Submission #574024

#	Time	Username	Problem	Language	Result	Execution time	Memory
574024		vovamr	Aliens (IOI16_aliens)	C++17	41 / 100	2061 ms	4000 KiB

aliens

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) 	(x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }

inline bool in(const pii &a, const pii &b) {
	auto &[l1, r1] = b; auto &[l2, r2] = a;
	return (l2 >= l1 && r2 <= r1);
}
inline int is(const pii &a, const pii &b) {
	auto &[l1, r1] = a; auto &[l2, r2] = b;
	return max(0, min(r1, r2) - max(l1, l2) + 1);
}

struct line {
	ll k, b, id;
	line() : k(0), b(0) {}
	line(ll k, ll b, ll id) : k(k), b(b), id(id) {}
	inline pll operator()(const ll &x) { return mpp(k * x + b, id); }
};
inline bool bad(const line &a, const line &b, const line &c) {
	return (a.b - c.b) * (b.k - a.k) >= (a.b - b.b) * (c.k - a.k);
}
deque<line> s;
inline void add(const line &c) {
	if (!sz(s)) return void(s.push_front(c));
	while (sz(s) >= 2) {
		line &a = s[1], &b = s[0];
		if (bad(c, b, a)) s.pop_front();
		else break;
	} s.push_front(c);
}
int ptr = 0;
inline pll qry(const ll &x) {
	while (ptr + 1 < sz(s) && s[ptr + 1](x) < s[ptr](x)) ++ptr;
	pll res = {inf, inf};
	for (int d = -1; d <= 2; ++d) {
		if (ptr + d >= 0 && ptr + d < sz(s)) {
			chmin(res, s[ptr + d](x));
		}
	} return res;
}

ll take_photos(int n, int m, int k, ve<int> R, ve<int> C) {
	ve<pii> pts(n);
	for (int i = 0; i < n; ++i) pts[i] = {min(R[i], C[i]), max(R[i], C[i])};
	sort(all(pts), [](const pii &a, const pii &b) { return mpp(a.se, a.fi) < mpp(b.se, b.fi); });
	pts.erase(unique(all(pts)), pts.end());

	ve<pii> nw;
	for (int i = sz(pts) - 1; ~i; --i) {
		if (!sz(nw) || !in(pts[i], nw.back())) nw.pb(pts[i]);
	} pts.swap(nw); reverse(all(pts));
	n = sz(pts);

	ve<ll> isec(n);
	for (int i = 1; i < n; ++i) isec[i] = is(pts[i - 1], pts[i]);
	for (int i = 0; i < n; ++i) isec[i] *= isec[i];
	ve<int> l(n), r(n);
	for (int i = 0; i < n; ++i) l[i] = pts[i].fi, r[i] = pts[i].se + 1;

	auto ok = [&](ll u) {
		s.clear();
		ve<pll> dp(n, {inf, inf});
		for (int i = 0; i < n; ++i) {
//			chmin(dp[i], {u + (r[i] - l[0]) * 1ll * (r[i] - l[0]), 1ll});
//			add(line(2 * l[i], (!i ? 0 : dp[i - 1].fi) - isec[i] + l[i] * 1ll * l[i], !i ? 0 : dp[i - 1].se));

//			auto need = (!i ? mpp(inf, inf) : qry(-r[i]));
//			chmin(dp[i], {need.fi + u + r[i] * 1ll * r[i], need.se + 1});

//			(u + r[i]^2) - (2l[j]) * r[i] + (l[j]^2 + dp[j - 1] - isec[j]);
			for (int j = 0; j <= i; ++j) {
				ll val = (r[i] - l[j]) * 1ll * (r[i] - l[j]);
				// (r[i]^2 + u) - 2l[j + 1] * r[i] + (l[j + 1]^2 - isec[j] + dp[j].fi)
				val += -isec[j] + u + (!j ? 0 : dp[j - 1].fi);
				chmin(dp[i], mpp(val, (!j ? 0 : dp[j - 1].se) + 1));
			}
		} return dp[n - 1];
	};

/*
	ve<ve<ll>> dp(n, ve<ll> (k + 1, inf));
	for (int i = 0; i < n; ++i) dp[i][1] = (r[i] - l[0]) * 1ll * (r[i] - l[0]);
	for (int j = 2; j <= k; ++j) {
		for (int i = 0; i < n; ++i) chmin(dp[i][j], dp[i][j - 1]);
		for (int i = 0; i < n; ++i) {
			for (int z = 0; z <= i; ++z) {
				ll val = (!z ? 0 : dp[z - 1][j - 1]);
				val += r[i] * r[i] + l[z] * l[z] - 2 * r[i] * l[z];
				val -= isec[z];
				chmin(dp[i][j], val);
			}
		}
	} return dp[n - 1][k];
*/

	ll le = 0, re = m * 1ll * m + 228, mid;
	ll ans = re;
	while (le <= re) {
		mid = le + re >> 1;
		ok(mid).se <= k ? ans = mid, re = mid - 1 : le = mid + 1;
	}
	auto f = ok(ans);
	return ok(ans).fi - ans * k;
}

#ifdef LOCAL
int main() {
    int n, m, k;
    assert(3 == scanf("%d %d %d", &n, &m, &k));
    std::vector<int> r(n), c(n);
    for (int i = 0; i < n; i++) {
        assert(2 == scanf("%d %d", &r[i], &c[i]));
    }
    long long ans = take_photos(n, m, k, r, c);
    
    
    printf("%lld\n", ans);
    return 0;
}
#endif

Compilation message (stderr)

aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:118:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  118 |   mid = le + re >> 1;
      |         ~~~^~~~
aliens.cpp:121:7: warning: variable 'f' set but not used [-Wunused-but-set-variable]
  121 |  auto f = ok(ans);
      |       ^

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 0 / 19
• Subtask 6: 0 / 40