oj.uz

Submission #594566

# Submission time Handle Problem Language Result Execution time Memory
594566 2022-07-12T16:57:23 Z piOOE Sandcastle 2 (JOI22_ho_t5) C++17
100 / 100
 990 ms 4788 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;

        int mid[n][m], L[n][m], R[n][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 12 ms 944 KB Output is correct
4 Correct 10 ms 912 KB Output is correct
5 Correct 11 ms 924 KB Output is correct
6 Correct 13 ms 920 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 1 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 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 1 ms 212 KB Output is correct
3 Correct 1 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 0 ms 212 KB Output is correct
7 Correct 1 ms 212 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 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 2 ms 340 KB Output is correct
15 Correct 4 ms 340 KB Output is correct
16 Correct 4 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 1 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 0 ms 212 KB Output is correct
7 Correct 1 ms 212 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 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 2 ms 340 KB Output is correct
15 Correct 4 ms 340 KB Output is correct
16 Correct 4 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 37 ms 852 KB Output is correct
19 Correct 12 ms 852 KB Output is correct
20 Correct 10 ms 852 KB Output is correct
21 Correct 25 ms 924 KB Output is correct
22 Correct 37 ms 852 KB Output is correct
23 Correct 35 ms 972 KB Output is correct
24 Correct 29 ms 852 KB Output is correct
25 Correct 40 ms 852 KB Output is correct
26 Correct 43 ms 912 KB Output is correct
27 Correct 43 ms 908 KB Output is correct
28 Correct 42 ms 912 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 1 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 0 ms 212 KB Output is correct
7 Correct 1 ms 212 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 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 2 ms 340 KB Output is correct
15 Correct 4 ms 340 KB Output is correct
16 Correct 4 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 37 ms 852 KB Output is correct
19 Correct 12 ms 852 KB Output is correct
20 Correct 10 ms 852 KB Output is correct
21 Correct 25 ms 924 KB Output is correct
22 Correct 37 ms 852 KB Output is correct
23 Correct 35 ms 972 KB Output is correct
24 Correct 29 ms 852 KB Output is correct
25 Correct 40 ms 852 KB Output is correct
26 Correct 43 ms 912 KB Output is correct
27 Correct 43 ms 908 KB Output is correct
28 Correct 42 ms 912 KB Output is correct
29 Correct 8 ms 912 KB Output is correct
30 Correct 247 ms 4560 KB Output is correct
31 Correct 979 ms 4436 KB Output is correct
32 Correct 19 ms 4788 KB Output is correct
33 Correct 161 ms 4472 KB Output is correct
34 Correct 431 ms 4472 KB Output is correct
35 Correct 343 ms 3140 KB Output is correct
36 Correct 544 ms 4432 KB Output is correct
37 Correct 990 ms 4432 KB Output is correct
38 Correct 986 ms 4424 KB Output is correct
39 Correct 980 ms 4432 KB Output is correct
40 Correct 986 ms 4444 KB Output is correct
41 Correct 982 ms 4432 KB Output is correct
42 Correct 990 ms 4424 KB Output is correct
43 Correct 986 ms 4468 KB Output is correct
44 Correct 972 ms 4432 KB Output is correct