oj.uz

Submission #594568

# Submission time Handle Problem Language Result Execution time Memory
594568 2022-07-12T16:59:05 Z piOOE Sandcastle 2 (JOI22_ho_t5) C++17
100 / 100
 989 ms 4756 KB 
#include <bits/stdc++.h>

using namespace std;

using ll = long long;

//O(min(H, W) * H * W)
//I also came up with O((H * W)^2) solution, but didn't know how to optimize it to O(min(H, W) * H * W)
//so now this is Radewoosh's solution

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, m;
    cin >> n >> m;

    bool swapped = false;
    if (n > m) {
        swapped = true;
        swap(n, m);
    }

    vector<vector<int>> a(n, vector<int>(m));
    vector<int> yy;
    for (int i = 0; i < (swapped ? m : n); ++i) {
        for (int j = 0; j < (swapped ? n : m); ++j) {
            if (!swapped) {
                cin >> a[i][j];
                yy.push_back(a[i][j]);
            } else {
                cin >> a[j][i];
                yy.push_back(a[j][i]);
            }
        }
    }

    sort(yy.begin(), yy.end());
    yy.resize(unique(yy.begin(), yy.end()) - yy.begin());

    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            a[i][j] = lower_bound(yy.begin(), yy.end(), a[i][j]) - yy.begin() + 1;
        }
    }

    const int dx[4] = {-1, 0, 1, 0};
    const int dy[4] = {0, 1, 0, -1};
    //  0
    // 3 1
    //  2

    auto solveM = [&](int k) {
        int ans = 0;
        for (int i = 0; i < m;) {
            int j = i + 1;
            while (j < m && a[k][j] < a[k][j - 1]) {
                j += 1;
            }
            int len = j - i;
            ans += len * ((ll) len - 1) / 2;
            i = j;
        }

        for (int i = m - 1; i > -1;) {
            int j = i - 1;
            while (j > -1 && a[k][j] < a[k][j + 1]) {
                j -= 1;
            }
            int len = i - j;
            ans += len * ((ll) len - 1) / 2;
            i = j;
        }

        return ans;
    };

    auto solveN = [&](int k) {
        int ans = 0;
        for (int i = 0; i < n;) {
            int j = i + 1;
            while (j < n && a[j][k] < a[j - 1][k]) {
                j += 1;
            }
            int len = j - i;
            ans += len * ((ll) len - 1) / 2;
            i = j;
        }

        for (int i = n - 1; i > -1;) {
            int j = i - 1;
            while (j > -1 && a[j][k] < a[j + 1][k]) {
                j -= 1;
            }
            int len = i - j;
            ans += len * ((ll) len - 1) / 2;
            i = j;
        }

        return ans;
    };

    int ans = 0;
    if (n == 1) {
        ans += solveM(0) + m;
    } else {
        int diff[16][n][m];

        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < m; ++j) {
                for (int mask = 0; mask < 16; ++mask) {
                    int lower = 0;
                    bool big = false;
                    for (int k = 0; k < 4; ++k) {
                        if (mask >> k & 1) {
                            int nx = i + dx[k];
                            int ny = j + dy[k];
                            if (nx >= 0 && nx < n && ny >= 0 && ny < m) {
                                if (a[nx][ny] < a[i][j]) {
                                    lower = max(lower, a[nx][ny]);
                                } else {
                                    big = true;
                                }
                            }
                        }
                    }
                    diff[mask][i][j] = a[i][j] - lower + (big ? 0 : n * m + 1 - a[i][j]);
                }
            }
        }

        //now handle rectangles with width or length = 1
        for (int i = 0; i < n; ++i) {
            ans += solveM(i);
        }
        for (int i = 0; i < m; ++i) {
            ans += solveN(i);
        }
        ans += n * m;

        vector<vector<int>> mid(n, vector<int>(m)), L(n, vector<int>(m)), R(n, vector<int>(m));

        for (int y = 0; y < m; ++y) {
            for (int x = 0; x < n; ++x) {
                mid[x][y] = (x ? mid[x - 1][y] : 0) + diff[15][x][y];
                L[x][y] = (x ? L[x - 1][y] : 0) + diff[7][x][y];
                R[x][y] = (x ? R[x - 1][y] : 0) + diff[13][x][y];
            }
        }

        //main part!
        for (int x1 = 0; x1 < n; ++x1) {
            for (int x2 = x1 + 1; x2 < n; ++x2) {
                vector<int> valMid(m), valR(m), valL(m);
                for (int y = 0; y < m; ++y) {
                    valMid[y] = mid[x2 - 1][y] - mid[x1][y] + diff[14][x1][y] + diff[11][x2][y];
                    valR[y] = R[x2 - 1][y] - R[x1][y] + diff[12][x1][y] + diff[9][x2][y];
                    valL[y] = L[x2 - 1][y] - L[x1][y] + diff[6][x1][y] + diff[3][x2][y];
                }
                unordered_map<int, int> cnt;
                int prefix = 0;
                for (int y1 = 0; y1 < m; ++y1) {
                    if (y1 > 0) {
                        prefix += valMid[y1 - 1];
                        ++cnt[prefix - valL[y1 - 1]];
                    }
                    ans += cnt[prefix + valR[y1] - (n * m + 1)];
                }
            }
        }
    }
    cout << ans;
    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 7 ms 912 KB Output is correct
3 Correct 15 ms 916 KB Output is correct
4 Correct 10 ms 912 KB Output is correct
5 Correct 11 ms 912 KB Output is correct
6 Correct 13 ms 912 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct

Subtask #3
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 5 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 4 ms 452 KB Output is correct
14 Correct 3 ms 340 KB Output is correct
15 Correct 3 ms 340 KB Output is correct
16 Correct 5 ms 340 KB Output is correct

Subtask #4
56.0 / 56.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 5 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 4 ms 452 KB Output is correct
14 Correct 3 ms 340 KB Output is correct
15 Correct 3 ms 340 KB Output is correct
16 Correct 5 ms 340 KB Output is correct
17 Correct 2 ms 340 KB Output is correct
18 Correct 39 ms 924 KB Output is correct
19 Correct 12 ms 852 KB Output is correct
20 Correct 9 ms 876 KB Output is correct
21 Correct 22 ms 904 KB Output is correct
22 Correct 41 ms 888 KB Output is correct
23 Correct 33 ms 880 KB Output is correct
24 Correct 27 ms 848 KB Output is correct
25 Correct 41 ms 896 KB Output is correct
26 Correct 45 ms 852 KB Output is correct
27 Correct 44 ms 892 KB Output is correct
28 Correct 42 ms 852 KB Output is correct

Subtask #5
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 5 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 4 ms 452 KB Output is correct
14 Correct 3 ms 340 KB Output is correct
15 Correct 3 ms 340 KB Output is correct
16 Correct 5 ms 340 KB Output is correct
17 Correct 2 ms 340 KB Output is correct
18 Correct 39 ms 924 KB Output is correct
19 Correct 12 ms 852 KB Output is correct
20 Correct 9 ms 876 KB Output is correct
21 Correct 22 ms 904 KB Output is correct
22 Correct 41 ms 888 KB Output is correct
23 Correct 33 ms 880 KB Output is correct
24 Correct 27 ms 848 KB Output is correct
25 Correct 41 ms 896 KB Output is correct
26 Correct 45 ms 852 KB Output is correct
27 Correct 44 ms 892 KB Output is correct
28 Correct 42 ms 852 KB Output is correct
29 Correct 7 ms 956 KB Output is correct
30 Correct 253 ms 4440 KB Output is correct
31 Correct 968 ms 4368 KB Output is correct
32 Correct 19 ms 4756 KB Output is correct
33 Correct 153 ms 4352 KB Output is correct
34 Correct 428 ms 4340 KB Output is correct
35 Correct 369 ms 3044 KB Output is correct
36 Correct 537 ms 4312 KB Output is correct
37 Correct 970 ms 4432 KB Output is correct
38 Correct 941 ms 4352 KB Output is correct
39 Correct 967 ms 4432 KB Output is correct
40 Correct 961 ms 4336 KB Output is correct
41 Correct 989 ms 4384 KB Output is correct
42 Correct 949 ms 4424 KB Output is correct
43 Correct 977 ms 4444 KB Output is correct
44 Correct 961 ms 4432 KB Output is correct