Submission #254362

#	Time	Username	Problem	Language	Result	Execution time	Memory
254362		mode149256	Aliens (IOI16_aliens)	C++14	100 / 100	217 ms	7156 KiB

aliens

/*input

*/
#include <bits/stdc++.h>
#ifndef GEDUTIS
#include "aliens.h"
#endif

using namespace std;

namespace my_template {
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef pair<ld, ld> pd;

typedef vector<int> vi;
typedef vector<vi> vii;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<vl> vll;
typedef vector<pi> vpi;
typedef vector<vpi> vpii;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
typedef vector<pd> vpd;
typedef vector<bool> vb;
typedef vector<vb> vbb;
typedef std::string str;
typedef std::vector<str> vs;

#define x first
#define y second
#define debug(...) cout<<"["<<#__VA_ARGS__<<": "<<__VA_ARGS__<<"]\n"

const ld PI = 3.14159265358979323846264338327950288419716939937510582097494L;

template<typename T>
pair<T, T> operator+(const pair<T, T> &a, const pair<T, T> &b) { return pair<T, T>(a.x + b.x, a.y + b.y); }
template<typename T>
pair<T, T> operator-(const pair<T, T> &a, const pair<T, T> &b) { return pair<T, T>(a.x - b.x, a.y - b.y); }
template<typename T>
T operator*(const pair<T, T> &a, const pair<T, T> &b) { return (a.x * b.x + a.y * b.y); }
template<typename T>
T operator^(const pair<T, T> &a, const pair<T, T> &b) { return (a.x * b.y - a.y * b.x); }

template<typename T>
void print(vector<T> vec, string name = "") {
	cout << name;
	for (auto u : vec)
		cout << u << ' ';
	cout << '\n';
}
}
using namespace my_template;

const int MOD = 1000000007;
const ll INF = std::numeric_limits<ll>::max();
const int MX = 100101;

int N, M, K;
vpl sk;

ll eval(pl line, ll at) {
	return at * line.x + line.y;
}

bool bad(pl x, pl y, pl z) {
	return (x.y - y.y) * (z.x - x.x) >= (x.y - z.y) * (y.x - x.x);
}

void daryk(vl &dp, vi &cnt, ll lambda) {
	dp.resize(N + 1, 0);
	cnt.resize(N + 1, 0);

	deque<pair<pl, int>> hull;

	hull.push_back({{ -2 * sk[1].y, (sk[1].y - 1) * (sk[1].y - 1) - 1}, 0});

	for (int i = 1; i <= N; ++i)
	{
		auto curr = hull.front(); hull.pop_front();

		while (hull.size() and eval(curr.x, sk[i].x) >= eval(hull.front().x, sk[i].x)) {
			curr = hull.front();
			hull.pop_front();
		}

		hull.push_front(curr);

		dp[i] = eval(curr.x, sk[i].x) + (sk[i].x + 1) * (sk[i].x + 1) + lambda;
		cnt[i] = cnt[curr.y] + 1;

		// printf("curr = %d %d, lambda = %lld, i = %d, dp = %lld, cnt = %d\n", curr.x.x, curr.x.y, lambda, i, dp[i], cnt[i]);
		if (i == N) break;
		ll h = max(sk[i].x - sk[i + 1].y + 1, 0ll);
		pl newLine = { -2 * sk[i + 1].y, dp[i] - h*h + (sk[i + 1].y - 1)*(sk[i + 1].y - 1) - 1};

		auto last = hull.back();
		hull.pop_back();
		while (hull.size() >= 1 and bad(hull.back().x, last.x, newLine)) {
			last = hull.back();
			hull.pop_back();
		}

		hull.push_back(last);
		hull.push_back({newLine, i});
	}

	dp[N] -= cnt[N] * lambda;
}

// y < x
void sanitize(vi &r, vi &c) {
	vector<pi> temp;
	for (int i = 0; i < N; ++i)
	{
		if (r[i] > c[i]) swap(r[i], c[i]);

		temp.emplace_back(c[i], r[i]);
	}
	sort(temp.begin(), temp.end(), [](const pi & a, const pi & b) {
		return a.x < b.x or (a.x == b.x and a.y > b.y);
	});

	for (int i = 0; i < N; ++i)
	{
		while (sk.size() and sk.back().y >= temp[i].y) sk.pop_back();

		sk.push_back(temp[i]);
	}
	N = (int)sk.size();
	sk.insert(sk.begin(), { -1, -1});
	// for (auto u : sk) printf("%d %d\n", u.x, u.y);
}

ll take_photos(int n, int m, int k, vi r, vi c) {
	N = n; M = m; K = k;
	sanitize(r, c);
	ll l = 0;
	ll h = 1e14;
	vl dp;
	vi cnt;

	while (l < h) {
		ll mi = (l + h + 1) / 2;
		daryk(dp, cnt, mi);
		if (cnt[N] >= K)
			l = mi;
		else
			h = mi - 1;
	}

	daryk(dp, cnt, l);

	pl V1 = {dp[N], cnt[N]};

	l++;
	daryk(dp, cnt, l);

	pl V2 = {dp[N], cnt[N]};

	if (V2.y == K or V1.y == V2.y) return V2.x;

	return V1.x + (K - V1.y) * (V2.x - V1.x) / (V2.y - V1.y);
}

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