oj.uz

Submission #594561

# Submission time Handle Problem Language Result Execution time Memory
594561 2022-07-12T16:48:30 Z piOOE Sandcastle 2 (JOI22_ho_t5) C++17
100 / 100
 2652 ms 4200 KB 
#include <bits/stdc++.h>

using namespace std;

using ll = long long;

//O((H * W)^2)
//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) {
        ll 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) {
        ll 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;
    };

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

        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;

        //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) {
                    for (int x = x1; x <= x2; ++x) {
                        valMid[y] += diff[15 - (x == x1 ? 1 : 0) - (x == x2 ? 4 : 0)][x][y];
                        valL[y] += diff[15 - 8 - (x == x1 ? 1 : 0) - (x == x2 ? 4 : 0)][x][y];
                        valR[y] += diff[15 - 2 - (x == x1 ? 1 : 0) - (x == x2 ? 4 : 0)][x][y];
                    }
                }
                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 9 ms 912 KB Output is correct
3 Correct 14 ms 916 KB Output is correct
4 Correct 10 ms 948 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 0 ms 244 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 0 ms 244 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 3 ms 436 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 6 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 7 ms 432 KB Output is correct
16 Correct 5 ms 440 KB Output is correct

Subtask #4
56.0 / 56.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 244 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 3 ms 436 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 6 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 7 ms 432 KB Output is correct
16 Correct 5 ms 440 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 39 ms 724 KB Output is correct
19 Correct 12 ms 872 KB Output is correct
20 Correct 32 ms 724 KB Output is correct
21 Correct 57 ms 824 KB Output is correct
22 Correct 65 ms 724 KB Output is correct
23 Correct 68 ms 724 KB Output is correct
24 Correct 48 ms 724 KB Output is correct
25 Correct 64 ms 824 KB Output is correct
26 Correct 67 ms 832 KB Output is correct
27 Correct 65 ms 824 KB Output is correct
28 Correct 66 ms 724 KB Output is correct

Subtask #5
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 244 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 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 3 ms 436 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 6 ms 340 KB Output is correct
14 Correct 4 ms 340 KB Output is correct
15 Correct 7 ms 432 KB Output is correct
16 Correct 5 ms 440 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 39 ms 724 KB Output is correct
19 Correct 12 ms 872 KB Output is correct
20 Correct 32 ms 724 KB Output is correct
21 Correct 57 ms 824 KB Output is correct
22 Correct 65 ms 724 KB Output is correct
23 Correct 68 ms 724 KB Output is correct
24 Correct 48 ms 724 KB Output is correct
25 Correct 64 ms 824 KB Output is correct
26 Correct 67 ms 832 KB Output is correct
27 Correct 65 ms 824 KB Output is correct
28 Correct 66 ms 724 KB Output is correct
29 Correct 8 ms 912 KB Output is correct
30 Correct 353 ms 3928 KB Output is correct
31 Correct 2024 ms 3892 KB Output is correct
32 Correct 20 ms 4200 KB Output is correct
33 Correct 1528 ms 3876 KB Output is correct
34 Correct 1929 ms 3920 KB Output is correct
35 Correct 744 ms 2744 KB Output is correct
36 Correct 1237 ms 3920 KB Output is correct
37 Correct 2373 ms 3920 KB Output is correct
38 Correct 2404 ms 3936 KB Output is correct
39 Correct 2464 ms 3908 KB Output is correct
40 Correct 2652 ms 3920 KB Output is correct
41 Correct 2363 ms 3928 KB Output is correct
42 Correct 2385 ms 3920 KB Output is correct
43 Correct 2299 ms 3920 KB Output is correct
44 Correct 2313 ms 3936 KB Output is correct