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Submission #154395

# Submission time Handle Problem Language Result Execution time Memory
154395 2019-09-21T16:55:34 Z rama_pang Rectangles (IOI19_rect) C++14
100 / 100
 4165 ms 838788 KB 
#include "rect.h"
#include <bits/stdc++.h>
using namespace std;

struct bit {
    vector<int> tree;
    
    bit(int &n) {
        tree.assign(n + 1, 0);
    }

    void update(int &n, int &x) {
        for (int i = n + 1; i < tree.size(); i += (i & -i)) tree[i] += x;
    }

    int query(int n) {
        int res = 0;
        for (int i = n + 1; i > 0; i -= (i & -i)) res += tree[i];
        return res;
    }
};

void get_interval(vector<int> &a, vector<int> &L, vector<int> &R) {
    int n = a.size(); vector<int> s; s.reserve(n);
    for (int i = 0; i < n; i++) L[i] = -1, R[i] = -1;
    for (int i = 0; i < n; i++) { //find biggest on left side
        while (s.size() && a[s.back()] < a[i]) s.pop_back();
        if (s.size()) L[i] = s.back();
        s.push_back(i);
    }
    s.clear();
    for (int i = n - 1; i >= 0; i--) { //find biggest on right side
        while (s.size() && a[s.back()] < a[i]) s.pop_back();
        if (s.size()) R[i] = s.back();
        s.push_back(i);
    }
}

long long count_rectangles(vector<vector<int>> a) {
    int n = a.size(), m = a[0].size();
    vector<vector<vector<int>>> right(n, vector<vector<int>>(m)), down(n, vector<vector<int>>(m));
    vector<int> b(m), L(m), R(m);
    for (int i = 1; i < n - 1; i++) { //get valid pairs horizontally and vertically
        for (int j = 0; j < m; j++) b[j] = a[i][j];
        get_interval(b, L, R);
        for (int j = 0; j < m; j++) {
            if (L[j] != -1 && L[j] + 1 <= j - 1) right[i][L[j] + 1].push_back(j - 1);
            if (R[j] != -1 && j + 1 <= R[j] - 1 && L[R[j]] != j) right[i][j + 1].push_back(R[j] - 1); //prevent double counting, when a[i][j1] = a[i][j2]
        }
    }
    b.resize(n), L.resize(n), R.resize(n);
    for (int j = 1; j < m - 1; j++) {
        for (int i = 0; i < n; i++) b[i] = a[i][j];
        get_interval(b, L, R);
        for (int i = 0; i < n; i++) {
            if (L[i] != -1 && L[i] + 1 <= i - 1) down[L[i] + 1][j].push_back(i - 1);
            if (R[i] != -1 && i + 1 <= R[i] - 1 && L[R[i]] != i) down[i + 1][j].push_back(R[i] - 1); //prevent double counting
        }
    }
    vector<vector<int>> last_right(m, vector<int>(m, -1)), span_right(m, vector<int>(m, 0)), last_down(n, vector<int>(n, -1)), span_down(n, vector<int>(n, 0));
    vector<pair<pair<int, int>, int>> update;
    long long res = 0;
    bit cnt(m);
    for (int i = n - 1; i >= 0; i--) {
        for (int j = m - 1; j >= 0; j--) {
            for (auto &k : right[i][j]) {
                if (last_right[j][k] != i + 1) span_right[j][k] = 0;
                span_right[j][k]++;
                last_right[j][k] = i;
            }
            for (auto &k : down[i][j]) {
                if (last_down[i][k] != j + 1) span_down[i][k] = 0;
                span_down[i][k]++;
                last_down[i][k] = j;
            }
            update.clear();
            for (auto &k : right[i][j]) {
                update.push_back({{i, k}, 1}); //adding a rectangle
                update.push_back({{i + span_right[j][k], k}, -1}); //erasing a rectangle
            }
            sort(update.begin(), update.end());
            sort(down[i][j].begin(), down[i][j].end());
            int p = 0; //check if a rectangle exists if valid_down and valid_right shares a cell in the top left corner
            for (auto &k : down[i][j]) { //also count the rectangle's spanning, not just width / height 1
                while (p < update.size() && update[p].first.first <= k) { //updating cnt
                    cnt.update(update[p].first.second, update[p].second); p++;
                }
                res += cnt.query(j + span_down[i][k] - 1);
            }
            while (p < update.size()) { //restoring cnt to default
                cnt.update(update[p].first.second, update[p].second); p++;
            }    
        }
    }
    return res;
}

Compilation message

rect.cpp: In member function 'void bit::update(int&, int&)':
rect.cpp:13:31: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for (int i = n + 1; i < tree.size(); i += (i & -i)) tree[i] += x;
                             ~~^~~~~~~~~~~~~
rect.cpp: In function 'long long int count_rectangles(std::vector<std::vector<int> >)':
rect.cpp:85:26: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
                 while (p < update.size() && update[p].first.first <= k) { //updating cnt
                        ~~^~~~~~~~~~~~~~~
rect.cpp:90:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
             while (p < update.size()) { //restoring cnt to default
                    ~~^~~~~~~~~~~~~~~

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 3 ms 504 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 3 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 3 ms 476 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 256 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 3 ms 376 KB Output is correct
16 Correct 2 ms 380 KB Output is correct
17 Correct 2 ms 376 KB Output is correct
18 Correct 2 ms 376 KB Output is correct
19 Correct 3 ms 380 KB Output is correct
20 Correct 2 ms 376 KB Output is correct
21 Correct 2 ms 256 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 3 ms 504 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 3 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 3 ms 476 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 256 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 3 ms 376 KB Output is correct
16 Correct 2 ms 380 KB Output is correct
17 Correct 4 ms 1144 KB Output is correct
18 Correct 5 ms 1144 KB Output is correct
19 Correct 4 ms 1144 KB Output is correct
20 Correct 4 ms 888 KB Output is correct
21 Correct 5 ms 1016 KB Output is correct
22 Correct 5 ms 1016 KB Output is correct
23 Correct 5 ms 1016 KB Output is correct
24 Correct 4 ms 632 KB Output is correct
25 Correct 2 ms 376 KB Output is correct
26 Correct 2 ms 376 KB Output is correct
27 Correct 3 ms 380 KB Output is correct
28 Correct 2 ms 376 KB Output is correct
29 Correct 2 ms 256 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 3 ms 504 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 3 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 3 ms 476 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 256 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 3 ms 376 KB Output is correct
16 Correct 2 ms 380 KB Output is correct
17 Correct 4 ms 1144 KB Output is correct
18 Correct 5 ms 1144 KB Output is correct
19 Correct 4 ms 1144 KB Output is correct
20 Correct 4 ms 888 KB Output is correct
21 Correct 5 ms 1016 KB Output is correct
22 Correct 5 ms 1016 KB Output is correct
23 Correct 5 ms 1016 KB Output is correct
24 Correct 4 ms 632 KB Output is correct
25 Correct 19 ms 5880 KB Output is correct
26 Correct 22 ms 5880 KB Output is correct
27 Correct 18 ms 5880 KB Output is correct
28 Correct 14 ms 4088 KB Output is correct
29 Correct 22 ms 4592 KB Output is correct
30 Correct 23 ms 4728 KB Output is correct
31 Correct 22 ms 4604 KB Output is correct
32 Correct 21 ms 4572 KB Output is correct
33 Correct 2 ms 376 KB Output is correct
34 Correct 2 ms 376 KB Output is correct
35 Correct 3 ms 380 KB Output is correct
36 Correct 2 ms 376 KB Output is correct
37 Correct 2 ms 256 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 3 ms 504 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 3 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 3 ms 476 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 256 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 3 ms 376 KB Output is correct
16 Correct 2 ms 380 KB Output is correct
17 Correct 4 ms 1144 KB Output is correct
18 Correct 5 ms 1144 KB Output is correct
19 Correct 4 ms 1144 KB Output is correct
20 Correct 4 ms 888 KB Output is correct
21 Correct 5 ms 1016 KB Output is correct
22 Correct 5 ms 1016 KB Output is correct
23 Correct 5 ms 1016 KB Output is correct
24 Correct 4 ms 632 KB Output is correct
25 Correct 19 ms 5880 KB Output is correct
26 Correct 22 ms 5880 KB Output is correct
27 Correct 18 ms 5880 KB Output is correct
28 Correct 14 ms 4088 KB Output is correct
29 Correct 22 ms 4592 KB Output is correct
30 Correct 23 ms 4728 KB Output is correct
31 Correct 22 ms 4604 KB Output is correct
32 Correct 21 ms 4572 KB Output is correct
33 Correct 151 ms 53496 KB Output is correct
34 Correct 154 ms 47388 KB Output is correct
35 Correct 116 ms 47224 KB Output is correct
36 Correct 118 ms 41336 KB Output is correct
37 Correct 241 ms 68728 KB Output is correct
38 Correct 238 ms 68728 KB Output is correct
39 Correct 240 ms 69192 KB Output is correct
40 Correct 222 ms 64888 KB Output is correct
41 Correct 137 ms 43620 KB Output is correct
42 Correct 178 ms 46200 KB Output is correct
43 Correct 274 ms 52600 KB Output is correct
44 Correct 282 ms 54520 KB Output is correct
45 Correct 138 ms 28536 KB Output is correct
46 Correct 141 ms 28304 KB Output is correct
47 Correct 261 ms 52148 KB Output is correct
48 Correct 264 ms 53392 KB Output is correct
49 Correct 2 ms 376 KB Output is correct
50 Correct 2 ms 376 KB Output is correct
51 Correct 3 ms 380 KB Output is correct
52 Correct 2 ms 376 KB Output is correct
53 Correct 2 ms 256 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 46 ms 50040 KB Output is correct
2 Correct 34 ms 36472 KB Output is correct
3 Correct 46 ms 49988 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 47 ms 50168 KB Output is correct
6 Correct 47 ms 50040 KB Output is correct
7 Correct 54 ms 50032 KB Output is correct
8 Correct 47 ms 50044 KB Output is correct
9 Correct 47 ms 50044 KB Output is correct
10 Correct 45 ms 49656 KB Output is correct
11 Correct 45 ms 49776 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 995 ms 262088 KB Output is correct
3 Correct 2065 ms 548404 KB Output is correct
4 Correct 2051 ms 551120 KB Output is correct
5 Correct 2059 ms 551440 KB Output is correct
6 Correct 372 ms 236672 KB Output is correct
7 Correct 703 ms 425688 KB Output is correct
8 Correct 753 ms 453748 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 3 ms 380 KB Output is correct
12 Correct 2 ms 376 KB Output is correct
13 Correct 2 ms 256 KB Output is correct

Subtask #7
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 3 ms 504 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 2 ms 376 KB Output is correct
5 Correct 2 ms 376 KB Output is correct
6 Correct 3 ms 376 KB Output is correct
7 Correct 2 ms 376 KB Output is correct
8 Correct 2 ms 376 KB Output is correct
9 Correct 3 ms 476 KB Output is correct
10 Correct 2 ms 376 KB Output is correct
11 Correct 2 ms 376 KB Output is correct
12 Correct 3 ms 376 KB Output is correct
13 Correct 2 ms 256 KB Output is correct
14 Correct 2 ms 376 KB Output is correct
15 Correct 3 ms 376 KB Output is correct
16 Correct 2 ms 380 KB Output is correct
17 Correct 4 ms 1144 KB Output is correct
18 Correct 5 ms 1144 KB Output is correct
19 Correct 4 ms 1144 KB Output is correct
20 Correct 4 ms 888 KB Output is correct
21 Correct 5 ms 1016 KB Output is correct
22 Correct 5 ms 1016 KB Output is correct
23 Correct 5 ms 1016 KB Output is correct
24 Correct 4 ms 632 KB Output is correct
25 Correct 19 ms 5880 KB Output is correct
26 Correct 22 ms 5880 KB Output is correct
27 Correct 18 ms 5880 KB Output is correct
28 Correct 14 ms 4088 KB Output is correct
29 Correct 22 ms 4592 KB Output is correct
30 Correct 23 ms 4728 KB Output is correct
31 Correct 22 ms 4604 KB Output is correct
32 Correct 21 ms 4572 KB Output is correct
33 Correct 151 ms 53496 KB Output is correct
34 Correct 154 ms 47388 KB Output is correct
35 Correct 116 ms 47224 KB Output is correct
36 Correct 118 ms 41336 KB Output is correct
37 Correct 241 ms 68728 KB Output is correct
38 Correct 238 ms 68728 KB Output is correct
39 Correct 240 ms 69192 KB Output is correct
40 Correct 222 ms 64888 KB Output is correct
41 Correct 137 ms 43620 KB Output is correct
42 Correct 178 ms 46200 KB Output is correct
43 Correct 274 ms 52600 KB Output is correct
44 Correct 282 ms 54520 KB Output is correct
45 Correct 138 ms 28536 KB Output is correct
46 Correct 141 ms 28304 KB Output is correct
47 Correct 261 ms 52148 KB Output is correct
48 Correct 264 ms 53392 KB Output is correct
49 Correct 46 ms 50040 KB Output is correct
50 Correct 34 ms 36472 KB Output is correct
51 Correct 46 ms 49988 KB Output is correct
52 Correct 2 ms 376 KB Output is correct
53 Correct 47 ms 50168 KB Output is correct
54 Correct 47 ms 50040 KB Output is correct
55 Correct 54 ms 50032 KB Output is correct
56 Correct 47 ms 50044 KB Output is correct
57 Correct 47 ms 50044 KB Output is correct
58 Correct 45 ms 49656 KB Output is correct
59 Correct 45 ms 49776 KB Output is correct
60 Correct 2 ms 376 KB Output is correct
61 Correct 995 ms 262088 KB Output is correct
62 Correct 2065 ms 548404 KB Output is correct
63 Correct 2051 ms 551120 KB Output is correct
64 Correct 2059 ms 551440 KB Output is correct
65 Correct 372 ms 236672 KB Output is correct
66 Correct 703 ms 425688 KB Output is correct
67 Correct 753 ms 453748 KB Output is correct
68 Correct 2470 ms 643132 KB Output is correct
69 Correct 2438 ms 562964 KB Output is correct
70 Correct 1613 ms 562804 KB Output is correct
71 Correct 1578 ms 481256 KB Output is correct
72 Correct 3917 ms 838716 KB Output is correct
73 Correct 2368 ms 407024 KB Output is correct
74 Correct 2546 ms 415780 KB Output is correct
75 Correct 3927 ms 645248 KB Output is correct
76 Correct 2423 ms 397576 KB Output is correct
77 Correct 3229 ms 521940 KB Output is correct
78 Correct 4165 ms 650112 KB Output is correct
79 Correct 2232 ms 387316 KB Output is correct
80 Correct 3903 ms 635912 KB Output is correct
81 Correct 3847 ms 617384 KB Output is correct
82 Correct 2337 ms 511236 KB Output is correct
83 Correct 3926 ms 838180 KB Output is correct
84 Correct 4025 ms 838788 KB Output is correct
85 Correct 3933 ms 838784 KB Output is correct
86 Correct 2 ms 376 KB Output is correct
87 Correct 2 ms 376 KB Output is correct
88 Correct 3 ms 380 KB Output is correct
89 Correct 2 ms 376 KB Output is correct
90 Correct 2 ms 256 KB Output is correct