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Submission #113540

# Submission time Handle Problem Language Result Execution time Memory
113540 2019-05-26T07:16:58 Z FutymyClone Chessboard (IZhO18_chessboard) C++14
70 / 100
 370 ms 4456 KB 
#include <bits/stdc++.h>

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 == 0 ? n + 1 : n + r - n % r + 1;
}

int round_down (int n, int r) {
    return n % r == 0 ? n - r : 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 / 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;
}

int 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 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 2 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 356 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 26 ms 2928 KB Output is correct
2 Correct 9 ms 1388 KB Output is correct
3 Correct 18 ms 2444 KB Output is correct
4 Correct 20 ms 2260 KB Output is correct
5 Correct 23 ms 2680 KB Output is correct
6 Correct 16 ms 2352 KB Output is correct
7 Correct 5 ms 768 KB Output is correct
8 Correct 16 ms 2400 KB Output is correct
9 Correct 37 ms 4216 KB Output is correct
10 Correct 22 ms 2572 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 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 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 3 ms 384 KB Output is correct
10 Correct 2 ms 512 KB Output is correct
11 Correct 3 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 2 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct

Subtask #4
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 3 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 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 3 ms 384 KB Output is correct
10 Correct 2 ms 512 KB Output is correct
11 Correct 3 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 2 ms 384 KB Output is correct
15 Correct 2 ms 384 KB Output is correct
16 Correct 12 ms 1408 KB Output is correct
17 Correct 29 ms 3824 KB Output is correct
18 Correct 41 ms 3832 KB Output is correct
19 Correct 87 ms 3824 KB Output is correct
20 Correct 112 ms 3824 KB Output is correct
21 Correct 28 ms 3888 KB Output is correct
22 Correct 2 ms 384 KB Output is correct
23 Correct 23 ms 2300 KB Output is correct
24 Correct 35 ms 3832 KB Output is correct
25 Correct 7 ms 896 KB Output is correct
26 Correct 22 ms 2300 KB Output is correct
27 Correct 31 ms 3880 KB Output is correct
28 Correct 39 ms 3892 KB Output is correct
29 Correct 11 ms 2016 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 26 ms 2928 KB Output is correct
2 Correct 9 ms 1388 KB Output is correct
3 Correct 18 ms 2444 KB Output is correct
4 Correct 20 ms 2260 KB Output is correct
5 Correct 23 ms 2680 KB Output is correct
6 Correct 16 ms 2352 KB Output is correct
7 Correct 5 ms 768 KB Output is correct
8 Correct 16 ms 2400 KB Output is correct
9 Correct 37 ms 4216 KB Output is correct
10 Correct 22 ms 2572 KB Output is correct
11 Correct 3 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 384 KB Output is correct
18 Correct 2 ms 384 KB Output is correct
19 Correct 3 ms 384 KB Output is correct
20 Correct 2 ms 512 KB Output is correct
21 Correct 3 ms 384 KB Output is correct
22 Correct 2 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 384 KB Output is correct
26 Correct 12 ms 1408 KB Output is correct
27 Correct 29 ms 3824 KB Output is correct
28 Correct 41 ms 3832 KB Output is correct
29 Correct 87 ms 3824 KB Output is correct
30 Correct 112 ms 3824 KB Output is correct
31 Correct 28 ms 3888 KB Output is correct
32 Correct 2 ms 384 KB Output is correct
33 Correct 23 ms 2300 KB Output is correct
34 Correct 35 ms 3832 KB Output is correct
35 Correct 7 ms 896 KB Output is correct
36 Correct 22 ms 2300 KB Output is correct
37 Correct 31 ms 3880 KB Output is correct
38 Correct 39 ms 3892 KB Output is correct
39 Correct 11 ms 2016 KB Output is correct
40 Correct 3 ms 512 KB Output is correct
41 Correct 79 ms 4336 KB Output is correct
42 Correct 42 ms 4360 KB Output is correct
43 Correct 54 ms 4336 KB Output is correct
44 Correct 40 ms 4336 KB Output is correct
45 Correct 38 ms 4336 KB Output is correct
46 Correct 85 ms 4336 KB Output is correct
47 Correct 33 ms 4336 KB Output is correct
48 Correct 47 ms 4336 KB Output is correct
49 Correct 38 ms 4304 KB Output is correct
50 Correct 295 ms 4336 KB Output is correct
51 Correct 311 ms 4336 KB Output is correct
52 Correct 298 ms 4336 KB Output is correct
53 Correct 312 ms 4260 KB Output is correct
54 Correct 292 ms 4336 KB Output is correct
55 Correct 329 ms 4456 KB Output is correct
56 Correct 285 ms 4340 KB Output is correct

Subtask #6
0 / 30.0

# 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 2 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 356 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 26 ms 2928 KB Output is correct
10 Correct 9 ms 1388 KB Output is correct
11 Correct 18 ms 2444 KB Output is correct
12 Correct 20 ms 2260 KB Output is correct
13 Correct 23 ms 2680 KB Output is correct
14 Correct 16 ms 2352 KB Output is correct
15 Correct 5 ms 768 KB Output is correct
16 Correct 16 ms 2400 KB Output is correct
17 Correct 37 ms 4216 KB Output is correct
18 Correct 22 ms 2572 KB Output is correct
19 Correct 3 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 384 KB Output is correct
26 Correct 2 ms 384 KB Output is correct
27 Correct 3 ms 384 KB Output is correct
28 Correct 2 ms 512 KB Output is correct
29 Correct 3 ms 384 KB Output is correct
30 Correct 2 ms 384 KB Output is correct
31 Correct 2 ms 384 KB Output is correct
32 Correct 2 ms 384 KB Output is correct
33 Correct 2 ms 384 KB Output is correct
34 Correct 12 ms 1408 KB Output is correct
35 Correct 29 ms 3824 KB Output is correct
36 Correct 41 ms 3832 KB Output is correct
37 Correct 87 ms 3824 KB Output is correct
38 Correct 112 ms 3824 KB Output is correct
39 Correct 28 ms 3888 KB Output is correct
40 Correct 2 ms 384 KB Output is correct
41 Correct 23 ms 2300 KB Output is correct
42 Correct 35 ms 3832 KB Output is correct
43 Correct 7 ms 896 KB Output is correct
44 Correct 22 ms 2300 KB Output is correct
45 Correct 31 ms 3880 KB Output is correct
46 Correct 39 ms 3892 KB Output is correct
47 Correct 11 ms 2016 KB Output is correct
48 Correct 3 ms 512 KB Output is correct
49 Correct 79 ms 4336 KB Output is correct
50 Correct 42 ms 4360 KB Output is correct
51 Correct 54 ms 4336 KB Output is correct
52 Correct 40 ms 4336 KB Output is correct
53 Correct 38 ms 4336 KB Output is correct
54 Correct 85 ms 4336 KB Output is correct
55 Correct 33 ms 4336 KB Output is correct
56 Correct 47 ms 4336 KB Output is correct
57 Correct 38 ms 4304 KB Output is correct
58 Correct 295 ms 4336 KB Output is correct
59 Correct 311 ms 4336 KB Output is correct
60 Correct 298 ms 4336 KB Output is correct
61 Correct 312 ms 4260 KB Output is correct
62 Correct 292 ms 4336 KB Output is correct
63 Correct 329 ms 4456 KB Output is correct
64 Correct 285 ms 4340 KB Output is correct
65 Correct 2 ms 384 KB Output is correct
66 Correct 3 ms 384 KB Output is correct
67 Incorrect 370 ms 4332 KB Output isn't correct
68 Halted 0 ms 0 KB -