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Submission #113270

# Submission time Handle Problem Language Result Execution time Memory
113270 2019-05-24T14:12:18 Z FutymyClone Chessboard (IZhO18_chessboard) C++14
70 / 100
 398 ms 2944 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 == 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;
}

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 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 30 ms 1656 KB Output is correct
2 Correct 8 ms 1152 KB Output is correct
3 Correct 16 ms 1660 KB Output is correct
4 Correct 17 ms 1532 KB Output is correct
5 Correct 21 ms 1532 KB Output is correct
6 Correct 15 ms 1660 KB Output is correct
7 Correct 5 ms 640 KB Output is correct
8 Correct 16 ms 1660 KB Output is correct
9 Correct 45 ms 2672 KB Output is correct
10 Correct 21 ms 1532 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 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 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 384 KB Output is correct
11 Correct 2 ms 384 KB Output is correct
12 Correct 2 ms 384 KB Output is correct
13 Correct 3 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 3 ms 432 KB Output is correct

Subtask #4
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 4 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 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 384 KB Output is correct
11 Correct 2 ms 384 KB Output is correct
12 Correct 2 ms 384 KB Output is correct
13 Correct 3 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 3 ms 432 KB Output is correct
16 Correct 12 ms 1280 KB Output is correct
17 Correct 28 ms 2808 KB Output is correct
18 Correct 37 ms 2816 KB Output is correct
19 Correct 90 ms 2764 KB Output is correct
20 Correct 112 ms 2800 KB Output is correct
21 Correct 29 ms 2800 KB Output is correct
22 Correct 2 ms 388 KB Output is correct
23 Correct 27 ms 1788 KB Output is correct
24 Correct 37 ms 2800 KB Output is correct
25 Correct 7 ms 896 KB Output is correct
26 Correct 23 ms 1788 KB Output is correct
27 Correct 33 ms 2820 KB Output is correct
28 Correct 44 ms 2800 KB Output is correct
29 Correct 13 ms 1788 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 30 ms 1656 KB Output is correct
2 Correct 8 ms 1152 KB Output is correct
3 Correct 16 ms 1660 KB Output is correct
4 Correct 17 ms 1532 KB Output is correct
5 Correct 21 ms 1532 KB Output is correct
6 Correct 15 ms 1660 KB Output is correct
7 Correct 5 ms 640 KB Output is correct
8 Correct 16 ms 1660 KB Output is correct
9 Correct 45 ms 2672 KB Output is correct
10 Correct 21 ms 1532 KB Output is correct
11 Correct 4 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 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 384 KB Output is correct
21 Correct 2 ms 384 KB Output is correct
22 Correct 2 ms 384 KB Output is correct
23 Correct 3 ms 384 KB Output is correct
24 Correct 2 ms 384 KB Output is correct
25 Correct 3 ms 432 KB Output is correct
26 Correct 12 ms 1280 KB Output is correct
27 Correct 28 ms 2808 KB Output is correct
28 Correct 37 ms 2816 KB Output is correct
29 Correct 90 ms 2764 KB Output is correct
30 Correct 112 ms 2800 KB Output is correct
31 Correct 29 ms 2800 KB Output is correct
32 Correct 2 ms 388 KB Output is correct
33 Correct 27 ms 1788 KB Output is correct
34 Correct 37 ms 2800 KB Output is correct
35 Correct 7 ms 896 KB Output is correct
36 Correct 23 ms 1788 KB Output is correct
37 Correct 33 ms 2820 KB Output is correct
38 Correct 44 ms 2800 KB Output is correct
39 Correct 13 ms 1788 KB Output is correct
40 Correct 3 ms 512 KB Output is correct
41 Correct 147 ms 2740 KB Output is correct
42 Correct 43 ms 2800 KB Output is correct
43 Correct 52 ms 2724 KB Output is correct
44 Correct 45 ms 2808 KB Output is correct
45 Correct 39 ms 2800 KB Output is correct
46 Correct 80 ms 2800 KB Output is correct
47 Correct 33 ms 2944 KB Output is correct
48 Correct 45 ms 2800 KB Output is correct
49 Correct 36 ms 2816 KB Output is correct
50 Correct 278 ms 2920 KB Output is correct
51 Correct 295 ms 2808 KB Output is correct
52 Correct 282 ms 2800 KB Output is correct
53 Correct 317 ms 2800 KB Output is correct
54 Correct 293 ms 2800 KB Output is correct
55 Correct 349 ms 2800 KB Output is correct
56 Correct 300 ms 2808 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 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 30 ms 1656 KB Output is correct
10 Correct 8 ms 1152 KB Output is correct
11 Correct 16 ms 1660 KB Output is correct
12 Correct 17 ms 1532 KB Output is correct
13 Correct 21 ms 1532 KB Output is correct
14 Correct 15 ms 1660 KB Output is correct
15 Correct 5 ms 640 KB Output is correct
16 Correct 16 ms 1660 KB Output is correct
17 Correct 45 ms 2672 KB Output is correct
18 Correct 21 ms 1532 KB Output is correct
19 Correct 4 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 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 2 ms 384 KB Output is correct
27 Correct 3 ms 384 KB Output is correct
28 Correct 2 ms 384 KB Output is correct
29 Correct 2 ms 384 KB Output is correct
30 Correct 2 ms 384 KB Output is correct
31 Correct 3 ms 384 KB Output is correct
32 Correct 2 ms 384 KB Output is correct
33 Correct 3 ms 432 KB Output is correct
34 Correct 12 ms 1280 KB Output is correct
35 Correct 28 ms 2808 KB Output is correct
36 Correct 37 ms 2816 KB Output is correct
37 Correct 90 ms 2764 KB Output is correct
38 Correct 112 ms 2800 KB Output is correct
39 Correct 29 ms 2800 KB Output is correct
40 Correct 2 ms 388 KB Output is correct
41 Correct 27 ms 1788 KB Output is correct
42 Correct 37 ms 2800 KB Output is correct
43 Correct 7 ms 896 KB Output is correct
44 Correct 23 ms 1788 KB Output is correct
45 Correct 33 ms 2820 KB Output is correct
46 Correct 44 ms 2800 KB Output is correct
47 Correct 13 ms 1788 KB Output is correct
48 Correct 3 ms 512 KB Output is correct
49 Correct 147 ms 2740 KB Output is correct
50 Correct 43 ms 2800 KB Output is correct
51 Correct 52 ms 2724 KB Output is correct
52 Correct 45 ms 2808 KB Output is correct
53 Correct 39 ms 2800 KB Output is correct
54 Correct 80 ms 2800 KB Output is correct
55 Correct 33 ms 2944 KB Output is correct
56 Correct 45 ms 2800 KB Output is correct
57 Correct 36 ms 2816 KB Output is correct
58 Correct 278 ms 2920 KB Output is correct
59 Correct 295 ms 2808 KB Output is correct
60 Correct 282 ms 2800 KB Output is correct
61 Correct 317 ms 2800 KB Output is correct
62 Correct 293 ms 2800 KB Output is correct
63 Correct 349 ms 2800 KB Output is correct
64 Correct 300 ms 2808 KB Output is correct
65 Correct 2 ms 384 KB Output is correct
66 Correct 2 ms 384 KB Output is correct
67 Incorrect 398 ms 2772 KB Output isn't correct
68 Halted 0 ms 0 KB -