Submission #579387

#	Time	Username	Problem	Language	Result	Execution time	Memory
579387		perchuts	Aliens (IOI16_aliens)	C++17	100 / 100	152 ms	6508 KiB

aliens

#include <bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define sz(x) (int) x.size()
#define endl '\n'
#define pb push_back
#define _ ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);
#define f first
#define s second
using namespace std;
#include "aliens.h"
using ll = long long;
using ull = unsigned long long;
using ii = pair<int,int>;
using iii = tuple<int,int,int>;

const int inf = 2e9+1;
const int mod = 1e9+7;
const int maxn = 1e5+100;

template<typename X, typename Y> bool ckmin(X& x, const Y& y) { return (y < x) ? (x=y,1):0; }
template<typename X, typename Y> bool ckmax(X& x, const Y& y) { return (x < y) ? (x=y,1):0; }

vector<pair<ll,ll>>pareto;

ll eval(pair<ll,ll>x,ll y){return x.f*y + x.s;}
ll sq(ll x){return x*x;}

bool cross(pair<ll,ll>back,pair<ll,ll>mid,pair<ll,ll>front){
    return (back.s-mid.s)*(front.f-mid.f)>(back.f-mid.f)*(front.s-mid.s);
}

pair<ll,ll> solve(ll lambda){
    //CHT
    deque<pair<pair<ll,ll>,ll>>lines={{{-2*pareto[0].f,sq(pareto[0].f)},0}};
    int n = sz(pareto);
    for(int i=0;i<n;++i){
        auto [x,y] = pareto[i];++y;
        while(sz(lines)>=2&&eval(lines[0].f,y)>eval(lines[1].f,y))lines.pop_front();
        ll dpi = eval(lines[0].f,y) + sq(y) + lambda, qnt = lines[0].s+1;
        if(i==n-1)return {dpi,qnt};
        else{
            dpi += sq(pareto[i+1].f) - sq(max(0ll,y-pareto[i+1].f));
            pair<ll,ll>cur = {-2*pareto[i+1].f,dpi};
            while(sz(lines)>=2&& cross(lines[sz(lines)-2].f,lines.back().f,cur))lines.pop_back();
            lines.pb({cur,qnt});
        }
    }
    return {0,0};
}

ll take_photos(int n, int m, int k, vector<int> r1, vector<int> c) {
    vector<ii>v(n);
    for(int i=0;i<n;++i){  
        if(r1[i]<=c[i])v[i] = {r1[i],c[i]};
        else v[i] = {c[i],r1[i]};
    }
    sort(all(v));
    for(int i=0;i<n;++i){
        if(pareto.empty()||pareto.back().second<v[i].s){
            if(!pareto.empty()&&pareto.back().first==v[i].f)pareto.pop_back();
            pareto.push_back(v[i]);
        }
    }
    //Lagrange opt.
    ll l = 0, r = 1e12;//max delta = 1e12 porque m<=1e6, logo lambda <= 1e12
    while(l<r){
        ll md = (l+r)/2;
        pair<ll,ll>cur = solve(md);
        if(cur.s>k)l = md+1ll;
        else r = md;
    }   
    pair<ll,ll>res = solve(r);
    ll ans = res.f - r*k;
    if(r){
        pair<ll,ll>res2 = solve(r-1);
        if(res2.s<=k)ckmin(ans,res2.f-k*(r-1));
    }
    return ans;
}

// 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;
// }

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