oj.uz

Submission #594560

# Submission time Handle Problem Language Result Execution time Memory
594560 2022-07-12T16:47:22 Z piOOE Sandcastle 2 (JOI22_ho_t5) C++17
100 / 100
 2870 ms 4628 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
    // 2 1
    //  3

    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<ll> 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<ll, int> cnt;
                ll 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 8 ms 912 KB Output is correct
3 Correct 16 ms 904 KB Output is correct
4 Correct 10 ms 912 KB Output is correct
5 Correct 11 ms 912 KB Output is correct
6 Correct 14 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 1 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 0 ms 212 KB Output is correct
6 Correct 1 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 1 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 0 ms 212 KB Output is correct
6 Correct 1 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 432 KB Output is correct
10 Correct 3 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 5 ms 340 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 5 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 1 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 0 ms 212 KB Output is correct
6 Correct 1 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 432 KB Output is correct
10 Correct 3 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 5 ms 340 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 5 ms 340 KB Output is correct
16 Correct 5 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 49 ms 736 KB Output is correct
19 Correct 11 ms 904 KB Output is correct
20 Correct 34 ms 724 KB Output is correct
21 Correct 58 ms 820 KB Output is correct
22 Correct 69 ms 724 KB Output is correct
23 Correct 67 ms 812 KB Output is correct
24 Correct 50 ms 780 KB Output is correct
25 Correct 70 ms 828 KB Output is correct
26 Correct 81 ms 832 KB Output is correct
27 Correct 64 ms 832 KB Output is correct
28 Correct 73 ms 832 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 1 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 0 ms 212 KB Output is correct
6 Correct 1 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 432 KB Output is correct
10 Correct 3 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 5 ms 340 KB Output is correct
14 Correct 5 ms 340 KB Output is correct
15 Correct 5 ms 340 KB Output is correct
16 Correct 5 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 49 ms 736 KB Output is correct
19 Correct 11 ms 904 KB Output is correct
20 Correct 34 ms 724 KB Output is correct
21 Correct 58 ms 820 KB Output is correct
22 Correct 69 ms 724 KB Output is correct
23 Correct 67 ms 812 KB Output is correct
24 Correct 50 ms 780 KB Output is correct
25 Correct 70 ms 828 KB Output is correct
26 Correct 81 ms 832 KB Output is correct
27 Correct 64 ms 832 KB Output is correct
28 Correct 73 ms 832 KB Output is correct
29 Correct 8 ms 912 KB Output is correct
30 Correct 344 ms 3932 KB Output is correct
31 Correct 2330 ms 3920 KB Output is correct
32 Correct 18 ms 4628 KB Output is correct
33 Correct 1657 ms 3940 KB Output is correct
34 Correct 2221 ms 3932 KB Output is correct
35 Correct 875 ms 2740 KB Output is correct
36 Correct 1268 ms 3920 KB Output is correct
37 Correct 2801 ms 3920 KB Output is correct
38 Correct 2870 ms 3920 KB Output is correct
39 Correct 2691 ms 3920 KB Output is correct
40 Correct 2817 ms 3920 KB Output is correct
41 Correct 2756 ms 3920 KB Output is correct
42 Correct 2709 ms 3920 KB Output is correct
43 Correct 2768 ms 3920 KB Output is correct
44 Correct 2766 ms 3920 KB Output is correct