Submission #171563

#	Time	Username	Problem	Language	Result	Execution time	Memory
171563		arnold518	Aliens (IOI16_aliens)	C++14	100 / 100	213 ms	11112 KiB

aliens

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

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int MAXN = 1e5;

struct Point { ll y, x; };

struct CHT
{
    struct Line { ll a, b, k; };
    double cross(const Line &p, const Line &q) { return (double)(q.b-p.b)/(p.a-q.a); }
    vector<Line> S;

    void update(Line p)
    {
        while(S.size()>1 && cross(S[S.size()-1], p)<=cross(S[S.size()-1], S[S.size()-2])) S.pop_back();
        S.push_back(p);
    }

    int pos=0;
    pll query(ll x)
    {
        if(S.size()<=pos) pos=S.size()-1;
        else while(pos+1<S.size() && cross(S[pos], S[pos+1])<=x) pos++;
        return {S[pos].a*x+S[pos].b, S[pos].k};
    }

    void init()
    {
        S.clear();
        pos=0;
    }
} cht;

int N, M, K;
Point B[MAXN+10], A[MAXN+10];
pll dp[MAXN+10];

ll solve(ll lambda)
{
    int i, j;
    cht.init();
    for(i=1; i<=N; i++)
    {
        dp[i]={2*(A[i].y-A[1].x+1)*(A[i].y-A[1].x+1)+lambda, 1};
        if(i!=1)
        {
            pll val=cht.query(A[i].y);
            dp[i]=min(dp[i], {val.first+2*A[i].y*A[i].y+lambda, val.second+1});
        }
        cht.update({-2*2*(A[i+1].x-1), 2*(A[i+1].x-1)*(A[i+1].x-1)-2*max(0ll, A[i].y-A[i+1].x+1)*max(0ll, A[i].y-A[i+1].x+1)+dp[i].first, dp[i].second});
    }
    return dp[N].second;
}

ll take_photos(int _N, int _M, int _K, vector<int> R, vector<int> C)
{
    int i, j, k;
    N=_N; M=_M; K=_K;

    for(i=1; i<=N; i++) B[i]={min(R[i-1], C[i-1]), max(R[i-1], C[i-1])};
    sort(B+1, B+N+1, [&](const Point &p, const Point &q)
         {
             if(p.y==q.y) return p.x>q.x;
             return p.y<q.y;
         });

    int cnt=1;
    ll val=-1;
    for(i=1; i<=N; i++) if(val<B[i].x) A[cnt++]=B[i], val=B[i].x;
    N=cnt-1;
    for(i=1; i<=N; i++) if(A[i].x>A[i].y) swap(A[i].x, A[i].y);

    ll lo=-1, hi=1e15;
    while(lo+1<hi)
    {
        ll mid=lo+hi>>1;
        if(solve(mid*2+1)>K) lo=mid;
        else hi=mid;
    }
    solve(hi*2);
    ll ans=dp[N].first/2-K*hi;

    return ans;
}

Compilation message (stderr)

aliens.cpp: In member function 'pll CHT::query(ll)':
aliens.cpp:28:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         if(S.size()<=pos) pos=S.size()-1;
            ~~~~~~~~^~~~~
aliens.cpp:29:25: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         else while(pos+1<S.size() && cross(S[pos], S[pos+1])<=x) pos++;
                    ~~~~~^~~~~~~~~
aliens.cpp: In function 'll solve(ll)':
aliens.cpp:46:12: warning: unused variable 'j' [-Wunused-variable]
     int i, j;
            ^
aliens.cpp: In function 'll take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:82:18: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
         ll mid=lo+hi>>1;
                ~~^~~
aliens.cpp:63:12: warning: unused variable 'j' [-Wunused-variable]
     int i, j, k;
            ^
aliens.cpp:63:15: warning: unused variable 'k' [-Wunused-variable]
     int i, j, k;
               ^

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