correct 2 ms 456 KB Output is correct
25 Correct 11 ms 2980 KB Output is correct
26 Correct 11 ms 2968 KB Output is correct
27 Correct 11 ms 3112 KB Output is correct
28 Correct 9 ms 2252 KB Output is correct
29 Correct 16 ms 2904 KB Output is correct
30 Correct 16 ms 3036 KB Output is correct
31 Correct 15 ms 2856 KB Output is correct
32 Correct 15 ms 2892 KB Output is correct
33 Correct 104 ms 33944 KB Output is correct
34 Correct 93 ms 28112 KB Output is correct
35 Correct 80 ms 28084 KB Output is correct
36 Correct 88 ms 23484 KB Output is correct
37 Correct 156 ms 33032 KB Output is correct
38 Correct 153 ms 33092 KB Output is correct
39 Correct 163 ms 33280 KB Output is correct
40 Correct 151 ms 31296 KB Output is correct
41 Correct 82 ms 22320 KB Output is correct
42 Correct 111 ms 24484 KB Output is correct
43 Correct 219 ms 32620 KB Output is correct
44 Correct 225 ms 33576 KB Output is correct
45 Correct 108 ms 17276 KB Output is correct
46 Correct 108 ms 17224 KB Output is correct
47 Correct 209 ms 31428 KB Output is correct
48 Correct 216 ms 32372 KB Output is correct
49 Correct 2 ms 716 KB Output is correct
50 Correct 1 ms 716 KB Output is correct
51 Correct 1 ms 588 KB Output is correct
52 Correct 0 ms 204 KB Output is correct
53 Correct 2 ms 716 KB Output is correct
54 Correct 2 ms 716 KB Output is correct
55 Correct 2 ms 716 KB Output is correct
56 Correct 2 ms 716 KB Output is correct
57 Correct 2 ms 636 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 292 KB Output is correct
61 Correct 503 ms 127404 KB Output is correct
62 Correct 1168 ms 272196 KB Output is correct
63 Correct 1177 ms 274540 KB Output is correct
64 Correct 1137 ms 276780 KB Output is correct
65 Correct 170 ms 103008 KB Output is correct
66 Correct 312 ms 190916 KB Output is correct
67 Correct 341 ms 203120 KB Output is correct
68 Correct 0 ms 284 KB Output is correct
69 Correct 0 ms 204 KB Output is correct
70 Correct 0 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 1769 ms 393576 KB Output is correct
74 Correct 1522 ms 325320 KB Output is correct
75 Correct 990 ms 325384 KB Output is correct
76 Correct 1221 ms 265496 KB Output is correct
77 Correct 2094 ms 392424 KB Output is correct
78 Correct 2001 ms 239708 KB Output is correct
79 Correct 1988 ms 250236 KB Output is correct
80 Correct 3205 ms 393752 KB Output is correct
81 Correct 1995 ms 240424 KB Output is correct
82 Correct 2576 ms 322140 KB Output is correct
83 Correct 3315 ms 402600 KB Output is correct
84 Correct 1834 ms 230860 KB Output is correct
85 Correct 3156 ms 387468 KB Output is correct
86 Correct 3067 ms 375960 KB Output is correct
87 Correct 1385 ms 238328 KB Output is correct
88 Correct 2124 ms 397632 KB Output is correct
89 Correct 2131 ms 396780 KB Output is correct
90 Correct 2119 ms 394972 KB Output is correct