Submission #394305

#	Time	Username	Problem	Language	Result	Execution time	Memory
394305		Drew_	Aliens (IOI16_aliens)	C++14	100 / 100	780 ms	9544 KiB

aliens

#include "aliens.h"
#include <vector>
#include <iostream>
#include <algorithm>
#include <cassert>
using namespace std;

#define ll long long
#define pb push_back
#define ii pair<int, int>
#define pl pair<ll, ll>
#define f1 first
#define s2 second

const int MAX = 1e5 + 7;

struct Line
{
	ll m, c, ctr;
	Line() : m(0), c(0), ctr(0) {}
	Line(ll m, ll c, ll ctr) : m(m), c(c), ctr(ctr) {}
	double inter(const Line &other) { return (double) (c - other.c) / (other.m - m); }
};

struct convex_hull
{
	int sz = 0;
	Line ar[MAX];

	void clear() { sz = 0; }
	bool cmp(Line a, Line b, Line c) { return a.inter(b) < b.inter(c); }
	void addLine(ll m, ll c, ll ctr)
	{
		//cerr << "L: " << m << " " << c << '\n';
		Line L(m, c, ctr);
		while (sz >= 2 && !cmp(ar[sz-2], ar[sz-1], L))
			sz--;
		ar[sz++] = L;
	}

	pl query(ll x)
	{
		int l = 0, r = sz-1;
		while (l < r)
		{
			int mid = (l + r) >> 1;
			if (ar[mid].inter(ar[mid+1]) >= x) r = mid;
			else l = mid + 1;
		}
		return {ar[l].ctr, ar[l].m * x + ar[l].c};
	}
} cht;

//cost for interval [i, j], assuming interval [0, i-1] have been fulfilled
/*
inline ll getCost(int i, int j)
{
	ll res = 1LL * (ivl[j].s2 - ivl[i].f1 + 1) * (ivl[j].s2 - ivl[i].f1 + 1);
	if (i)
	{
		if (ivl[i-1].s2 >= ivl[i].f1)
			res -= 1LL * (ivl[i-1].s2 - ivl[i].f1 + 1) * (ivl[i-1].s2 - ivl[i].f1 + 1);
	}
	return res;
}
*/
vector<pl> ivl;

pl dp[MAX];
pl solve(ll slope)
{
	cht.clear();
	cht.addLine(-2 * ivl[0].f1, ivl[0].f1 * ivl[0].f1, 0);
	for (int i = 0; i < ivl.size(); ++i)
	{
		pl tmp = cht.query(ivl[i].s2);
		dp[i] = {tmp.f1 + 1, tmp.s2 + ivl[i].s2 * ivl[i].s2 - slope};

		if (i+1 < ivl.size())
		{
			ll m = -2 * ivl[i+1].f1;
			ll c = (ivl[i+1].f1 * ivl[i+1].f1) + dp[i].s2;
			if (ivl[i+1].f1 < ivl[i].s2)
				c -= (ivl[i].s2 - ivl[i+1].f1) * (ivl[i].s2 - ivl[i+1].f1);
			
			ll ctr = dp[i].f1;
			cht.addLine(m, c, ctr);
		}

	}
	return dp[ivl.size() - 1];
}

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
	vector<ii> v(n);
	for (int i = 0; i < n; ++i)
		v[i] = {min(r[i], c[i]), max(r[i], c[i])};
	sort(v.begin(), v.end(), [](const ii &x, const ii &y){
		return x.f1 < y.f1 || (x.f1 == y.f1 && x.s2 > y.s2);
	});

	ivl.pb(v[0]);
	for (int i = 1; i < n; ++i)
	{
		if (ivl.back().f1 <= v[i].f1 && v[i].s2 <= ivl.back().s2)
			continue;
		ivl.pb(v[i]);
	}
	for (auto &x : ivl)
		x.s2++;

	ll L = -(ll)1e12 - 7, R = 1;
	k = min(k, (int)ivl.size());
	while (L < R)
	{
		ll mid = (L + R + 1) >> 1;
		pl res = solve(mid);

		if (res.f1 > k) R = mid - 1;
		else L = mid;
	}
	pl res = solve(L);
	return L * k + res.s2;
}

/*
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;
}
*/

Compilation message (stderr)

aliens.cpp: In function 'std::pair<long long int, long long int> solve(long long int)':
aliens.cpp:74:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   74 |  for (int i = 0; i < ivl.size(); ++i)
      |                  ~~^~~~~~~~~~~~
aliens.cpp:79:11: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::pair<long long int, long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   79 |   if (i+1 < ivl.size())
      |       ~~~~^~~~~~~~~~~~

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