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P-sequences

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  • ammar_kothari
    5 years ago+ 0 comments

    Hello,

    I don't know how to speed up the runtime of my solution. I think I am missing a way to enumerate all the possible subsequences. If you have any ideas on how I can reduce the runtime, I would really appreciate it.

    One idea I had is to create a map of the parameters (length of sequence, max value, and starting number) that can be used to look up values instead of running through the recursion each time. This seems a little too complicated, but I am currently trying it out.

    Quick Summary of Code: Use recursion to determine the number of subsequences that are valid given a starting number for the sequence. For each recursion, a shorter sequence with a different inint

    #include <bits/stdc++.h>
    
    using namespace std;
    
    int pSequences2(int n, int p, int prev_num) {
        int count = 0;
        if (n == 1) {
            // if its the last number
            // all subsequent numbers are those that are less than p/prev
            count += (p/prev_num);
        }
        else {
            for (int i_p=1; i_p<=p; i_p++) {
                if (prev_num*i_p<=p) {
                    count += pSequences2(n-1, p, i_p);
                }
                else {
                    break;
                }
            }
        }
        return count;
    }
    
    
    int pSequences(int n, int p) {
        int count = 0;
        // generate all possible first values of sequence
        count = pSequences2(n, p, 0);
        return count;
    }
    
    int main()
    {
        ofstream fout(getenv("OUTPUT_PATH"));
        vector< vector<int> > seqs;
    
        int n;
        cin >> n;
        cin.ignore(numeric_limits<streamsize>::max(), '\n');
    
        int p;
        cin >> p;
        cin.ignore(numeric_limits<streamsize>::max(), '\n');
        
        int result = pSequences(n, p);
        
        fout << result << "\n";
    
        fout.close();
    
        return 0;
    }
    
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