Submission #1301450

#	Time	Username	Problem	Language	Result	Execution time	Memory
1301450		ProtonDecay314	Aliens (IOI16_aliens)	C++20	41 / 100	2095 ms	3684 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<bool> vb;

#define fi first
#define se second

/*
Suppose the penalty for using another picture is +y
*/
pll solve_lambda_brute(const vpll& pts, ll y) {
    ll np = pts.size();
    
    // note: stores NEGATIVE area, num pictures
    // then, the DP just gets the maximum state
    vpll dp(np, {0ll, 0ll});

    for(ll i = 0ll; i < np; i++) {
        ll cl = pts[i].fi, cr = pts[i].se;

        dp[i] = {-(cr - pts[0ll].fi + 1ll) * (cr - pts[0ll].fi + 1ll) - y, 1ll};
        for(ll j = 1ll; j <= i; j++) {
            ll overlap = max(pts[j - 1ll].se - pts[j].fi + 1ll, 0ll);
            pll cand = {dp[j - 1ll].fi + overlap * overlap -(cr - pts[j].fi + 1ll) * (cr - pts[j].fi + 1ll) - y, dp[j - 1ll].se + 1ll};
            if(cand > dp[i]) dp[i] = cand;
        }
    }

    return dp[np - 1ll];
}

ll take_photos(int i_n, int i_m, int i_k, vi r, vi c) {
    ll n = i_n, m = i_m, k = i_k;

    // first, we preprocess. remove all redundant points

    vpll pts;

    for(ll i = 0ll; i < n; i++) {
        if(r[i] > c[i]) swap(r[i], c[i]);

        pts.push_back({r[i], c[i]});
    }

    sort(pts.begin(), pts.end(), [](pll p1, pll p2){return p1.fi < p2.fi || (p1.fi == p2.fi && p1.se > p2.se);});

    ll max_r = -1ll;

    vpll filt_pts;

    for(ll i = 0ll; i < n; i++) {
        ll cl = pts[i].fi, cr = pts[i].se;

        if(cr > max_r) {
            filt_pts.push_back(pts[i]);
            // cerr << cl << " " << cr << endl;
            max_r = cr;
        }
    }

    // Performing lagrangian relaxation
    ll lo = 0ll, hi = 1e12;

    while(hi - lo > 1ll) {
        ll mid = (lo + hi) >> 1ll;

        pll cpair = solve_lambda_brute(filt_pts, mid);

        ll c_val = cpair.fi, c_k = cpair.se;

        if(c_k >= k) lo = mid;
        else hi = mid;
    }

    return -(solve_lambda_brute(filt_pts, lo).fi + k * lo);
}

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: 0 / 19
• Subtask 6: 0 / 40