Submission #93969

#	Time	Username	Problem	Language	Result	Execution time	Memory
93969		qkxwsm	Chessboard (IZhO18_chessboard)	C++14	100 / 100	1732 ms	5880 KiB

chessboard

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;

random_device(rd);
mt19937 rng(rd());
const long long FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();

struct custom_hash
{
	template<class T>
	unsigned long long operator()(T v) const
	{
		unsigned long long x = v;
		x += FIXED_RANDOM;
		// x += 11400714819323198485ull;
		// x = (x ^ (x >> 30)) * 13787848793156543929ull;
		x = (x ^ (x >> 27)) * 10723151780598845931ull;
		return x ^ (x >> 31);
	}
};

template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class U> using hash_table = gp_hash_table<T, U, custom_hash>;

template<class T>
T randomize(T mod)
{
	return (uniform_int_distribution<T>(0, mod - 1))(rng);
}
template<class T>
void readi(T &x)
{
	x = 0;
	bool negative = false;
	char c = ' ';
	while (c < '-')
	{
		c = getchar();
	}
	if (c == '-')
	{
		negative = true;
		c = getchar();
	}
	while (c >= '0')
	{
		x = x * 10 + (c - '0');
		c = getchar();
	}
	if (negative)
	{
		x = -x;
	}
}
template<class T>
void printi(T output)
{
	if (output == 0)
	{
		putchar('0');
		return;
	}
	if (output < 0)
	{
		putchar('-');
		output = -output;
	}
	int buf[20], n = 0;
	while(output)
	{
		buf[n] = ((output % 10));
		output /= 10;
		n++;
	}
	for (n--; n >= 0; n--)
	{
		putchar(buf[n] + '0');
	}
	return;
}
template<class T>
void ckmin(T &a, T b)
{
	a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
	a = max(a, b);
}
long long expo(long long a, long long e, long long mod)
{
	return ((e == 0) ? 1 : ((expo(a * a % mod, e >> 1, mod)) * ((e & 1) ? a : 1) % mod));
}
template<class T, class U>
void nmod(T &x, U mod)
{
	if (x >= mod) x -= mod;
}
template<class T>
T gcd(T a, T b)
{
	return (b ? gcd(b, a % b) : a);
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define DBG(x) cerr << #x << " = " << (x) << endl
#define SZ(x) ((int) ((x).size()))
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)
#define ALL(x) (x).begin(), (x).end()

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-9;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ld, ld> pdd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<ld> vd;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef vector<pdd> vpd;
typedef pair<pll, pll> ppp;

int N, K;
vi factors;
ppp coor[MAXN];
ll ans = LLINF;

ll cn1(ll x, ll c)
{
	//how many in 0...x are ODD when divided by c
	if (x < 0) return 0;
	ll num = (x / c);
	if (num % 2)
	{
		return c * (num / 2) + (x + 1 - num * c);
	}
	else
	{
		return c * (num / 2);
	}
}
ll cn(ll x, ll y, ll c)
{
	//how many in (x, y) are ODD when divided by c?
	return cn1(y, c) - cn1(x - 1, c);
}
ll get(ll x1, ll x2, ll y1, ll y2, ll c, bool flag)
{
	ll res = 0;
	ll x[2], y[2];
	x[1] = cn(x1, x2, c);
	x[0] = (x2 - x1 + 1) - x[1];
	y[1] = cn(y1, y2, c);
	y[0] = (y2 - y1 + 1) - y[1];
	FOR(i, 0, 2)
	{
		res += x[i] * y[1 ^ i ^ flag];
	}
	return res;
	// for (int i = x1; i <= x2; i++)
	// {
	// 	for (int j = y1; j <= y2; j++)
	// 	{
	// 		if (((flag) + (i / c) + (j / c)) % 2) res++;
	// 	}
	// }
}


int32_t main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	// cout << fixed << setprecision(10);
	// cerr << fixed << setprecision(10);
	// if (fopen("file.in", "r"))
	// {
	// 	freopen ("file.in", "r", stdin);
	// 	freopen ("file.out", "w", stdout);
	// }
	cin >> N >> K;
	FOR(i, 1, N)
	{
		if (N % i == 0) factors.PB(i);
	}
	FOR(i, 0, K)
	{
		cin >> coor[i].fi.fi >> coor[i].fi.se >> coor[i].se.fi >> coor[i].se.se;
		coor[i].fi.fi--; coor[i].fi.se--; coor[i].se.fi--; coor[i].se.se--;
	}
	for (int c : factors)
	{
		//try having each square have side length x!
		FOR(flag, 0, 2)
		{
			//flag is whether the top left is black or white!
			ll res = (1ll * (N / c) * (N / c) + flag) / 2 * c * c;
			// DBG(res);
			FOR(i, 0, K)
			{
				ll x1 = coor[i].fi.fi, x2 = coor[i].se.fi, y1 = coor[i].fi.se, y2 = coor[i].se.se;
				// DBG(x1); DBG(x2); DBG(y1); DBG(y2);
				ll num = get(x1, x2, y1, y2, c, flag);
				// DBG(num);
				res += (x2 - x1 + 1) * (y2 - y1 + 1) - 2 * num;
				// DBG((x2 - x1 + 1) * (y2 - y1 + 1));
			}
			// cerr << c << ' ' << flag << ' ' << res << endl;
			ckmin(ans, res);
		}
	}
	cout << ans << '\n';
	// cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}
/* READ READ READ
* int overflow, maxn too small, special cases (n=1?, two distinct?), cin.tie() interactive
* reread the problem, try small cases
* note down possible sources of error as you go
* do smth instead of nothing
*/

• Subtask 1: 8 / 8
• Subtask 2: 8 / 8
• Subtask 3: 15 / 15
• Subtask 4: 16 / 16
• Subtask 5: 23 / 23
• Subtask 6: 30 / 30