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답안 #1009488

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
1009488 2024-06-27T15:01:44 Z boris_mihov Rectangles (IOI19_rect) C++17
59 / 100
 791 ms 1048576 KB 
#include "rect.h"
#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>
#include <stack>

typedef long long llong;
const int MAXLOG = 12;
const int MAXN = 2500 + 10;
const int INF  = 1e8;

int n, m;
int getLOG[MAXN];
struct SparseMIN
{
    int sparse[MAXLOG][MAXN];
    int len;

    void build(int a[], int length)
    {
        len = length;
        for (int i = 1 ; i <= len ; ++i)
        {
            sparse[0][i] = a[i]; 
        }

        for (int lg = 1 ; (1 << lg) <= len ; ++lg)
        {
            for (int i = 1 ; i + (1 << lg) - 1 <= len ; ++i)
            {
                sparse[lg][i] = std::min(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
            }
        }
    }

    int findMIN(int l, int r)
    {
        int lg = getLOG[r - l + 1];
        return std::min(sparse[lg][l], sparse[lg][r - (1 << lg) + 1]);
    }
};

struct SparseMAX
{
    int sparse[MAXLOG][MAXN];
    int len;

    void build(int a[], int length)
    {
        len = length;
        for (int i = 1 ; i <= len ; ++i)
        {
            sparse[0][i] = a[i]; 
        }

        for (int lg = 1 ; (1 << lg) <= len ; ++lg)
        {
            for (int i = 1 ; i + (1 << lg) - 1 <= len ; ++i)
            {
                sparse[lg][i] = std::max(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
            }
        }
    }

    int findMAX(int l, int r)
    {
        assert(r - l + 1 <= len);
        int lg = getLOG[r - l + 1];
        return std::max(sparse[lg][l], sparse[lg][r - (1 << lg) + 1]);
    }
};

int a[MAXN][MAXN]; // >
int b[MAXN][MAXN]; // v
int c[MAXN][MAXN]; // <
int d[MAXN][MAXN]; // ^
int t[MAXN][MAXN];
int cpy[MAXN];

SparseMIN sparseRD[MAXN];
SparseMAX sparseRU[MAXN];
SparseMIN sparseCL[MAXN];
SparseMAX sparseCR[MAXN];
std::vector <int> possibleColE[MAXN][MAXN];
std::vector <int> possibleRowE[MAXN][MAXN];

bool isOK(int rowB, int colB, int rowE, int colE)
{
    assert(rowB <= rowE);
    assert(colB <= colE);
    rowB--; colB--; rowE++; colE++;
    if (sparseRD[rowB].findMIN(colB + 1, colE - 1) < rowE) return false;
    if (sparseRU[rowE].findMAX(colB + 1, colE - 1) > rowB) return false;
    if (sparseCL[colB].findMIN(rowB + 1, rowE - 1) < colE) return false;
    if (sparseCR[colE].findMAX(rowB + 1, rowE - 1) > colB) return false;
    return true;
}

llong count_rectangles(std::vector <std::vector<int>> _a)
{
    n = _a.size(); m = _a[0].size();
    for (int i = 0 ; i < n ; ++i)
    {
        for (int j = 0 ; j < m ; ++j)
        {
            t[i + 1][j + 1] = _a[i][j];
        }
    }

    for (int i = 0 ; i <= n + 1 ; ++i)
    {
        t[i][0] = t[i][m + 1] = INF;
    }

    for (int i = 0 ; i <= m + 1 ; ++i)
    {
        t[0][i] = t[n + 1][i] = INF;
    }

    std::stack <int> st;
    for (int i = 1 ; i <= n ; ++i)
    {
        while (st.size()) st.pop(); st.push(m + 1);
        for (int j = m ; j >= 1 ; --j)
        {
            while (t[i][j] > t[i][st.top()])
            {
                st.pop();
            }

            a[i][j] = st.top();
            st.push(j);
        }

        while (st.size()) st.pop(); st.push(0);
        for (int j = 1 ; j <= m ; ++j)
        {
            while (t[i][j] > t[i][st.top()])
            {
                st.pop();
            }

            c[i][j] = st.top();
            st.push(j);
        }
    }

    for (int i = 1 ; i <= m ; ++i)
    {
        while (st.size()) st.pop(); st.push(n + 1);
        for (int j = n ; j >= 1 ; --j)
        {
            while (t[j][i] > t[st.top()][i])
            {
                st.pop();
            }

            b[j][i] = st.top();
            st.push(j);
        }

        while (st.size()) st.pop(); st.push(0);
        for (int j = 1 ; j <= n ; ++j)
        {
            while (t[j][i] > t[st.top()][i])
            {
                st.pop();
            }

            d[j][i] = st.top();
            st.push(j);
        }
    }

    for (int i = 1 ; i <= std::max(n, m) ; ++i)
    {
        getLOG[i] = getLOG[i - 1];
        if ((1 << getLOG[i] + 1) < i) getLOG[i]++;
    }

    for (int i = 1 ; i <= n ; ++i)
    {
        sparseRD[i].build(b[i], m);
        sparseRU[i].build(d[i], m);
    }

    for (int i = 1 ; i <= m ; ++i)
    {
        for (int j = 1 ; j <= n ; ++j)
        {
            cpy[j] = a[j][i];
        }

        sparseCL[i].build(cpy, n);

        for (int j = 1 ; j <= n ; ++j)
        {
            cpy[j] = c[j][i];
        }

        sparseCR[i].build(cpy, n);
    }

    for (int i = 2 ; i <= n ; ++i)
    {
        for (int j = 2 ; j <= m ; ++j)
        {
            if (d[i][j] < i - 1) possibleRowE[d[i][j] + 1][j].push_back(i - 1);
            if (c[i][j] < j - 1) possibleColE[i][c[i][j] + 1].push_back(j - 1);
        }
    }

    for (int i = 2 ; i <= n ; ++i)
    {
        for (int j = 2 ; j <= m ; ++j)
        {
            if (i < b[i - 1][j] && b[i - 1][j] != n + 1 && (possibleRowE[i][j].empty() || possibleRowE[i][j].back() != b[i - 1][j] - 1)) possibleRowE[i][j].push_back(b[i - 1][j] - 1);
            if (j < a[i][j - 1] && a[i][j - 1] != m + 1 && (possibleColE[i][j].empty() || possibleColE[i][j].back() != a[i][j - 1] - 1)) possibleColE[i][j].push_back(a[i][j - 1] - 1);
        }
    }

    int answer = 0;
    for (int rowB = 2 ; rowB < n ; ++rowB)
    {
        for (int colB = 2 ; colB < m ; ++colB)
        {
            for (const int &rowE : possibleRowE[rowB][colB])
            {
                for (const int &colE : possibleColE[rowB][colB])
                {
                    answer += isOK(rowB, colB, rowE, colE);
                }
            }
        }
    }

    return answer;
}

Compilation message

rect.cpp: In member function 'void SparseMIN::build(int*, int)':
rect.cpp:33:89: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
   33 |                 sparse[lg][i] = std::min(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
      |                                                                                      ~~~^~~
rect.cpp: In member function 'void SparseMAX::build(int*, int)':
rect.cpp:62:89: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
   62 |                 sparse[lg][i] = std::max(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
      |                                                                                      ~~~^~~
rect.cpp: In function 'llong count_rectangles(std::vector<std::vector<int> >)':
rect.cpp:125:9: warning: this 'while' clause does not guard... [-Wmisleading-indentation]
  125 |         while (st.size()) st.pop(); st.push(m + 1);
      |         ^~~~~
rect.cpp:125:37: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'while'
  125 |         while (st.size()) st.pop(); st.push(m + 1);
      |                                     ^~
rect.cpp:137:9: warning: this 'while' clause does not guard... [-Wmisleading-indentation]
  137 |         while (st.size()) st.pop(); st.push(0);
      |         ^~~~~
rect.cpp:137:37: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'while'
  137 |         while (st.size()) st.pop(); st.push(0);
      |                                     ^~
rect.cpp:152:9: warning: this 'while' clause does not guard... [-Wmisleading-indentation]
  152 |         while (st.size()) st.pop(); st.push(n + 1);
      |         ^~~~~
rect.cpp:152:37: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'while'
  152 |         while (st.size()) st.pop(); st.push(n + 1);
      |                                     ^~
rect.cpp:164:9: warning: this 'while' clause does not guard... [-Wmisleading-indentation]
  164 |         while (st.size()) st.pop(); st.push(0);
      |         ^~~~~
rect.cpp:164:37: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'while'
  164 |         while (st.size()) st.pop(); st.push(0);
      |                                     ^~
rect.cpp:180:29: warning: suggest parentheses around '+' inside '<<' [-Wparentheses]
  180 |         if ((1 << getLOG[i] + 1) < i) getLOG[i]++;
      |                   ~~~~~~~~~~^~~

Subtask #1
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 94 ms 296532 KB Output is correct
2 Correct 104 ms 299348 KB Output is correct
3 Correct 103 ms 299536 KB Output is correct
4 Correct 101 ms 299348 KB Output is correct
5 Correct 107 ms 299348 KB Output is correct
6 Correct 103 ms 299456 KB Output is correct
7 Correct 122 ms 298324 KB Output is correct
8 Correct 104 ms 298064 KB Output is correct
9 Correct 102 ms 299348 KB Output is correct
10 Correct 104 ms 299344 KB Output is correct
11 Correct 104 ms 299452 KB Output is correct
12 Correct 103 ms 299532 KB Output is correct
13 Correct 103 ms 296256 KB Output is correct
14 Correct 103 ms 296784 KB Output is correct
15 Correct 104 ms 296976 KB Output is correct
16 Correct 110 ms 296528 KB Output is correct
17 Correct 104 ms 296272 KB Output is correct
18 Correct 99 ms 296272 KB Output is correct
19 Correct 102 ms 299396 KB Output is correct
20 Correct 104 ms 298576 KB Output is correct
21 Correct 105 ms 296788 KB Output is correct

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 94 ms 296532 KB Output is correct
2 Correct 104 ms 299348 KB Output is correct
3 Correct 103 ms 299536 KB Output is correct
4 Correct 101 ms 299348 KB Output is correct
5 Correct 107 ms 299348 KB Output is correct
6 Correct 103 ms 299456 KB Output is correct
7 Correct 122 ms 298324 KB Output is correct
8 Correct 104 ms 298064 KB Output is correct
9 Correct 102 ms 299348 KB Output is correct
10 Correct 104 ms 299344 KB Output is correct
11 Correct 104 ms 299452 KB Output is correct
12 Correct 103 ms 299532 KB Output is correct
13 Correct 103 ms 296256 KB Output is correct
14 Correct 103 ms 296784 KB Output is correct
15 Correct 104 ms 296976 KB Output is correct
16 Correct 110 ms 296528 KB Output is correct
17 Correct 104 ms 296272 KB Output is correct
18 Correct 99 ms 296272 KB Output is correct
19 Correct 102 ms 299396 KB Output is correct
20 Correct 104 ms 298576 KB Output is correct
21 Correct 105 ms 296788 KB Output is correct
22 Correct 106 ms 308052 KB Output is correct
23 Correct 106 ms 308048 KB Output is correct
24 Correct 107 ms 308048 KB Output is correct
25 Correct 110 ms 307796 KB Output is correct
26 Correct 106 ms 307800 KB Output is correct
27 Correct 110 ms 307792 KB Output is correct
28 Correct 113 ms 307920 KB Output is correct
29 Correct 109 ms 304348 KB Output is correct

Subtask #3
12.0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 94 ms 296532 KB Output is correct
2 Correct 104 ms 299348 KB Output is correct
3 Correct 103 ms 299536 KB Output is correct
4 Correct 101 ms 299348 KB Output is correct
5 Correct 107 ms 299348 KB Output is correct
6 Correct 103 ms 299456 KB Output is correct
7 Correct 122 ms 298324 KB Output is correct
8 Correct 104 ms 298064 KB Output is correct
9 Correct 102 ms 299348 KB Output is correct
10 Correct 104 ms 299344 KB Output is correct
11 Correct 104 ms 299452 KB Output is correct
12 Correct 103 ms 299532 KB Output is correct
13 Correct 103 ms 296256 KB Output is correct
14 Correct 103 ms 296784 KB Output is correct
15 Correct 104 ms 296976 KB Output is correct
16 Correct 110 ms 296528 KB Output is correct
17 Correct 106 ms 308052 KB Output is correct
18 Correct 106 ms 308048 KB Output is correct
19 Correct 107 ms 308048 KB Output is correct
20 Correct 110 ms 307796 KB Output is correct
21 Correct 106 ms 307800 KB Output is correct
22 Correct 110 ms 307792 KB Output is correct
23 Correct 113 ms 307920 KB Output is correct
24 Correct 109 ms 304348 KB Output is correct
25 Correct 104 ms 296272 KB Output is correct
26 Correct 99 ms 296272 KB Output is correct
27 Correct 102 ms 299396 KB Output is correct
28 Correct 104 ms 298576 KB Output is correct
29 Correct 105 ms 296788 KB Output is correct
30 Correct 116 ms 333908 KB Output is correct
31 Correct 125 ms 333908 KB Output is correct
32 Correct 119 ms 333800 KB Output is correct
33 Correct 116 ms 332112 KB Output is correct
34 Correct 126 ms 332624 KB Output is correct
35 Correct 124 ms 332696 KB Output is correct
36 Correct 122 ms 332624 KB Output is correct
37 Correct 134 ms 332276 KB Output is correct

Subtask #4
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 94 ms 296532 KB Output is correct
2 Correct 104 ms 299348 KB Output is correct
3 Correct 103 ms 299536 KB Output is correct
4 Correct 101 ms 299348 KB Output is correct
5 Correct 107 ms 299348 KB Output is correct
6 Correct 103 ms 299456 KB Output is correct
7 Correct 122 ms 298324 KB Output is correct
8 Correct 104 ms 298064 KB Output is correct
9 Correct 102 ms 299348 KB Output is correct
10 Correct 104 ms 299344 KB Output is correct
11 Correct 104 ms 299452 KB Output is correct
12 Correct 103 ms 299532 KB Output is correct
13 Correct 103 ms 296256 KB Output is correct
14 Correct 103 ms 296784 KB Output is correct
15 Correct 104 ms 296976 KB Output is correct
16 Correct 110 ms 296528 KB Output is correct
17 Correct 106 ms 308052 KB Output is correct
18 Correct 106 ms 308048 KB Output is correct
19 Correct 107 ms 308048 KB Output is correct
20 Correct 110 ms 307796 KB Output is correct
21 Correct 106 ms 307800 KB Output is correct
22 Correct 110 ms 307792 KB Output is correct
23 Correct 113 ms 307920 KB Output is correct
24 Correct 109 ms 304348 KB Output is correct
25 Correct 116 ms 333908 KB Output is correct
26 Correct 125 ms 333908 KB Output is correct
27 Correct 119 ms 333800 KB Output is correct
28 Correct 116 ms 332112 KB Output is correct
29 Correct 126 ms 332624 KB Output is correct
30 Correct 124 ms 332696 KB Output is correct
31 Correct 122 ms 332624 KB Output is correct
32 Correct 134 ms 332276 KB Output is correct
33 Correct 104 ms 296272 KB Output is correct
34 Correct 99 ms 296272 KB Output is correct
35 Correct 102 ms 299396 KB Output is correct
36 Correct 104 ms 298576 KB Output is correct
37 Correct 105 ms 296788 KB Output is correct
38 Correct 222 ms 520052 KB Output is correct
39 Correct 209 ms 512308 KB Output is correct
40 Correct 195 ms 512412 KB Output is correct
41 Correct 791 ms 504920 KB Output is correct
42 Correct 233 ms 532272 KB Output is correct
43 Correct 237 ms 532220 KB Output is correct
44 Correct 243 ms 532340 KB Output is correct
45 Correct 263 ms 520260 KB Output is correct
46 Correct 240 ms 509384 KB Output is correct
47 Correct 400 ms 511968 KB Output is correct
48 Correct 310 ms 517460 KB Output is correct
49 Correct 314 ms 517732 KB Output is correct
50 Correct 218 ms 434716 KB Output is correct
51 Correct 201 ms 427668 KB Output is correct
52 Correct 304 ms 516432 KB Output is correct
53 Correct 294 ms 516432 KB Output is correct

Subtask #5
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 120 ms 338576 KB Output is correct
2 Correct 118 ms 332368 KB Output is correct
3 Correct 123 ms 338516 KB Output is correct
4 Correct 107 ms 296276 KB Output is correct
5 Correct 122 ms 338512 KB Output is correct
6 Correct 124 ms 338648 KB Output is correct
7 Correct 120 ms 338604 KB Output is correct
8 Correct 117 ms 338516 KB Output is correct
9 Correct 132 ms 338624 KB Output is correct
10 Correct 115 ms 317776 KB Output is correct
11 Correct 153 ms 338260 KB Output is correct

Subtask #6
0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 104 ms 296272 KB Output is correct
2 Correct 99 ms 296272 KB Output is correct
3 Correct 102 ms 299396 KB Output is correct
4 Correct 104 ms 298576 KB Output is correct
5 Correct 105 ms 296788 KB Output is correct
6 Correct 110 ms 297040 KB Output is correct
7 Runtime error 531 ms 1048576 KB Execution killed with signal 9
8 Halted 0 ms 0 KB -

Subtask #7
0 / 28.0

# 결과 실행 시간 메모리 Grader output
1 Correct 94 ms 296532 KB Output is correct
2 Correct 104 ms 299348 KB Output is correct
3 Correct 103 ms 299536 KB Output is correct
4 Correct 101 ms 299348 KB Output is correct
5 Correct 107 ms 299348 KB Output is correct
6 Correct 103 ms 299456 KB Output is correct
7 Correct 122 ms 298324 KB Output is correct
8 Correct 104 ms 298064 KB Output is correct
9 Correct 102 ms 299348 KB Output is correct
10 Correct 104 ms 299344 KB Output is correct
11 Correct 104 ms 299452 KB Output is correct
12 Correct 103 ms 299532 KB Output is correct
13 Correct 103 ms 296256 KB Output is correct
14 Correct 103 ms 296784 KB Output is correct
15 Correct 104 ms 296976 KB Output is correct
16 Correct 110 ms 296528 KB Output is correct
17 Correct 106 ms 308052 KB Output is correct
18 Correct 106 ms 308048 KB Output is correct
19 Correct 107 ms 308048 KB Output is correct
20 Correct 110 ms 307796 KB Output is correct
21 Correct 106 ms 307800 KB Output is correct
22 Correct 110 ms 307792 KB Output is correct
23 Correct 113 ms 307920 KB Output is correct
24 Correct 109 ms 304348 KB Output is correct
25 Correct 116 ms 333908 KB Output is correct
26 Correct 125 ms 333908 KB Output is correct
27 Correct 119 ms 333800 KB Output is correct
28 Correct 116 ms 332112 KB Output is correct
29 Correct 126 ms 332624 KB Output is correct
30 Correct 124 ms 332696 KB Output is correct
31 Correct 122 ms 332624 KB Output is correct
32 Correct 134 ms 332276 KB Output is correct
33 Correct 222 ms 520052 KB Output is correct
34 Correct 209 ms 512308 KB Output is correct
35 Correct 195 ms 512412 KB Output is correct
36 Correct 791 ms 504920 KB Output is correct
37 Correct 233 ms 532272 KB Output is correct
38 Correct 237 ms 532220 KB Output is correct
39 Correct 243 ms 532340 KB Output is correct
40 Correct 263 ms 520260 KB Output is correct
41 Correct 240 ms 509384 KB Output is correct
42 Correct 400 ms 511968 KB Output is correct
43 Correct 310 ms 517460 KB Output is correct
44 Correct 314 ms 517732 KB Output is correct
45 Correct 218 ms 434716 KB Output is correct
46 Correct 201 ms 427668 KB Output is correct
47 Correct 304 ms 516432 KB Output is correct
48 Correct 294 ms 516432 KB Output is correct
49 Correct 120 ms 338576 KB Output is correct
50 Correct 118 ms 332368 KB Output is correct
51 Correct 123 ms 338516 KB Output is correct
52 Correct 107 ms 296276 KB Output is correct
53 Correct 122 ms 338512 KB Output is correct
54 Correct 124 ms 338648 KB Output is correct
55 Correct 120 ms 338604 KB Output is correct
56 Correct 117 ms 338516 KB Output is correct
57 Correct 132 ms 338624 KB Output is correct
58 Correct 115 ms 317776 KB Output is correct
59 Correct 153 ms 338260 KB Output is correct
60 Correct 110 ms 297040 KB Output is correct
61 Runtime error 531 ms 1048576 KB Execution killed with signal 9
62 Halted 0 ms 0 KB -