1085. Perfect Sequence (25)

the problem is from PAT,which website is http://pat.zju.edu.cn/contests/pat-a-practise/1085

At first, i decide to write the code as follows:

/*
firstly: sort the array using the algorithm "sort"
secondly: traverse all the possible answer and find the most suitable one.
*/
#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

int main()
{
    long long int n,p;
    vector<long long int> v;
    while (cin>>n>>p)
    {
        long long int temp;
        while (n--)
        {
            cin>>temp;
            v.push_back(temp);
        }
        sort(v.begin(),v.end());
        long long int max = -1;
        for (int i = 0; i < v.size(); i++)
        {
            long long int count = 1;
            for (int j = i + 1; j < v.size(); j++)
            {
                if (v[i] * p >= v[j])
                    count += 1;
                else break;
            }
            if (count >= max)
            {
                max = count ;
            }
        }
        cout<<max<<endl;
    }
}

but the result of one example is time running out, so i evaluate the time complexity of the

code. i think the most time-consuming part is the double circulation,whose time complexity is

O(n*2). then i searched the web and found a better solution. its url is http://blog.csdn.net/nan327347465/article/details/39104721. he uses the binary search and successfully reduces the

tiem complexity down to O(n * log (n)).