Submission #1275548

#	Time	Username	Problem	Language	Result	Execution time	Memory
1275548		afonsopereira	Aliens (IOI16_aliens)	C++20	4 / 100	11 ms	424 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>

using namespace std;
using ll=long long;

#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())

ll pow2(ll v){return v*v;}

struct Line {
    ll a, b;
    ll eval(ll x){return a*x+b;}
};

struct CHT {
    deque<Line> deq;
    
    void add(Line line) {
        if (!deq.empty() && deq.front().a==line.a) {
            if (deq.front().b < line.b) return;
            else deq.pop_front();
        }
        while (sz(deq)>=2) {
            if ((__int128_t)(deq[0].a-line.a)*(__int128_t)(deq[1].b-deq[0].b)<=
                (__int128_t)(deq[0].b-line.b)*(__int128_t)(deq[1].a-deq[0].a)) {
                deq.pop_front();
            } else break;
        }
        deq.push_front(line);
    }
    
    ll query(ll x) {
        while (sz(deq)>=2){
            if (deq[sz(deq)-1].eval(x)>=deq[sz(deq)-2].eval(x)){
                deq.pop_back();
            } else break;
        }
        return deq.back().eval(x);
    }
};

long long take_photos(int n, int m, int K, vector<int> r, vector<int> c) {
    vector<pair<int, int>> pts(n);
    for(int i=0;i<n;i++){
        if (r[i]>c[i]) swap(r[i],c[i]);
        pts[i]=make_pair(r[i],c[i]);
    }
    sort(all(pts));
    
    // remove dominated points
    {
        vector<pair<int,int>> pts2;
        for(int i=0;i<n;i++){
            if (i!=n-1 && pts[i].first==pts[i+1].first) continue;
            pts2.push_back(pts[i]);
        }
        pts=pts2;
        n=sz(pts);
    }
    
    {
        vector<pair<int,int>> pts2;
        int mx_c = -1;
        for(int i=0;i<n;i++){
            if (pts[i].second<=mx_c) continue;
            pts2.push_back(pts[i]);
            mx_c=max(mx_c, pts[i].second);
        }
        pts=pts2;
        n=sz(pts);
    }
    
    auto relax=[&](ll lambda) -> pair<ll,ll> {
        vector<ll> dp(n+1,1LL<<60);
        vector<int> cnt(n+1, 1<<30);
        dp[0]=0;
        cnt[0]=0;
        CHT cht;
        
        for(int i=0;i<=n;i++){
            if(i!=0) {
                ll x=pts[i-1].second+1;
                ll mn=cht.query(x);
                ll res=mn+x*x;
                dp[i]=res;
                // track count
                for(int j=0;j<i;j++){
                    ll diff=0;
                    if(j>0 && pts[j-1].second>=pts[j].first){
                        diff=pow2(pts[j-1].second-pts[j].first+1);
                    }
                    ll cost = dp[j] + pow2(pts[i-1].second-pts[j].first+1) - diff;
                    if(cost + lambda * (cnt[j]+1) < dp[i] + lambda * cnt[i] + 1e-9){
                        dp[i] = cost;
                        cnt[i] = cnt[j] + 1;
                    }
                }
            }
            if(i==n) continue;
            
            ll a = -2*(pts[i].first);
            ll diff=0;
            if(i>0 && pts[i-1].second>=pts[i].first){
                diff=pow2(pts[i-1].second-pts[i].first+1);
            }
            ll b=dp[i]+pow2(pts[i].first)-diff;
            cht.add({a, b});
        }
        return {dp[n] - lambda * K, cnt[n]};
    };
    
    ll lo=0, hi=1LL*m*m;
    
    while(hi-lo>1) {
        ll mid=(lo+hi)/2;
        auto [val, cnt] = relax(mid);
        if(cnt <= K) hi = mid;
        else lo = mid;
    }
    
    ll ans = 1LL<<60;
    for(ll lambda=max(0LL,lo-2); lambda<=hi+2; lambda++){
        auto [val, cnt] = relax(lambda);
        if(cnt <= K){
            ans = min(ans, val + lambda * K);
        }
    }
    
    return ans;
}

Compilation message (stderr)

aliens.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~
aliens_c.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~

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