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Submission #113273

# Submission time Handle Problem Language Result Execution time Memory
113273 2019-05-24T14:43:35 Z FutymyClone Chessboard (IZhO18_chessboard) C++14
70 / 100
 378 ms 2680 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 (len == 3) cout << upx << " " << downx << " " << upy << " " << downy << "\n";
        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 4 ms 384 KB Output is correct
3 Correct 6 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 26 ms 1532 KB Output is correct
2 Correct 9 ms 1024 KB Output is correct
3 Correct 19 ms 1532 KB Output is correct
4 Correct 17 ms 1556 KB Output is correct
5 Correct 21 ms 1532 KB Output is correct
6 Correct 14 ms 1532 KB Output is correct
7 Correct 5 ms 640 KB Output is correct
8 Correct 15 ms 1532 KB Output is correct
9 Correct 35 ms 2552 KB Output is correct
10 Correct 19 ms 1532 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 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 2 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 2 ms 384 KB Output is correct
14 Correct 2 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 384 KB Output is correct
8 Correct 2 ms 384 KB Output is correct
9 Correct 2 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 2 ms 384 KB Output is correct
14 Correct 2 ms 384 KB Output is correct
15 Correct 3 ms 384 KB Output is correct
16 Correct 12 ms 1024 KB Output is correct
17 Correct 30 ms 2544 KB Output is correct
18 Correct 36 ms 2528 KB Output is correct
19 Correct 80 ms 2680 KB Output is correct
20 Correct 90 ms 2524 KB Output is correct
21 Correct 26 ms 2540 KB Output is correct
22 Correct 2 ms 384 KB Output is correct
23 Correct 21 ms 1532 KB Output is correct
24 Correct 35 ms 2552 KB Output is correct
25 Correct 6 ms 768 KB Output is correct
26 Correct 22 ms 1660 KB Output is correct
27 Correct 29 ms 2544 KB Output is correct
28 Correct 36 ms 2552 KB Output is correct
29 Correct 12 ms 1532 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 1532 KB Output is correct
2 Correct 9 ms 1024 KB Output is correct
3 Correct 19 ms 1532 KB Output is correct
4 Correct 17 ms 1556 KB Output is correct
5 Correct 21 ms 1532 KB Output is correct
6 Correct 14 ms 1532 KB Output is correct
7 Correct 5 ms 640 KB Output is correct
8 Correct 15 ms 1532 KB Output is correct
9 Correct 35 ms 2552 KB Output is correct
10 Correct 19 ms 1532 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 384 KB Output is correct
18 Correct 2 ms 384 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 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 3 ms 384 KB Output is correct
26 Correct 12 ms 1024 KB Output is correct
27 Correct 30 ms 2544 KB Output is correct
28 Correct 36 ms 2528 KB Output is correct
29 Correct 80 ms 2680 KB Output is correct
30 Correct 90 ms 2524 KB Output is correct
31 Correct 26 ms 2540 KB Output is correct
32 Correct 2 ms 384 KB Output is correct
33 Correct 21 ms 1532 KB Output is correct
34 Correct 35 ms 2552 KB Output is correct
35 Correct 6 ms 768 KB Output is correct
36 Correct 22 ms 1660 KB Output is correct
37 Correct 29 ms 2544 KB Output is correct
38 Correct 36 ms 2552 KB Output is correct
39 Correct 12 ms 1532 KB Output is correct
40 Correct 3 ms 512 KB Output is correct
41 Correct 72 ms 2552 KB Output is correct
42 Correct 38 ms 2544 KB Output is correct
43 Correct 50 ms 2552 KB Output is correct
44 Correct 39 ms 2544 KB Output is correct
45 Correct 35 ms 2544 KB Output is correct
46 Correct 79 ms 2544 KB Output is correct
47 Correct 33 ms 2552 KB Output is correct
48 Correct 44 ms 2580 KB Output is correct
49 Correct 35 ms 2544 KB Output is correct
50 Correct 275 ms 2544 KB Output is correct
51 Correct 290 ms 2544 KB Output is correct
52 Correct 270 ms 2544 KB Output is correct
53 Correct 369 ms 2540 KB Output is correct
54 Correct 266 ms 2552 KB Output is correct
55 Correct 345 ms 2544 KB Output is correct
56 Correct 305 ms 2544 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 4 ms 384 KB Output is correct
3 Correct 6 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 26 ms 1532 KB Output is correct
10 Correct 9 ms 1024 KB Output is correct
11 Correct 19 ms 1532 KB Output is correct
12 Correct 17 ms 1556 KB Output is correct
13 Correct 21 ms 1532 KB Output is correct
14 Correct 14 ms 1532 KB Output is correct
15 Correct 5 ms 640 KB Output is correct
16 Correct 15 ms 1532 KB Output is correct
17 Correct 35 ms 2552 KB Output is correct
18 Correct 19 ms 1532 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 384 KB Output is correct
26 Correct 2 ms 384 KB Output is correct
27 Correct 2 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 2 ms 384 KB Output is correct
32 Correct 2 ms 384 KB Output is correct
33 Correct 3 ms 384 KB Output is correct
34 Correct 12 ms 1024 KB Output is correct
35 Correct 30 ms 2544 KB Output is correct
36 Correct 36 ms 2528 KB Output is correct
37 Correct 80 ms 2680 KB Output is correct
38 Correct 90 ms 2524 KB Output is correct
39 Correct 26 ms 2540 KB Output is correct
40 Correct 2 ms 384 KB Output is correct
41 Correct 21 ms 1532 KB Output is correct
42 Correct 35 ms 2552 KB Output is correct
43 Correct 6 ms 768 KB Output is correct
44 Correct 22 ms 1660 KB Output is correct
45 Correct 29 ms 2544 KB Output is correct
46 Correct 36 ms 2552 KB Output is correct
47 Correct 12 ms 1532 KB Output is correct
48 Correct 3 ms 512 KB Output is correct
49 Correct 72 ms 2552 KB Output is correct
50 Correct 38 ms 2544 KB Output is correct
51 Correct 50 ms 2552 KB Output is correct
52 Correct 39 ms 2544 KB Output is correct
53 Correct 35 ms 2544 KB Output is correct
54 Correct 79 ms 2544 KB Output is correct
55 Correct 33 ms 2552 KB Output is correct
56 Correct 44 ms 2580 KB Output is correct
57 Correct 35 ms 2544 KB Output is correct
58 Correct 275 ms 2544 KB Output is correct
59 Correct 290 ms 2544 KB Output is correct
60 Correct 270 ms 2544 KB Output is correct
61 Correct 369 ms 2540 KB Output is correct
62 Correct 266 ms 2552 KB Output is correct
63 Correct 345 ms 2544 KB Output is correct
64 Correct 305 ms 2544 KB Output is correct
65 Correct 2 ms 384 KB Output is correct
66 Correct 2 ms 384 KB Output is correct
67 Incorrect 378 ms 2544 KB Output isn't correct
68 Halted 0 ms 0 KB -