Submission #821427

#	Time	Username	Problem	Language	Result	Execution time	Memory
821427		bane	Aliens (IOI16_aliens)	C++17	4 / 100	1 ms	1876 KiB

aliens

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <array>
#include <iomanip>
using namespace std;
 
//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
 
/*
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template <class T>
using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
*/
 
 
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i < (n); ++i)
#define rep1n(i, n) for (int i = 1; i <= (n); ++i)
#define repr(i, n) for (int i = (n) - 1; i >= 0; --i)
 
 
#define fr first
#define sc second
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define endl '\n'
 
 
using lint = long long;
using ulint = unsigned long long;
using ld = long double;
using str = string;
using pi = pair<int, int>;
 
 
using vi = vector<int>;
using vl = vector<lint>;
using vpi = vector<pair<int, int>>;
using vvi = vector<vi>;
 
const int mod = (int)1e9 + 7;

vector<pair<lint,lint>> unq;
vl W(200000);

struct CHT{
    struct Line{
        lint m,y;
        Line(lint a, lint b): m(a), y(b){}

        lint eval(lint x){
            return x * m + y;
        }

        lint intercept(Line& b){
            //m2x + c2 = m1x + c1
            //x * (m2 - m1) = c1 - c2
            //x = (c1 - c2) / (m2 - m1)
            return (y - b.y + (b.m - m - 1)) / (b.m - m);
        }
    };
    deque<pair<Line,pair<lint,lint>>>dq;

    void insert(lint m, lint y, int c){
        Line New_Line(m,y);
        while(dq.size() > 1){
            if (dq[dq.size() - 2].fr.intercept(New_Line) <= dq.back().sc.fr){
                dq.pop_back();
            }else{
                break;
            }
        }

        if (dq.empty()){
            dq.push_back({New_Line, {-(lint)1e14,c}});
        }else{
            dq.push_back({New_Line, {New_Line.intercept(dq.back().fr),c}});
        }
    }

    pair<lint,lint>query(lint x){
        while(dq.size() > 1 && dq[1].sc.fr <= x)dq.pop_front();
        return {dq[0].fr.eval(x), dq[0].sc.sc + 1};
    }
};

pair<lint,lint> Lagrangian_Relaxation(lint lambda){
    pair<lint,lint> dp[unq.size()];
    CHT cht;
    rep(i,(int)unq.size()){
        if(i){
            cht.insert(-2 * unq[i].fr, unq[i].fr * unq[i].fr - W[i-1] * W[i - 1] - 2 * unq[i].fr + dp[i - 1].fr + lambda, dp[i-1].sc);
            dp[i] = cht.query(unq[i].sc);
            dp[i].fr += 1 + 2 * unq[i].sc + unq[i].sc * unq[i].sc;
        }else{
            dp[i].fr = lambda + (unq[i].second - unq[i].first + 1) * (unq[i].second - unq[i].first + 1);
            dp[i].sc = 1;
        }
        
    }
    return dp[unq.size() - 1];
}

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
    
    vector<pair<lint,lint>> Segments;
    rep(i,n){
        Segments.push_back(mp(min(r[i], c[i]), max(r[i], c[i])));
    }
    sort(all(Segments), [&](auto x, auto y){
        if (x.fr < y.fr)return true;
        else if (x.fr == y.fr)return x.sc > y.sc;
        else return false;
    });

    int most_right = -1;
    unq.pb(Segments[0]);
    for (int i = 1; i < n; i++) {
        if (!(unq.back().fr <= Segments[i].first && Segments[i].second <= unq.back().sc)) {
            unq.pb(Segments[i]);
        }
    }
    rep1(i,(int)unq.size()){
        W[i - 1] = 0;
        if (unq[i - 1].sc - unq[i].fr >= 0)W[i-1] =unq[i - 1].sc - unq[i].fr + 1; 
    }
    W[unq.size() - 1] = 0;
    lint L = 0, R = (lint)1e12, a = 0;
    while(L <= R){
        lint mid = (L+R) / 2;
        if (Lagrangian_Relaxation(mid).sc <= k){
            a = mid;
            R = mid - 1;
        }else{
            L = mid + 1;
        }
    }
    auto ans =  Lagrangian_Relaxation(a);
    return ans.fr - (a) * ans.sc;
}

Compilation message (stderr)

aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:137:9: warning: unused variable 'most_right' [-Wunused-variable]
  137 |     int most_right = -1;
      |         ^~~~~~~~~~

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