Submission #963024

#	Time	Username	Problem	Language	Result	Execution time	Memory
963024		penguin133	Aliens (IOI16_aliens)	C++17	25 / 100	13 ms	11868 KiB

aliens

#include <bits/stdc++.h>
using namespace std;
#include "aliens.h"
//#define int long long
typedef long long ll;
#define pi pair<ll, ll>
#define pii pair<int, pi>
#define fi first
#define se second
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#endif
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
 
deque<pii>dq;
 
ll f(pi x, ll y){
	return x.fi * y + x.se;
}
 
long double intersect(ll a, ll b, ll c, ll d){
	return (long double)(d-b)/(a-c);
}
 
void ins(ll m, ll c, ll in){
	
	
	while(dq.size() > 1){
		int s = dq.size();
		if(dq[s-1].fi == m){
			if(dq[s-1].se.fi < c)dq.pop_back();
			else break;
			continue;
		}
		if(intersect(dq[s-1].fi, dq[s-1].se.fi, m, c) <= intersect(dq[s-2].fi, dq[s-2].se.fi, m, c))dq.pop_back();
		else break;
	}
	dq.push_back({m, {c, in}});
	
}
 
pi query(ll x){
	while(dq.size() > 1){
		if(f({dq[0].fi, dq[0].se.fi}, x) < f({dq[1].fi, dq[1].se.fi}, x))dq.pop_front();
		else break;
	}
	return {f({dq[0].fi, dq[0].se.fi}, x), dq[0].se.se};
}
 
ll mn[1000005], val[100005], N;
pi dp[100005];
pi stuf[1000005];
 
pi cst(ll x){
	dq.clear();
	for(int i = 0; i < N; i++){
		ins(mn[i] * 2, -((i ? dp[i - 1].fi : 0) - 2 * mn[i] + mn[i] * mn[i] - (i ? max(0ll, stuf[i - 1].fi - mn[i] + 1) * (stuf[i - 1].fi - mn[i] + 1) : 0)), (i ? dp[i - 1].se : 0));
		pi res = query(stuf[i].fi);
		res.fi = -res.fi;
		res.fi += stuf[i].fi * stuf[i].fi + 2 * stuf[i].fi + 1;
		res.fi += x;
		res.se++;
		dp[i] = res;
	}
	return dp[N - 1];
}
 
long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
	N = n;
	for(int i = 0; i <= m; i++)mn[i] = 1e18;
	for(int i = 0; i < n; i++){
		if(r[i] > c[i])swap(r[i], c[i]);
		mn[c[i]] = min(mn[c[i]], (ll)r[i]);
		stuf[i] = {c[i], r[i]};
	}
	sort(stuf, stuf + n);
	for(int i = 0; i < n; i++)mn[i] = stuf[i].se, val[i] = 4e18;
	val[n] = 1e18;
	for(int i = n - 2; i >= 0; i--)mn[i] = min(mn[i], mn[i + 1]);
	//return 0;
	/*
	ll dp[n + 1][k + 1];
	for(int i = 0; i <= n; i++)dp[i][0] = 1e18;
 
	for(int j = 1; j <= k; j++){
		for(int i = 0; i < n; i++){
			ins(mn[i] * 2, -((i ? dp[i - 1][j - 1] : 0) - 2 * mn[i] + mn[i] * mn[i] - (i ? max(0ll, stuf[i - 1].fi - mn[i] + 1) * (stuf[i - 1].fi - mn[i] + 1) : 0)));
			dp[i][j] = -query(stuf[i].fi) + stuf[i].fi * stuf[i].fi + 2 * stuf[i].fi + 1;
			
			dp[i][j] = 1e18;
			for(int a = i; a >= 0; a--){
				dp[i][j] = min(dp[i][j], (a ? dp[a - 1][j - 1] - max(0ll, stuf[a - 1].fi - mn[a] + 1) * (stuf[a - 1].fi - mn[a] + 1) : 0) + (stuf[i].fi - mn[a] + 1) * (stuf[i].fi - mn[a] + 1));
			}
			
			//cout << dp[i][j] << ' ';
		}
		//cout << '\n';
		dq.clear();
	}
	*/
	ll lo = 0, hi = 1e13;
	ll ans = 5e18;
	while(lo <= hi){
		ll mid = (lo + hi) >> 1;
		pi res = cst(mid);
		if(res.se <= k)ans = min(ans, res.fi - mid * res.se);
		if(res.se <= n){
			val[res.se] = min(val[res.se], res.fi - mid * res.se);
		}
		if(res.se > k)lo = mid + 1;
		else hi = mid - 1;
	}
	if(val[k] < 4e18)return ans;
	int lft = k, rgt = k;
	while(lft >= 0 && val[lft] >= (int)4e18)lft--;
	while(rgt <= n && val[rgt] >= (int)4e18)rgt++;
	if(lft >= 0 && rgt <= n)ans = min(ans, val[lft] + (val[rgt] - val[lft]) * (k - lft) / (rgt - lft));
    return ans;
}

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