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Submission #113272

# Submission time Handle Problem Language Result Execution time Memory
113272 2019-05-24T14:33:11 Z FutymyClone Chessboard (IZhO18_chessboard) C++14
70 / 100
 791 ms 4768 KB 
#include <bits/stdc++.h>

#define int long long

using namespace std;

struct Rect {
    int x, y, x2, y2;
    Rect (int x = 0, int y = 0, int x2 = 0, int y2 = 0): x(x), y(y), x2(x2), y2(y2) {}
};

int n, k;
vector <Rect> vec;
long long ans = 1e18;

int round_up (int n, int r) {
    return n % r == 1 ? n : (n % r == 0 ? n + 1 : n + r - n % r + 1);
}

int round_down (int n, int r) {
    return n - n % r;
}

bool is_black (int x, int y, int len) {
    int cellx = (x % len == 0 ? x / len : x / len + 1) % 2;
    int celly = (y % len == 0 ? y / len : y / len + 1) % 2;
    return cellx == celly;
}

int getcellx (int x, int len) {
    return x % len == 0 ? x / len : x / len + 1;
}

int getcelly (int y, int len) {
    return y % len == 0 ? y / len : y / len + 1;
}

long long solve (int len) {
    int nsquare = n / len; //Number of square in each row and each column
    long long res = (1LL * nsquare * nsquare + 1) / 2 * len * len; //initialize result as number of needed black squares

    for (auto rect: vec) {
        int x = rect.x, y = rect.y, x2 = rect.x2, y2 = rect.y2;
        int upx = round_up(x, len), upy = round_up(y, len), downx = round_down(x2, len), downy = round_down(y2, len);
        if (downx >= upx && downy >= upy) {
            long long sq = 1LL * (downx - upx + 1) * (downy - upy + 1) / len;
            long long nblack = is_black(x, y, len) ? (sq + 1) / 2 : sq / 2;
            long long nwhite = sq - nblack;
            res -= nblack * len * len, res += nwhite * len * len;
        }

        if (downx >= upx) {
            long long sq = 1LL * (downx - upx + 1) / len;
            long long nblack = is_black(x, y, len) ? sq / 2 : (sq + 1) / 2;
            long long nwhite = sq - nblack;
            res -= nblack * len * (min(upy - 1, y2) - y + 1);
            res += nwhite * len * (min(upy - 1, y2) - y + 1);
            if (getcelly(y, len) != getcelly(y2, len)) {
                res -= nblack * len * (y2 - max(y, downy + 1) + 1);
                res += nwhite * len * (y2 - max(y, downy + 1) + 1);
            }
        }

        if (downy >= upy) {
            long long sq = 1LL * (downy - upy + 1) / len;
            long long nblack = is_black(x, y, len) ? sq / 2 : (sq + 1) / 2;
            long long nwhite = sq - nblack;
            res -= nblack * len * (min(upx - 1, x2) - x + 1);
            res += nwhite * len * (min(upx - 1, x2) - x + 1);
            if (getcellx(x, len) != getcellx(x2, len)) {
                res -= nblack * len * (x2 - max(x, downx + 1) + 1);
                res += nwhite * len * (x2 - max(x, downx + 1) + 1);
            }
        }

        if (getcellx(x, len) == getcellx(x2, len) && getcelly(y, len) == getcelly(y2, len)) {
            if (is_black(x, y, len)) res -= 1LL * (x2 - x + 1) * (y2 - y + 1);
            else res += 1LL * (x2 - x + 1) * (y2 - y + 1);
        }
        else if (getcellx(x, len) == getcellx(x2, len)) {
            if (is_black(x, y, len)) res -= 1LL * (x2 - x + 1) * (upy - y);
            else res += 1LL * (x2 - x + 1) * (upy - y);

            if (is_black(x, y2, len)) res -= 1LL * (x2 - x + 1) * (y2 - downy);
            else res += 1LL * (x2 - x + 1) * (y2 - downy);
        }
        else if (getcelly(y, len) == getcelly(y2, len)) {
            if (is_black(x, y, len)) res -= 1LL * (upx - x) * (y2 - y + 1);
            else res += 1LL * (upx - x) * (y2 - y + 1);

            if (is_black(x2, y, len)) res -= 1LL * (x2 - downx) * (y2 - y + 1);
            else res += 1LL * (x2 - downx) * (y2 - y + 1);
        }
        else {
            if (is_black(x, y, len)) res -= 1LL * (upx - x) * (upy - y);
            else res += 1LL * (upx - x) * (upy - y);

            if (is_black(x2, y, len)) res -= 1LL * (x2 - downx) * (upy - y);
            else res += 1LL * (x2 - downx) * (upy - y);

            if (is_black(x, y2, len)) res -= 1LL * (upx - x) * (y2 - downy);
            else res += 1LL * (upx - x) * (y2 - downy);

            if (is_black(x2, y2, len)) res -= 1LL * (x2 - downx) * (y2 - downy);
            else res += 1LL * (x2 - downx) * (y2 - downy);
        }
    }

    return res;
}

long long calc() {
    long long res = (1LL * n * n + 1) / 2;
    for (auto rect: vec) {
        int x = rect.x, y = rect.y, x2 = rect.x2, y2 = rect.y2;
        long long sq = 1LL * (x2 - x + 1) * (y2 - y + 1);
        long long nblack = is_black(x, y, 1) ? (sq + 1) / 2 : sq / 2;
        long long nwhite = sq - nblack;
        res -= nblack; res += nwhite;
    }

    return res;
}

int32_t main(){
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    cin >> n >> k;
    for (int i = 1; i <= k; i++) {
        int x, y, x2, y2;
        cin >> x >> y >> x2 >> y2;
        vec.push_back(Rect(x, y, x2, y2));
    }

    long long res = calc();
    ans = min(ans, min(res, 1LL * n * n - res));
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            long long temp = solve(i);
            ans = min(ans, min(temp, 1LL * n * n - temp));
            temp = solve(n / i);
            ans = min(ans, min(temp, 1LL * n * n - temp));
        }
    }

    cout << ans;
    return 0;
}
/*
6 8
3 3 3 3
1 2 1 2
3 4 3 4
5 5 5 5
4 3 4 3
4 4 4 4
2 1 2 1
3 6 3 6
*/

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 380 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 384 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 2552 KB Output is correct
2 Correct 8 ms 1532 KB Output is correct
3 Correct 17 ms 2552 KB Output is correct
4 Correct 18 ms 2552 KB Output is correct
5 Correct 23 ms 2552 KB Output is correct
6 Correct 16 ms 2552 KB Output is correct
7 Correct 5 ms 768 KB Output is correct
8 Correct 16 ms 2552 KB Output is correct
9 Correct 45 ms 4584 KB Output is correct
10 Correct 25 ms 2516 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 3 ms 384 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 384 KB Output is correct
7 Correct 2 ms 512 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 2 ms 384 KB Output is correct
10 Correct 7 ms 384 KB Output is correct
11 Correct 2 ms 384 KB Output is correct
12 Correct 3 ms 512 KB Output is correct
13 Correct 3 ms 384 KB Output is correct
14 Correct 3 ms 384 KB Output is correct
15 Correct 3 ms 384 KB Output is correct

Subtask #4
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 384 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 3 ms 384 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 384 KB Output is correct
7 Correct 2 ms 512 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 2 ms 384 KB Output is correct
10 Correct 7 ms 384 KB Output is correct
11 Correct 2 ms 384 KB Output is correct
12 Correct 3 ms 512 KB Output is correct
13 Correct 3 ms 384 KB Output is correct
14 Correct 3 ms 384 KB Output is correct
15 Correct 3 ms 384 KB Output is correct
16 Correct 15 ms 1532 KB Output is correct
17 Correct 33 ms 4668 KB Output is correct
18 Correct 50 ms 4596 KB Output is correct
19 Correct 165 ms 4596 KB Output is correct
20 Correct 179 ms 4596 KB Output is correct
21 Correct 28 ms 4596 KB Output is correct
22 Correct 2 ms 384 KB Output is correct
23 Correct 31 ms 2552 KB Output is correct
24 Correct 56 ms 4588 KB Output is correct
25 Correct 8 ms 1024 KB Output is correct
26 Correct 30 ms 2680 KB Output is correct
27 Correct 41 ms 4596 KB Output is correct
28 Correct 44 ms 4588 KB Output is correct
29 Correct 13 ms 2552 KB Output is correct
30 Correct 3 ms 512 KB Output is correct

Subtask #5
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 2552 KB Output is correct
2 Correct 8 ms 1532 KB Output is correct
3 Correct 17 ms 2552 KB Output is correct
4 Correct 18 ms 2552 KB Output is correct
5 Correct 23 ms 2552 KB Output is correct
6 Correct 16 ms 2552 KB Output is correct
7 Correct 5 ms 768 KB Output is correct
8 Correct 16 ms 2552 KB Output is correct
9 Correct 45 ms 4584 KB Output is correct
10 Correct 25 ms 2516 KB Output is correct
11 Correct 2 ms 384 KB Output is correct
12 Correct 2 ms 384 KB Output is correct
13 Correct 2 ms 384 KB Output is correct
14 Correct 3 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct
16 Correct 2 ms 384 KB Output is correct
17 Correct 2 ms 512 KB Output is correct
18 Correct 2 ms 384 KB Output is correct
19 Correct 2 ms 384 KB Output is correct
20 Correct 7 ms 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 3 ms 512 KB Output is correct
23 Correct 3 ms 384 KB Output is correct
24 Correct 3 ms 384 KB Output is correct
25 Correct 3 ms 384 KB Output is correct
26 Correct 15 ms 1532 KB Output is correct
27 Correct 33 ms 4668 KB Output is correct
28 Correct 50 ms 4596 KB Output is correct
29 Correct 165 ms 4596 KB Output is correct
30 Correct 179 ms 4596 KB Output is correct
31 Correct 28 ms 4596 KB Output is correct
32 Correct 2 ms 384 KB Output is correct
33 Correct 31 ms 2552 KB Output is correct
34 Correct 56 ms 4588 KB Output is correct
35 Correct 8 ms 1024 KB Output is correct
36 Correct 30 ms 2680 KB Output is correct
37 Correct 41 ms 4596 KB Output is correct
38 Correct 44 ms 4588 KB Output is correct
39 Correct 13 ms 2552 KB Output is correct
40 Correct 3 ms 512 KB Output is correct
41 Correct 130 ms 4536 KB Output is correct
42 Correct 48 ms 4588 KB Output is correct
43 Correct 89 ms 4588 KB Output is correct
44 Correct 60 ms 4768 KB Output is correct
45 Correct 45 ms 4588 KB Output is correct
46 Correct 143 ms 4584 KB Output is correct
47 Correct 35 ms 4596 KB Output is correct
48 Correct 71 ms 4560 KB Output is correct
49 Correct 43 ms 4688 KB Output is correct
50 Correct 625 ms 4584 KB Output is correct
51 Correct 669 ms 4588 KB Output is correct
52 Correct 625 ms 4584 KB Output is correct
53 Correct 791 ms 4716 KB Output is correct
54 Correct 666 ms 4584 KB Output is correct
55 Correct 763 ms 4724 KB Output is correct
56 Correct 666 ms 4588 KB Output is correct

Subtask #6
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 256 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 256 KB Output is correct
4 Correct 2 ms 380 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 2 ms 384 KB Output is correct
7 Correct 2 ms 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 25 ms 2552 KB Output is correct
10 Correct 8 ms 1532 KB Output is correct
11 Correct 17 ms 2552 KB Output is correct
12 Correct 18 ms 2552 KB Output is correct
13 Correct 23 ms 2552 KB Output is correct
14 Correct 16 ms 2552 KB Output is correct
15 Correct 5 ms 768 KB Output is correct
16 Correct 16 ms 2552 KB Output is correct
17 Correct 45 ms 4584 KB Output is correct
18 Correct 25 ms 2516 KB Output is correct
19 Correct 2 ms 384 KB Output is correct
20 Correct 2 ms 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 3 ms 384 KB Output is correct
23 Correct 2 ms 384 KB Output is correct
24 Correct 2 ms 384 KB Output is correct
25 Correct 2 ms 512 KB Output is correct
26 Correct 2 ms 384 KB Output is correct
27 Correct 2 ms 384 KB Output is correct
28 Correct 7 ms 384 KB Output is correct
29 Correct 2 ms 384 KB Output is correct
30 Correct 3 ms 512 KB Output is correct
31 Correct 3 ms 384 KB Output is correct
32 Correct 3 ms 384 KB Output is correct
33 Correct 3 ms 384 KB Output is correct
34 Correct 15 ms 1532 KB Output is correct
35 Correct 33 ms 4668 KB Output is correct
36 Correct 50 ms 4596 KB Output is correct
37 Correct 165 ms 4596 KB Output is correct
38 Correct 179 ms 4596 KB Output is correct
39 Correct 28 ms 4596 KB Output is correct
40 Correct 2 ms 384 KB Output is correct
41 Correct 31 ms 2552 KB Output is correct
42 Correct 56 ms 4588 KB Output is correct
43 Correct 8 ms 1024 KB Output is correct
44 Correct 30 ms 2680 KB Output is correct
45 Correct 41 ms 4596 KB Output is correct
46 Correct 44 ms 4588 KB Output is correct
47 Correct 13 ms 2552 KB Output is correct
48 Correct 3 ms 512 KB Output is correct
49 Correct 130 ms 4536 KB Output is correct
50 Correct 48 ms 4588 KB Output is correct
51 Correct 89 ms 4588 KB Output is correct
52 Correct 60 ms 4768 KB Output is correct
53 Correct 45 ms 4588 KB Output is correct
54 Correct 143 ms 4584 KB Output is correct
55 Correct 35 ms 4596 KB Output is correct
56 Correct 71 ms 4560 KB Output is correct
57 Correct 43 ms 4688 KB Output is correct
58 Correct 625 ms 4584 KB Output is correct
59 Correct 669 ms 4588 KB Output is correct
60 Correct 625 ms 4584 KB Output is correct
61 Correct 791 ms 4716 KB Output is correct
62 Correct 666 ms 4584 KB Output is correct
63 Correct 763 ms 4724 KB Output is correct
64 Correct 666 ms 4588 KB Output is correct
65 Correct 2 ms 384 KB Output is correct
66 Correct 2 ms 384 KB Output is correct
67 Incorrect 772 ms 4588 KB Output isn't correct
68 Halted 0 ms 0 KB -