Submission #982055

#	Time	Username	Problem	Language	Result	Execution time	Memory
982055		vjudge1	Aliens (IOI16_aliens)	C++14	100 / 100	777 ms	20404 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;

int n;

vector <pair <__int128,__int128> > v;

struct Line{
    mutable __int128 m,c,p;
    bool operator<(const Line&o) const {
        return m<o.m;
    };
    bool operator<(__int128 val) const {
        return p<val;
    };
};

struct LineContainer:multiset <Line,less<> > {
    const __int128 inf=1e36;
    __int128 div(__int128 a,__int128 b){
        return a/b-((a^b)<0&&a%b);
    }
    bool intrs(iterator a,iterator b){
        if (b==end()) return a->p=inf,0;
        if (a->m==b->m) a->p=(a->c>b->c?inf:-inf);
        else a->p=div(b->c-a->c,a->m-b->m);
        return a->p>=b->p;
    }
    void addline(__int128 m,__int128 c){
        auto z=insert({-m,-c,0});
        auto a=z++;
        auto b=a;
        while (intrs(b,z)) z=erase(z);
        if (a!=begin()&&intrs(--a,b)) intrs(a,b=erase(b));
        while ((b=a)!=begin()&&(--a)->p>=b->p) intrs(a,erase(b));
    }
    __int128 query(__int128 val){
        auto l=*lower_bound(val);
        return -l.m*val-l.c;
    }
};

const __int128 C = 2e5;
__int128 dp[100050];

pair<long long, long long> calc(__int128 add) {
    LineContainer lc;
    dp[0] = 0;
    lc.addline(C * (-2) * v[1].first, C * (v[1].first - 1) * (v[1].first - 1) + C * add + 1);
    for (int i = 1; i <= n; i++) {
        dp[i] = lc.query(v[i].second) + C * v[i].second * (v[i].second + 2);
        if (i < n) {
            __int128 tp = max((__int128)0, v[i].second - v[i + 1].first + 1);
            lc.addline(C * -2 * v[i + 1].first, dp[i] - C * tp * tp + C * (v[i + 1].first - 1) * (v[i + 1].first - 1) + C * add + 1);
        }
    }
    return {dp[n] / C - (dp[n] % C) * add, dp[n] % C};
}


long long take_photos(int num_photos, int num_segments, int target_photos, vector<int> row, vector<int> col) {
    int til[num_segments];
    for (int i = 0; i < num_segments; i++)
        til[i] = i - 1;
    
    for (int i = 0; i < num_photos; i++) {
        int rr = row[i], cc = col[i];
        if (rr > cc) swap(rr, cc);
        til[rr] = max(til[rr], cc);
    }

    int mx = -1;
    for (int i = 0; i < num_segments; i++) {
        if (til[i] > mx && i <= til[i]) {
            v.push_back({i, til[i]});
            mx = til[i];
        }
    }

    n = v.size();
    v.insert(v.begin(), {0, 0});

    long long L = 0, R = 1e12;
    while (L < R) {
        long long mid = (L + R) / 2;
        if (calc(mid).second > target_photos)
            L = mid + 1;
        else
            R = mid;
    }

    pair<long long, long long> cur = calc(L);
    if (cur.second == target_photos) return cur.first;
    pair<long long, long long> nxt = calc(L - 1);
    if (nxt.second == cur.second) return cur.first;
    return cur.first + (target_photos - cur.second) * (nxt.first - cur.first) / (nxt.second - cur.second);
}

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