oj.uz

Submission #281608

# Submission time Handle Problem Language Result Execution time Memory
281608 2020-08-23T09:05:03 Z stoyan_malinin Rectangles (IOI19_rect) C++14
72 / 100
 5000 ms 982036 KB 
#include "rect.h"
//#include "grader.cpp"

#include <map>
#include <stack>
#include <deque>
#include <vector>
#include <assert.h>
#include <iostream>
#include <functional>

using namespace std;

const int MAXN = 2505;
const int MAXLog = 15;

struct FenwickTree
{
    vector <int> tree;

    FenwickTree(){}
    FenwickTree(int n)
    {
        this->tree.assign(n+5, 0);
    }

    void update(int ind, int val)
    {
        ind++;
        while(ind<tree.size())
        {
            tree[ind] += val;
            ind += ind&(-ind);
        }
    }

    int query(int ind)
    {
        ind++;
        int sum = 0;

        while(ind>0)
        {
            sum += tree[ind];
            ind -= ind&(-ind);
        }

        return sum;
    }
};

int n, m;
int a[MAXN][MAXN];

int helpRotate[MAXN][MAXN];
void rotate90()
{
    for(int j = 0;j<m;j++)
        for(int i = n-1;i>=0;i--)
            helpRotate[j][n - 1 - i] = a[i][j];

    swap(n, m);
    for(int i = 0;i<n;i++)
        for(int j = 0;j<m;j++)
        a[i][j] = helpRotate[i][j];
}

int rightBad[MAXN][MAXN], leftBad[MAXN][MAXN];
short int downBad[MAXN][MAXN][20], upBad[MAXN][MAXN][20];

int logVal[MAXN];

void initSparse(short int sparse[MAXN][MAXN][20], int row, int mode)
{
    for(int step = 1;step<=MAXLog;step++)
    {
        for(int j = 0;j<m;j++)
        {
            if(j+(1<<(step-1))<m)
            {
                if(mode==0)
                    sparse[row][j][step] = min(sparse[row][j][step-1], sparse[row][j+(1<<(step-1))][step-1]);
                else
                    sparse[row][j][step] = max(sparse[row][j][step-1], sparse[row][j+(1<<(step-1))][step-1]);
            }
            else
            {
                sparse[row][j][step] = sparse[row][j][step-1];
            }
        }
    }
}

map <pair <int, int>, vector <int>> pairRows;
void init()
{
    //if(n<m) rotate90();

    logVal[0] = logVal[1] = 0;
    for(int i = 2;i<=max(n, m)+2;i++)
    {
        logVal[i] = logVal[i/2] + 1;
    }

    for(int i = 0;i<n;i++)
    {
        stack <int> st;
        for(int j = 0;j<m;j++)
        {
            while(st.empty()==false && a[i][st.top()]<a[i][j]) st.pop();
            leftBad[i][j] = ((st.empty()==true)?-1:st.top());

            st.push(j);
        }

        while(st.empty()==false) st.pop();
        for(int j = m-1;j>=0;j--)
        {
            while(st.empty()==false && a[i][st.top()]<a[i][j]) st.pop();
            rightBad[i][j] = ((st.empty()==true)?m-1:st.top());

            st.push(j);
        }
    }

    for(int j = 0;j<m;j++)
    {
        stack <int> st;
        for(int i = 0;i<n;i++)
        {
            while(st.empty()==false && a[st.top()][j]<a[i][j]) st.pop();
            upBad[i][j][0] = ((st.empty()==true)?-1:st.top());

            st.push(i);
        }

        while(st.empty()==false) st.pop();
        for(int i = n-1;i>=0;i--)
        {
            while(st.empty()==false && a[st.top()][j]<a[i][j]) st.pop();
            downBad[i][j][0] = ((st.empty()==true)?n-1:st.top());

            st.push(i);
        }
    }

    for(int row = 0;row<n;row++)
    {
        initSparse(downBad, row, 0);
        initSparse(upBad, row, 1);
    }

    for(int i = 1;i<n-1;i++)
    {
        vector <int> v;
        for(int j = 0;j<m;j++)
        {
            for(int p = v.size()-1;p>=0;p--)
            {
                if(v[p]<leftBad[i][j]) break;
                pairRows[{v[p], j}].push_back(i);
            }

            while(v.empty()==false && a[i][v.back()]<=a[i][j]) v.pop_back();
            v.push_back(j);
        }
    }
}

int getVal(int row, int l, int r, short int sparse[MAXN][MAXN][20], int mode)
{
    int log2 = logVal[r-l+1];

    if(mode==0)
    {
        if(l>r) return n;
        return min(sparse[row][l][log2], sparse[row][r-(1<<log2)+1][log2]);
    }
    else
    {
        if(l>r) return -1;
        return max(sparse[row][l][log2], sparse[row][r-(1<<log2)+1][log2]);
    }
}

vector <int> toRemove[MAXN];
long long evalRowSeq(int lRow, int rRow, int c1, int c2)
{
    if(lRow>rRow) return 0;

    FenwickTree T(rRow-lRow+1);
    for(int row = rRow;row>=lRow;row--)
    {
        toRemove[row].clear();
    }

    int ans = 0;
    for(int row = rRow;row>=lRow;row--)
    {
        int maxRow = getVal(row-1, c1+1, c2-1, downBad, 0);

        T.update(row-lRow, +1);
        toRemove[getVal(row+1, c1+1, c2-1, upBad, 1)].push_back(row);

        for(int x: toRemove[row]) T.update(x-lRow, -1);

        ans += T.query(min(maxRow-1, rRow)-lRow);
        //if(c1==0 && c2==2) cout << "add " << row << " until " << getVal(row+1, c1+1, c2-1, upBad, 1) << '\n';
    }

    return ans;
}

long long evalN3log()
{
    long long answer = 0;
    for(int c1 = 0;c1<m;c1++)
    {
        for(int c2 = c1+2;c2<m;c2++)
        {
            vector <int> v = pairRows[{c1, c2}];
            if(v.empty()==true) continue;

            for(int i = 0;i<v.size();)
            {
                int startInd = i;
                for(;i<v.size();i++)
                {
                    if(i-startInd!=v[i]-v[startInd]) break;
                }

                answer += evalRowSeq(v[startInd], v[i-1], c1, c2);
            }
        }
    }

    return answer;
}

short int downOne[MAXN][MAXN][20];
int leftZero[MAXN][MAXN], rightZero[MAXN][MAXN], downZero[MAXN][MAXN];

void init01()
{
    logVal[0] = logVal[1] = 0;
    for(int i = 2;i<=max(n, m)+2;i++)
    {
        logVal[i] = logVal[i/2] + 1;
    }

    for(int i = 0;i<n;i++)
    {
        int zero = -1;
        for(int j = 0;j<m;j++)
        {
            if(a[i][j]==0) zero = j;
            leftZero[i][j] = zero;
        }

        zero = m;
        for(int j = m-1;j>=0;j--)
        {
            if(a[i][j]==0) zero = j;
            rightZero[i][j] = zero;
        }
    }

    for(int j = 0;j<m;j++)
    {
        int one = n, zero = n;
        for(int i = n-1;i>=0;i--)
        {
            if(a[i][j]==1) one = i;
            if(a[i][j]==0) zero = i;

            downOne[i][j][0] = one;
            downZero[i][j] = zero;
        }
    }

    for(int row = 0;row<n;row++)
        initSparse(downOne, row, 0);
}

long long eval01()
{
    init01();

    function <bool(int, int, int)> eval = [&](int l, int r, int row)
    {
        if(l+1>=r) return false;

        int oneRow = getVal(row+1, l+1, r-1, downOne, 0);
        if(oneRow>=n) return false;

        //cout << oneRow << '\n';
        if(downZero[row+1][l]<oneRow) return false;
        if(downZero[row+1][r]<oneRow) return false;

        //cout << "ok" << '\n';
        if(rightZero[row][l+1]<=r-1) return false;
        if(rightZero[oneRow][l+1]<=r-1) return false;

        return true;
    };

    int answer = 0;
    for(int i = 0;i<n-2;i++)
    {
        int last = -1;
        for(int j = 0;j<m;j++)
        {
            if(a[i+1][j]==1)
            {
                if(last==-1)
                {
                    last = j;
                    continue;
                }

                //cout << i << " -> " << last << " " << j << '\n';

                answer += eval(last, j, i);
                last = j;
            }
        }
    }

    return answer;
}

int recogniseSubtask()
{
    int maxVal = 0;
    for(int i = 0;i<n;i++)
        for(int j = 0;j<m;j++)
            maxVal = max(maxVal, a[i][j]);

    if(maxVal<=1) return 6;
    return 1;
}

long long count_rectangles(vector<vector<int>> _a)
{
    n = _a.size();
    m = _a[0].size();
    for(int i = 0;i<n;i++)
        for(int j = 0;j<m;j++)
            a[i][j] = _a[i][j];

    init();

    //
    if(recogniseSubtask()==6) return eval01();
    return evalN3log();

    /*
    cout << '\n';
    for(int i = 0;i<n;i++)
    {
        for(int j = 0;j<m;j++) cout << a[i][j] << " ";
        cout << '\n';
    }
    cout << '\n';

    cout << '\n';
    for(int i = 0;i<n;i++)
    {
        for(int j = 0;j<m;j++) cout << downBad[i][j][0] << " ";
        cout << '\n';
    }
    cout << '\n';
    */


}
/*
6 5
4 8 7 5 6
7 4 10 3 5
9 7 20 14 2
9 14 7 3 6
5 7 5 2 7
4 5 13 5 6

4 4
1 1 1 1
1 0 0 1
1 0 0 1
1 1 1 1

4 5
1 1 1 0 1
1 0 1 1 1
1 1 1 0 1
1 1 1 1 1

2 2
1 1
1 1

3 3
1 1 1
1 1 1
1 0 1

5 5
1 1 1 1 1
1 1 1 1 1
1 1 0 1 1
1 1 1 1 1
1 1 1 1 1
*/

Compilation message

rect.cpp: In member function 'void FenwickTree::update(int, int)':
rect.cpp:30:18: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   30 |         while(ind<tree.size())
      |               ~~~^~~~~~~~~~~~
rect.cpp: In function 'long long int evalN3log()':
rect.cpp:224:28: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  224 |             for(int i = 0;i<v.size();)
      |                           ~^~~~~~~~~
rect.cpp:227:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  227 |                 for(;i<v.size();i++)
      |                      ~^~~~~~~~~

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 512 KB Output is correct
2 Correct 1 ms 1152 KB Output is correct
3 Correct 1 ms 1152 KB Output is correct
4 Correct 2 ms 1152 KB Output is correct
5 Correct 1 ms 1664 KB Output is correct
6 Correct 1 ms 1152 KB Output is correct
7 Correct 1 ms 1024 KB Output is correct
8 Correct 1 ms 768 KB Output is correct
9 Correct 1 ms 1152 KB Output is correct
10 Correct 2 ms 1128 KB Output is correct
11 Correct 1 ms 1152 KB Output is correct
12 Correct 1 ms 1152 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 640 KB Output is correct
15 Correct 1 ms 768 KB Output is correct
16 Correct 1 ms 512 KB Output is correct
17 Correct 0 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct
19 Correct 2 ms 1664 KB Output is correct
20 Correct 1 ms 1536 KB Output is correct
21 Correct 1 ms 768 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 512 KB Output is correct
2 Correct 1 ms 1152 KB Output is correct
3 Correct 1 ms 1152 KB Output is correct
4 Correct 2 ms 1152 KB Output is correct
5 Correct 1 ms 1664 KB Output is correct
6 Correct 1 ms 1152 KB Output is correct
7 Correct 1 ms 1024 KB Output is correct
8 Correct 1 ms 768 KB Output is correct
9 Correct 1 ms 1152 KB Output is correct
10 Correct 2 ms 1128 KB Output is correct
11 Correct 1 ms 1152 KB Output is correct
12 Correct 1 ms 1152 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 640 KB Output is correct
15 Correct 1 ms 768 KB Output is correct
16 Correct 1 ms 512 KB Output is correct
17 Correct 5 ms 3104 KB Output is correct
18 Correct 4 ms 3072 KB Output is correct
19 Correct 4 ms 3072 KB Output is correct
20 Correct 4 ms 2944 KB Output is correct
21 Correct 5 ms 2944 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 5 ms 3072 KB Output is correct
24 Correct 3 ms 2432 KB Output is correct
25 Correct 0 ms 384 KB Output is correct
26 Correct 1 ms 384 KB Output is correct
27 Correct 2 ms 1664 KB Output is correct
28 Correct 1 ms 1536 KB Output is correct
29 Correct 1 ms 768 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 512 KB Output is correct
2 Correct 1 ms 1152 KB Output is correct
3 Correct 1 ms 1152 KB Output is correct
4 Correct 2 ms 1152 KB Output is correct
5 Correct 1 ms 1664 KB Output is correct
6 Correct 1 ms 1152 KB Output is correct
7 Correct 1 ms 1024 KB Output is correct
8 Correct 1 ms 768 KB Output is correct
9 Correct 1 ms 1152 KB Output is correct
10 Correct 2 ms 1128 KB Output is correct
11 Correct 1 ms 1152 KB Output is correct
12 Correct 1 ms 1152 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 640 KB Output is correct
15 Correct 1 ms 768 KB Output is correct
16 Correct 1 ms 512 KB Output is correct
17 Correct 5 ms 3104 KB Output is correct
18 Correct 4 ms 3072 KB Output is correct
19 Correct 4 ms 3072 KB Output is correct
20 Correct 4 ms 2944 KB Output is correct
21 Correct 5 ms 2944 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 5 ms 3072 KB Output is correct
24 Correct 3 ms 2432 KB Output is correct
25 Correct 20 ms 10616 KB Output is correct
26 Correct 20 ms 10624 KB Output is correct
27 Correct 21 ms 10716 KB Output is correct
28 Correct 22 ms 10496 KB Output is correct
29 Correct 30 ms 10616 KB Output is correct
30 Correct 31 ms 10872 KB Output is correct
31 Correct 28 ms 10752 KB Output is correct
32 Correct 28 ms 10624 KB Output is correct
33 Correct 0 ms 384 KB Output is correct
34 Correct 1 ms 384 KB Output is correct
35 Correct 2 ms 1664 KB Output is correct
36 Correct 1 ms 1536 KB Output is correct
37 Correct 1 ms 768 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 512 KB Output is correct
2 Correct 1 ms 1152 KB Output is correct
3 Correct 1 ms 1152 KB Output is correct
4 Correct 2 ms 1152 KB Output is correct
5 Correct 1 ms 1664 KB Output is correct
6 Correct 1 ms 1152 KB Output is correct
7 Correct 1 ms 1024 KB Output is correct
8 Correct 1 ms 768 KB Output is correct
9 Correct 1 ms 1152 KB Output is correct
10 Correct 2 ms 1128 KB Output is correct
11 Correct 1 ms 1152 KB Output is correct
12 Correct 1 ms 1152 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 640 KB Output is correct
15 Correct 1 ms 768 KB Output is correct
16 Correct 1 ms 512 KB Output is correct
17 Correct 5 ms 3104 KB Output is correct
18 Correct 4 ms 3072 KB Output is correct
19 Correct 4 ms 3072 KB Output is correct
20 Correct 4 ms 2944 KB Output is correct
21 Correct 5 ms 2944 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 5 ms 3072 KB Output is correct
24 Correct 3 ms 2432 KB Output is correct
25 Correct 20 ms 10616 KB Output is correct
26 Correct 20 ms 10624 KB Output is correct
27 Correct 21 ms 10716 KB Output is correct
28 Correct 22 ms 10496 KB Output is correct
29 Correct 30 ms 10616 KB Output is correct
30 Correct 31 ms 10872 KB Output is correct
31 Correct 28 ms 10752 KB Output is correct
32 Correct 28 ms 10624 KB Output is correct
33 Correct 399 ms 94832 KB Output is correct
34 Correct 331 ms 94456 KB Output is correct
35 Correct 295 ms 93304 KB Output is correct
36 Correct 324 ms 93408 KB Output is correct
37 Correct 266 ms 88540 KB Output is correct
38 Correct 261 ms 88440 KB Output is correct
39 Correct 267 ms 88568 KB Output is correct
40 Correct 255 ms 84472 KB Output is correct
41 Correct 237 ms 103928 KB Output is correct
42 Correct 289 ms 86904 KB Output is correct
43 Correct 427 ms 89084 KB Output is correct
44 Correct 439 ms 89080 KB Output is correct
45 Correct 189 ms 47736 KB Output is correct
46 Correct 234 ms 55160 KB Output is correct
47 Correct 377 ms 88696 KB Output is correct
48 Correct 399 ms 88824 KB Output is correct
49 Correct 0 ms 384 KB Output is correct
50 Correct 1 ms 384 KB Output is correct
51 Correct 2 ms 1664 KB Output is correct
52 Correct 1 ms 1536 KB Output is correct
53 Correct 1 ms 768 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 734 ms 246152 KB Output is correct
2 Correct 531 ms 177656 KB Output is correct
3 Correct 3 ms 1792 KB Output is correct
4 Correct 1 ms 512 KB Output is correct
5 Correct 733 ms 245928 KB Output is correct
6 Correct 732 ms 245884 KB Output is correct
7 Correct 731 ms 245880 KB Output is correct
8 Correct 768 ms 245940 KB Output is correct
9 Correct 734 ms 245884 KB Output is correct
10 Correct 1159 ms 245116 KB Output is correct
11 Correct 1094 ms 245348 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 768 KB Output is correct
2 Correct 1323 ms 473516 KB Output is correct
3 Correct 2955 ms 977764 KB Output is correct
4 Correct 2971 ms 982036 KB Output is correct
5 Correct 3063 ms 982000 KB Output is correct
6 Correct 1012 ms 480880 KB Output is correct
7 Correct 2028 ms 947108 KB Output is correct
8 Correct 2112 ms 969936 KB Output is correct
9 Correct 0 ms 384 KB Output is correct
10 Correct 1 ms 384 KB Output is correct
11 Correct 2 ms 1664 KB Output is correct
12 Correct 1 ms 1536 KB Output is correct
13 Correct 1 ms 768 KB Output is correct

Subtask #7
0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 512 KB Output is correct
2 Correct 1 ms 1152 KB Output is correct
3 Correct 1 ms 1152 KB Output is correct
4 Correct 2 ms 1152 KB Output is correct
5 Correct 1 ms 1664 KB Output is correct
6 Correct 1 ms 1152 KB Output is correct
7 Correct 1 ms 1024 KB Output is correct
8 Correct 1 ms 768 KB Output is correct
9 Correct 1 ms 1152 KB Output is correct
10 Correct 2 ms 1128 KB Output is correct
11 Correct 1 ms 1152 KB Output is correct
12 Correct 1 ms 1152 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 640 KB Output is correct
15 Correct 1 ms 768 KB Output is correct
16 Correct 1 ms 512 KB Output is correct
17 Correct 5 ms 3104 KB Output is correct
18 Correct 4 ms 3072 KB Output is correct
19 Correct 4 ms 3072 KB Output is correct
20 Correct 4 ms 2944 KB Output is correct
21 Correct 5 ms 2944 KB Output is correct
22 Correct 5 ms 3072 KB Output is correct
23 Correct 5 ms 3072 KB Output is correct
24 Correct 3 ms 2432 KB Output is correct
25 Correct 20 ms 10616 KB Output is correct
26 Correct 20 ms 10624 KB Output is correct
27 Correct 21 ms 10716 KB Output is correct
28 Correct 22 ms 10496 KB Output is correct
29 Correct 30 ms 10616 KB Output is correct
30 Correct 31 ms 10872 KB Output is correct
31 Correct 28 ms 10752 KB Output is correct
32 Correct 28 ms 10624 KB Output is correct
33 Correct 399 ms 94832 KB Output is correct
34 Correct 331 ms 94456 KB Output is correct
35 Correct 295 ms 93304 KB Output is correct
36 Correct 324 ms 93408 KB Output is correct
37 Correct 266 ms 88540 KB Output is correct
38 Correct 261 ms 88440 KB Output is correct
39 Correct 267 ms 88568 KB Output is correct
40 Correct 255 ms 84472 KB Output is correct
41 Correct 237 ms 103928 KB Output is correct
42 Correct 289 ms 86904 KB Output is correct
43 Correct 427 ms 89084 KB Output is correct
44 Correct 439 ms 89080 KB Output is correct
45 Correct 189 ms 47736 KB Output is correct
46 Correct 234 ms 55160 KB Output is correct
47 Correct 377 ms 88696 KB Output is correct
48 Correct 399 ms 88824 KB Output is correct
49 Correct 734 ms 246152 KB Output is correct
50 Correct 531 ms 177656 KB Output is correct
51 Correct 3 ms 1792 KB Output is correct
52 Correct 1 ms 512 KB Output is correct
53 Correct 733 ms 245928 KB Output is correct
54 Correct 732 ms 245884 KB Output is correct
55 Correct 731 ms 245880 KB Output is correct
56 Correct 768 ms 245940 KB Output is correct
57 Correct 734 ms 245884 KB Output is correct
58 Correct 1159 ms 245116 KB Output is correct
59 Correct 1094 ms 245348 KB Output is correct
60 Correct 1 ms 768 KB Output is correct
61 Correct 1323 ms 473516 KB Output is correct
62 Correct 2955 ms 977764 KB Output is correct
63 Correct 2971 ms 982036 KB Output is correct
64 Correct 3063 ms 982000 KB Output is correct
65 Correct 1012 ms 480880 KB Output is correct
66 Correct 2028 ms 947108 KB Output is correct
67 Correct 2112 ms 969936 KB Output is correct
68 Execution timed out 5092 ms 855092 KB Time limit exceeded
69 Halted 0 ms 0 KB -