Submission #1247903

#	Time	Username	Problem	Language	Result	Execution time	Memory
1247903		shidou26	Aliens (IOI16_aliens)	C++17	100 / 100	290 ms	11316 KiB

aliens

#ifndef KURUMI
    #include "aliens.h"
#endif

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

#define endl '\n'
#define sz(v) (int)v.size()
#define all(v) v.begin(), v.end()
#define filter(v) v.resize(unique(all(v)) - v.begin())
#define dbg(x) "[" #x " = " << (x) << "]"
 
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

template<typename T> bool maximize(T &a, T b) {
    if(a < b) {
        a = b;
        return true; 
    }else return false;
}
template<typename T> bool minimize(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }else return false;
}
template<typename T> T rnd(T a, T b) {
    return uniform_int_distribution<T>(a, b)(rng);
}

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<long long, int> li;

bool compare(li x, li y) {
    return (x.first == y.first ? x.second >= y.second : x.first < y.first);
}

struct Line {
    ll m, c;
    int cnt;

    li compute(ll x) {
        return {m * x + c, cnt};
    }

    friend bool bad(Line d1, Line d2, Line d3) {
        return (d1.c - d2.c) * (d3.m - d2.m) >= (d2.c - d3.c) * (d2.m - d1.m); 
    }
};

struct CHT {
    vector<Line> lines;

    void reload() {
        lines.clear();
    }

    void addLine(Line d) {
        while(sz(lines) >= 2 && bad(lines[sz(lines) - 2], lines.back(), d))
            lines.pop_back();
        lines.push_back(d);
    }

    li query(ll x) {
        int l = 0, r = sz(lines) - 1;
        while(l < r) {
            int mid = (l + r) >> 1;
            if(compare(lines[mid + 1].compute(x), lines[mid].compute(x))) l = mid + 1;
            else r = mid;
        }

        return lines[l].compute(x);

        // int best = 0;
        // for(int i = 0; i < sz(lines); i++) {
        //     if(compare(lines[i].compute(x), lines[best].compute(x)))
        //         best = i;
        // }

        // return lines[best].compute(x);
    }
};

const int N = 1e5 + 3;

int n, m, k;
int r[N], c[N];

pair<ll, ll> a[N];
li dp[N];
CHT evoker; 

ll square(ll x) {
    return x * x;
}

li f(ll lambda) {
    evoker.reload();

    dp[0] = {0, 0}; 
    for(int i = 1; i <= n; i++) {
        evoker.addLine({
            -2LL * a[i].first, 
            dp[i - 1].first + square(a[i].first) - (i > 1 ? square(max(0LL, a[i - 1].second - a[i].first)) : 0),
            dp[i - 1].second,
        });

        li previous = evoker.query(a[i].second);
        dp[i].first = square(a[i].second) + lambda + previous.first;
        dp[i].second = previous.second + 1;
    }

    return dp[n];
}

ll process() {
    vector<ii> segments;
    for(int i = 1; i <= n; i++) {
        segments.emplace_back(min(r[i], c[i]), max(r[i], c[i]));
    }

    sort(all(segments), [&](ii a, ii b){
        return (a.first == b.first ? a.second > b.second : a.first < b.first);
    });

    vector<ii> tmp;
    for(auto [l, r] : segments) {
        if(tmp.empty() || tmp.back().second < r) 
            tmp.emplace_back(l, r);
    }

    n = sz(tmp);
    for(int i = 1; i <= n; i++) {
        a[i] = tmp[i - 1]; 
        a[i].first--;
    }

    ll l = 1, r = 1LL * m * m, result = 0;
    k = min(k, n);

    while(l <= r) {
        ll mid = (l + r) >> 1;
        if(f(mid).second >= k) result = mid, l = mid + 1;
        else r = mid - 1;
    }

    return f(result).first - k * result;
}

ll take_photos(int _n, int _m, int _k, vector<int> _r, vector<int> _c) {
    n = _n; 
    m = _m;
    k = _k;

    for(int i = 1; i <= n; i++) {
        r[i] = _r[i - 1] + 1;
        c[i] = _c[i - 1] + 1;
    }

    return process();
}

#ifdef KURUMI
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    #define task "Deeto"
    if(fopen(task".inp", "r")) {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    
    int n, m, k; 
    vector<int> r, c;

    cin >> n >> m >> k;
    r.resize(n); c.resize(n);

    for(int i = 0; i < n; i++) cin >> r[i];
    for(int i = 0; i < n; i++) cin >> c[i];

    cout << take_photos(n, m, k, r, c) << endl;

    cerr << "Saa, watashtachi no deito hajimemashou" << endl;
    cerr << "Atarashii kiseki wo koko kara hajimeru shining place nee mou ichido kimi to..." << endl;

    return 0;
}
#endif

/*
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*/

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