Submission #1297823

#	Time	Username	Problem	Language	Result	Execution time	Memory
1297823		hiepsimauhong	Aliens (IOI16_aliens)	C++20	100 / 100	113 ms	11224 KiB

aliens

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

using namespace std;

//#define int long long
using Maxint = long long;

#define FOR(I, L, R) for(Maxint I(L) ; I <= (Maxint)R ; ++I)
#define FOD(I, R, L) for(Maxint I(R) ; I >= (Maxint)L ; --I)
#define FOA(I, A) for(auto &I : A)

#define print(A,L,R) FOR(OK, L, R){if(abs(A[OK]) >= oo / 10)cout<<"- ";else cout<<A[OK]<<' ';}cout<<'\n';
#define prints(A) FOA(OK, A){cout<<OK<<' ';}cout << '\n';
#define printz(A,L,R) FOR(OK, 0, L){FOR(KO, 0, R){if(abs(A[OK][KO]) <= oo / 10)cout<<A[OK][KO]<<' ';else cout << "- ";} cout << '\n';}cout << '\n';

#define fs first
#define sd second
#define ii pair<Maxint, Maxint>
#define iii pair<Maxint, ii>
#define all(A) A.begin(), A.end()
#define quickly ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define FILE "BUFF"

const Maxint N = 1e5 + 5;
const Maxint oo = 1e18;

Maxint n, m, k;
ii ary[N], rl[N], dp[N];
Maxint cost[N];

void PreWork(){
        sort(ary + 1, ary + 1 + n, [&](ii &u, ii &v){
                if(u.sd == v.sd){
                        return u.fs > v.fs;
                }
                return u.sd < v.sd;
        });

        stack<Maxint> st;
        FOR(i, 1, n){
                while(!st.empty() && ary[st.top()].fs >= ary[i].fs){
                        st.pop();
                }
                st.push(i);
        }

        n = 0;
        while(!st.empty()){
                rl[++n] = ary[st.top()];
                st.pop();
        }
        reverse(rl + 1, rl + 1 + n);

        FOR(i, 2, n){
                Maxint x = rl[i].fs;
                Maxint y = rl[i - 1].sd;

                if(x <= y){
                        cost[i] = (y - x + 1) * (y - x + 1);
                }
        }
}

struct line{
        Maxint a, b, c;

        line(){a = b = 0;}
        line(Maxint _a, Maxint _b, Maxint _c){a = _a, b = _b, c = _c;}

        Maxint eval(Maxint x) const { return a * x + b; }

        long double intersectX(const line &other) const{
                return (long double)(other.b - b) / (long double)(a - other.a);
        }
};

ii compare(ii u, ii v){
        if(u.fs == v.fs){
                return {u.fs, max(u.sd, v.sd)};
        }
        return min(u, v);
}

struct ConvexHullTrick{
        vector<line> hull;
        Maxint ptr = 0;

        bool bad(const line &L2, const line &L1, const line &L3){
                long double x1 = L2.intersectX(L1);
                long double x2 = L1.intersectX(L3);
                return x1 >= x2;
        }

        void add_line(line L){
                while(hull.size() >= 2){
                        if(bad(hull[hull.size() - 2], hull[hull.size() - 1], L)){
                                hull.pop_back();
                                if(ptr > (Maxint)hull.size() - 1) ptr = max<Maxint>(0, (Maxint)hull.size() - 1);
                        }
                        else{
                                break;
                        }
                }
                hull.push_back(L);
        }

        ii get(Maxint x){
                if(hull.empty()) return {oo, 0};

                while(ptr + 1 < (Maxint)hull.size() && hull[ptr].eval(x) >= hull[ptr + 1].eval(x)) ++ptr;
                return ii(hull[ptr].eval(x), hull[ptr].c);
        }

        void clear(){
                hull.clear();
                ptr = 0;
        }
} cht;

ii calc(Maxint lambda){
        cht.clear();
        FOR(i, 1, n){
                dp[i] = {oo, 0};
        }

        FOR(i, 1, n){
                Maxint x = rl[i].fs;
                Maxint y = rl[i].sd + 1;
                cht.add_line(line(-2 * x, x * x + dp[i - 1].fs - cost[i], dp[i - 1].sd));

                ii val = cht.get(y);

                dp[i] = ii(val.fs + y * y + lambda, val.sd + 1);
        }

        return dp[n];
}

Maxint Alien(){
        Maxint l = 0, r = 3 * oo;
        Maxint res = 0;

        while(l <= r){
                Maxint mid = (l + r) >> 1;

                if(calc(mid).sd >= k){
                        l = mid + 1;
                        res = mid;
                }
                else{
                        r = mid - 1;
                }
        }

        return calc(res).fs - k * res;
}

Maxint take_photos(int _n, int _m, int _k, vector<int> r, vector<int> c){
        n = _n;
        m = _m;
        k = _k;

        FOR(i, 1, n){
                ary[i].fs = r[i - 1];
                ary[i].sd = c[i - 1];

                if(ary[i].fs > ary[i].sd) swap(ary[i].fs, ary[i].sd);
        }

        PreWork();
        return Alien();
}

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