Submission #417358

#	Time	Username	Problem	Language	Result	Execution time	Memory
417358		Benq	Izvanzemaljci (COI21_izvanzemaljci)	C++17	100 / 100	1342 ms	25616 KiB

izvanzemaljci

#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!

using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;

using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>; 
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>; 
using vpd = vector<pd>;

#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 
tcT> using PR = pair<T,T>;

// pairs
#define mp make_pair
#define f first
#define s second

// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back 
#define pf push_front
#define rtn return

#define lb lower_bound
#define ub upper_bound 
tcT> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); }

// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;

// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
	return x == 0 ? 0 : 31-__builtin_clz(x); } // floor(log2(x)) 
constexpr int p2(int x) { return 1<<x; }
constexpr int msk2(int x) { return p2(x)-1; }

ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down

tcT> bool ckmin(T& a, const T& b) {
	return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
	return a < b ? a = b, 1 : 0; }

tcTU> T fstTrue(T lo, T hi, U f) {
	hi ++; assert(lo <= hi); // assuming f is increasing
	while (lo < hi) { // find first index such that f is true 
		T mid = lo+(hi-lo)/2;
		f(mid) ? hi = mid : lo = mid+1; 
	} 
	return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
	lo --; assert(lo <= hi); // assuming f is decreasing
	while (lo < hi) { // find first index such that f is true 
		T mid = lo+(hi-lo+1)/2;
		f(mid) ? lo = mid : hi = mid-1;
	} 
	return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
	sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
	auto it = t.find(u); assert(it != end(t));
	t.erase(it); } // element that doesn't exist from (multi)set

#define tcTUU tcT, class ...U

inline namespace Helpers {
	//////////// is_iterable
	// https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
	// this gets used only when we can call begin() and end() on that type
	tcT, class = void> struct is_iterable : false_type {};
	tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
	                                  decltype(end(declval<T>()))
	                                 >
	                       > : true_type {};
	tcT> constexpr bool is_iterable_v = is_iterable<T>::value;

	//////////// is_readable
	tcT, class = void> struct is_readable : false_type {};
	tcT> struct is_readable<T,
	        typename std::enable_if_t<
	            is_same_v<decltype(cin >> declval<T&>()), istream&>
	        >
	    > : true_type {};
	tcT> constexpr bool is_readable_v = is_readable<T>::value;

	//////////// is_printable
	// // https://nafe.es/posts/2020-02-29-is-printable/
	tcT, class = void> struct is_printable : false_type {};
	tcT> struct is_printable<T,
	        typename std::enable_if_t<
	            is_same_v<decltype(cout << declval<T>()), ostream&>
	        >
	    > : true_type {};
	tcT> constexpr bool is_printable_v = is_printable<T>::value;
}

inline namespace Input {
	tcT> constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
	tcTUU> void re(T& t, U&... u);
	tcTU> void re(pair<T,U>& p); // pairs

	// re: read
	tcT> typename enable_if<is_readable_v<T>,void>::type re(T& x) { cin >> x; } // default
	tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; } // complex
	tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i); // ex. vectors, arrays
	tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
	tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i) {
		each(x,i) re(x); }
	tcTUU> void re(T& t, U&... u) { re(t); re(u...); } // read multiple

	// rv: resize and read vectors
	void rv(size_t) {}
	tcTUU> void rv(size_t N, V<T>& t, U&... u);
	template<class...U> void rv(size_t, size_t N2, U&... u);
	tcTUU> void rv(size_t N, V<T>& t, U&... u) {
		t.rsz(N); re(t);
		rv(N,u...); }
	template<class...U> void rv(size_t, size_t N2, U&... u) {
		rv(N2,u...); }

	// dumb shortcuts to read in ints
	void decrement() {} // subtract one from each
	tcTUU> void decrement(T& t, U&... u) { --t; decrement(u...); }
	#define ints(...) int __VA_ARGS__; re(__VA_ARGS__);
	#define int1(...) ints(__VA_ARGS__); decrement(__VA_ARGS__);
}

inline namespace ToString {
	tcT> constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;

	// ts: string representation to print
	tcT> typename enable_if<is_printable_v<T>,str>::type ts(T v) {
		stringstream ss; ss << fixed << setprecision(15) << v;
		return ss.str(); } // default
	tcT> str bit_vec(T t) { // bit vector to string
		str res = "{"; F0R(i,sz(t)) res += ts(t[i]);
		res += "}"; return res; }
	str ts(V<bool> v) { return bit_vec(v); }
	template<size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
	tcTU> str ts(pair<T,U> p); // pairs
	tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v); // vectors, arrays
	tcTU> str ts(pair<T,U> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; }
	tcT> typename enable_if<is_iterable_v<T>,str>::type ts_sep(T v, str sep) {
		// convert container to string w/ separator sep
		bool fst = 1; str res = "";
		for (const auto& x: v) {
			if (!fst) res += sep;
			fst = 0; res += ts(x);
		}
		return res;
	}
	tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v) {
		return "{"+ts_sep(v,", ")+"}"; }

	// for nested DS
	template<int, class T> typename enable_if<!needs_output_v<T>,vs>::type 
	  ts_lev(const T& v) { return {ts(v)}; }
	template<int lev, class T> typename enable_if<needs_output_v<T>,vs>::type 
	  ts_lev(const T& v) {
		if (lev == 0 || !sz(v)) return {ts(v)};
		vs res;
		for (const auto& t: v) {
			if (sz(res)) res.bk += ",";
			vs tmp = ts_lev<lev-1>(t);
			res.ins(end(res),all(tmp));
		}
		F0R(i,sz(res)) {
			str bef = " "; if (i == 0) bef = "{";
			res[i] = bef+res[i];
		}
		res.bk += "}";
		return res;
	}
}

inline namespace Output {
	template<class T> void pr_sep(ostream& os, str, const T& t) { os << ts(t); }
	template<class T, class... U> void pr_sep(ostream& os, str sep, const T& t, const U&... u) {
		pr_sep(os,sep,t); os << sep; pr_sep(os,sep,u...); }
	// print w/ no spaces
	template<class ...T> void pr(const T&... t) { pr_sep(cout,"",t...); } 
	// print w/ spaces, end with newline
	void ps() { cout << "\n"; }
	template<class ...T> void ps(const T&... t) { pr_sep(cout," ",t...); ps(); } 
	// debug to cerr
	template<class ...T> void dbg_out(const T&... t) {
		pr_sep(cerr," | ",t...); cerr << endl; }
	void loc_info(int line, str names) {
		cerr << "Line(" << line << ") -> [" << names << "]: "; }
	template<int lev, class T> void dbgl_out(const T& t) {
		cerr << "\n\n" << ts_sep(ts_lev<lev>(t),"\n") << "\n" << endl; }
	#ifdef LOCAL
		#define dbg(...) loc_info(__LINE__,#__VA_ARGS__), dbg_out(__VA_ARGS__)
		#define dbgl(lev,x) loc_info(__LINE__,#x), dbgl_out<lev>(x)
	#else // don't actually submit with this
		#define dbg(...) 0
		#define dbgl(lev,x) 0
	#endif
}

inline namespace FileIO {
	void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
	void setOut(str s) { freopen(s.c_str(),"w",stdout); }
	void setIO(str s = "") {
		cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
		// cin.exceptions(cin.failbit);
		// throws exception when do smth illegal
		// ex. try to read letter into int
		if (sz(s)) setIn(s+".in"), setOut(s+".out"); // for old USACO
	}
}

int N,K;
vpl points;
pair<ll,V<pair<pl,pl>>> ans;

tcT> void order(T& a, T& b) {
	if (a > b) swap(a,b);
}

const ll BIG = 3e9;

pair<pl,pl> make_square(ll x, ll y, ll len) { // OK
	assert(len > 0);
	assert(abs(x) <= BIG);
	assert(abs(y) <= BIG);
	assert(abs(x+len) <= BIG);
	assert(abs(y+len) <= BIG);
	return {{x,y},{x+len,y+len}};
}

void fail(bool b, bool flag) {
	if (b) {
		exit(flag);
	}
}

pair<ll,V<pair<pl,pl>>> eval(V<pair<pl,pl>> cand) {
	ll len = 0;
	each(t,cand) ckmax(len,abs(t.s.f-t.f.f));
	return {len,cand};
}

void check(V<pair<pl,pl>> cand, bool flag = false) { // OK
	assert(sz(cand) <= K);
	// ll len = 0;
	// each(t,cand) ckmax(len,abs(t.s.f-t.f.f));
	each(t,cand) {
		fail(abs(t.f.f) > BIG,flag);
		fail(abs(t.f.s) > BIG,flag);
		fail(abs(t.s.f) > BIG,flag);
		fail(abs(t.s.s) > BIG,flag);
	}
	int cnt = 0;
	while (sz(cand) < K) {
		if (cnt == 0) {
			cand.pb(make_square(BIG-5,BIG-5,1));
		} else {
			cand.pb(make_square(-BIG+5,-BIG+5,1));
		}
		++cnt;
	}
	each(t,cand) {
		fail(abs(t.f.f) > BIG,flag);
		fail(abs(t.f.s) > BIG,flag);
		fail(abs(t.s.f) > BIG,flag);
		fail(abs(t.s.s) > BIG,flag);
	}
	ckmin(ans,eval(cand));
	// dbg("AH",len,cand,ans.f);
	// if (len < ans.f) ans = {len,cand};
}

using Square = pair<pl,pl>;

vpl rev(vpl v) { // OK
	reverse(all(v));
	return v;
}

vpl neg(vpl v) { // OK
	each(t,v) t.f *= -1;
	return v;
}

V<Square> get_prefs(vpl v) {
	ll xl = v[0].f, xr = v[0].f;
	ll yl = v[0].s, yr = v[0].s;
	V<Square> prefs;
	F0R(i,sz(v)) {
		ckmin(xl,v[i].f), ckmax(xr,v[i].f);
		ckmin(yl,v[i].s), ckmax(yr,v[i].s);
		ll len = max({xr-xl,yr-yl,1LL});
		prefs.pb(make_square(xr-len,yl,len)); // maximize the y-coordinate, minimize the x-coordinate
	}
	return prefs;
}

V<Square> neg(V<Square> v) {// OK, negate x values
	each(t,v) t.f.f *= -1, t.s.f *= -1;
	return v;
}

ll get_len(Square sq) {
	ll dif = sq.s.f-sq.f.f; assert(dif > 0);
	return dif;
}

pair<ll,V<Square>> solve_opt_2(vpl rem) {
	assert(sz(rem));
	V<Square> pref_square = get_prefs(rem);
	V<Square> suf_square = neg(get_prefs(rev(neg(rem))));
	reverse(all(suf_square));
	pair<ll,V<Square>> res = eval({pref_square.bk});
	F0R(i,sz(rem)-1) if (rem.at(i).f < rem.at(i+1).f) 
		ckmin(res,eval({pref_square.at(i),suf_square.at(i+1)}));
	return res;
}

V<Square> swap_xy_sq(V<Square> v) {
	each(t,v) {
		swap(t.f.f,t.f.s);
		swap(t.s.f,t.s.s);
	}
	return v;
}

void solve() {
	sor(points);
	V<Square> pref_square = get_prefs(points);
	V<Square> suf_square = neg(get_prefs(rev(neg(points))));
	reverse(all(suf_square));
	{ // K == 1
		check({pref_square.bk});
	}
	if (K >= 2) { // K == 2
		F0R(i,sz(pref_square)-1) if (points[i].f < points[i+1].f) {
			check({pref_square[i],suf_square[i+1]}, true);
		}
		// dbg("HUH",v);
		// dbg(pref_square);
		// dbg(suf_square);
		// dbg(ans);
	}
	if (K >= 3) {
		vi tri_inds;
		F0R(i,sz(points)-1) if (points.at(i).f < points.at(i+1).f) {
			tri_inds.pb(i);
		}
		vl huh;
		auto check_sol = [&](int ind) -> ll {
			// everything <= ind accounted for
			auto swap_xy = [&](pl p) {
				swap(p.f,p.s);
				return p;
			};
			// check distinct y
			vpl rem; 
			// for (int i: sort_by_y) if (i >= ind+1) {

			// }
			FOR(i,ind+1,sz(points)) rem.pb(swap_xy(points.at(i)));
			sort(all(rem));
			auto ans_y = solve_opt_2(rem);
			ans_y.s = swap_xy_sq(ans_y.s);
			each(t,ans_y.s) assert(t.f.f > points.at(ind).f && t.s.f > points.at(ind).f);
			// check distinct x
			ll xl = MOD, xr = -MOD;
			ll yl = MOD, yr = -MOD;
			FOR(i,ind+1,sz(points)-1) {
				ckmin(xl,points.at(i).f); ckmax(xr,points.at(i).f);
				ckmin(yl,points.at(i).s); ckmax(yr,points.at(i).s);
				if (points.at(i).f < points.at(i+1).f) {
					ll len = max({xr-xl,yr-yl,1LL});
					ll nxl = max(points.at(ind).f+1,xr-len);
					ll nxr = nxl+len;
					if (nxr < points.at(i+1).f) {
						ckmin(ans_y,eval({make_square(nxl,yl,len),suf_square.at(i+1)}));
					}
				}
			}
			huh.pb(ans_y.f);
			// dbg(ans_y.f);
			ans_y.s.pb(pref_square.at(ind));
			ans_y = eval(ans_y.s); ckmin(ans,ans_y);
			// if (ans_y.f <= 6) {
			// 	dbg("AH",points,ans_y);
			// }
			return ans_y.f;
		};
		int lo = 0, hi = sz(tri_inds)-1;
		// dbg("BOUNDS",points,lo,hi);
		while (lo <= hi) {
			int mid = (lo+hi)/2;
			// dbg("TRIED",mid);
			// dbg("TRYING",mid);
			int x = tri_inds.at(mid);
			ll len = check_sol(x);
			// dbg(x,len,get_len(pref_square[x]));
			if (len > get_len(pref_square.at(x))) lo = mid+1;
			else hi = mid-1;
		}
		// for (int i: tri_inds) {
		// 	ll prev_ans = ans.f;
		// 	check_sol(i);
		// 	ll new_ans = ans.f;
		// 	if (prev_ans != new_ans) {
		// 		dbg("AH",prev_ans,new_ans,i);
		// 		exit(0);
		// 	}
		// 	// pr(check_sol(i) > get_len(pref_square[i]));
		// }
		// reverse(all(huh));
		// dbg(is_sorted(all(huh)));
		// ps();
	}
}

tcT> void rot(T& p) {
	p = mp(-p.s,p.f);
	// fassert(abs(p.f) <= BIG && abs(p.s) <= BIG)
}

int main() {
	setIO(); re(N,K);
	points.rsz(N); re(points);
	ans.f = 2*MOD;
	rep(4) {
		solve();
		each(t,points) rot(t);
		each(t,ans.s) rot(t.f), rot(t.s);
	}
	ll len = 0;
	each(t,ans.s) {
		pl a = t.f;
		pl b = t.s;
		order(a.f,b.f);
		order(a.s,b.s);
		assert(b.f-a.f == b.s-a.s);
		ckmax(len,b.f-a.f);
		assert(abs(a.f) <= BIG);
		assert(abs(a.s) <= BIG);
		ps(a.f,a.s,b.f-a.f);
	}
	dbg(len);
	// you should actually read the stuff at the bottom
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
	* do smth instead of nothing and stay organized
	* WRITE STUFF DOWN
	* DON'T GET STUCK ON ONE APPROACH
*/

Compilation message (stderr)

izvanzemaljci.cpp: In function 'int main()':
izvanzemaljci.cpp:239:20: warning: statement has no effect [-Wunused-value]
  239 |   #define dbg(...) 0
      |                    ^
izvanzemaljci.cpp:488:2: note: in expansion of macro 'dbg'
  488 |  dbg(len);
      |  ^~~
izvanzemaljci.cpp: In function 'void FileIO::setIn(str)':
izvanzemaljci.cpp:245:30: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  245 |  void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
      |                       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
izvanzemaljci.cpp: In function 'void FileIO::setOut(str)':
izvanzemaljci.cpp:246:30: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  246 |  void setOut(str s) { freopen(s.c_str(),"w",stdout); }
      |                       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 21 / 21
• Subtask 3: 12 / 12
• Subtask 4: 30 / 30
• Subtask 5: 32 / 32