Submission #224915

#	Time	Username	Problem	Language	Result	Execution time	Memory
224915		jhnah917	Aliens (IOI16_aliens)	C++14	4 / 100	7 ms	3072 KiB

aliens

#include "aliens.h"
#include <bits/stdc++.h>
#define x first
#define y second
#define all(v) v.begin(), v.end()
using namespace std;
 
typedef long long ll;
typedef pair<ll, ll> p;
 
int n, m, k;
ll dp[555][101010];
p a[101010];
vector<p> v;
 
struct CHT{
    struct Line{
        ll a, b, c;
        Line(ll a = 0, ll b = 0, ll c = 0) : a(a), b(b), c(c) {}
        ll f(ll x){ return a * x + b; }
    };
    Line v[101010]; int pv, top;
    ll f(int x, ll y){ return v[x].f(y); }
    void init(){ pv = top = 0; }
    int chk(const Line &a, const Line &b, const Line &c){
        return (double)(a.b - b.b) / (b.a - a.a) >= (double)(c.b - b.b) / (b.a - c.a);
    }
    void update(Line l){
        while(top >= 2 && chk(v[top-2], v[top-1], l)) top--;
        v[top++] = l;
    }
    p query(ll x){
        while(pv+1 < top && v[pv].f(x) >= v[pv+1].f(x)) pv++;
        return {v[pv].f(x), v[pv].c};
    }
} cht;
 
void init(int N, int M, int K, const vector<int> &R, const vector<int> &C){
    m = M, k = K; v.clear();
    for(int i=0; i<N; i++) v.emplace_back(min(R[i], C[i]), max(R[i], C[i]) + 1);
    sort(all(v), [](p a, p b){
        if(a.y != b.y) return a.y < b.y;
        return a.x > b.x;
    });
    n = 0;
    for(auto &i : v){
        while(n && a[n].x > i.x) n--;
        a[++n] = i;
    }
    for(int i=1; i<=n; i++) dp[1][i] = (a[i].y - a[1].x) * (a[i].y - a[1].x);
}
 
ll take_photos(int N, int M, int K, vector<int> R, vector<int> C){
    init(N, M, K, R, C);
    int q = min(n, k);
 
    for(int i=2; i<=q; i++){
        cht.init(); cht.update(CHT::Line(-2*a[1].x, a[1].x * a[1].x, 0));
        for(int j=1; j<=n; j++){
            //cout << i << " "  << j << " : " << cht.query(a[j].y).x << " " << a[j].y << "\n";
            dp[i][j] = cht.query(a[j].y).x + a[j].y * a[j].y;
            ll ta = a[j+1].x, tb = max(0LL, a[j].y - a[j+1].x);
            ll aa = -2*a[j+1].x;
            ll bb = dp[i-1][j] + ta*ta - tb*tb;
            cht.update(CHT::Line(aa, bb, i));
        }
    }
    // for(int i=1; i<=q; i++){
    //     for(int j=1; j<=n; j++) cout << dp[i][j] << " ";
    //     cout << "\n";
    // }
    return dp[q][n];
}
 
// g++ -O2 -std=c++11 -static -o main grader.cpp aliens.cpp aliens.h

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