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84 lines
1.8 KiB
84 lines
1.8 KiB
/*
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Calculates the optimal fourier transform(s) for a number
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Also outputs distribution of least-fouerist-base
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Inspired by http://www.smbc-comics.com/?id=2874
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A very naive implementation :)
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*/
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#include <map>
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#include <vector>
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#include <iomanip>
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#include <iostream>
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#include <algorithm>
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#include <iterator>
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using namespace std;
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int length(int number, int base){
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int length = 1;
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int acc = base;
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while(number >= acc){
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length++;
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acc *= base;
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}
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return length;
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}
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int fours(int number, int base){
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int count = (number % base) == 4;
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while(number > base){
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number /= base;
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if(number % base == 4) count++;
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}
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return count;
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}
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// Performs a fourier transform to make the input fourier
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// Done with a linear search, there are probably betters ways
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// There is not always a unique base in which the input is fouriest, so we output a vector
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vector<int> fourier(int input){
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int base = 1;
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int current_best = 0;
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vector<int> bests{};
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do {
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base++;
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int current = fours(input, base);
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if(current >= current_best){
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if(current > current_best){
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bests.clear();
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current_best = current;
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}
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bests.push_back(base);
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}
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} while(length(input, base) > 1);
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return bests;
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}
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// The input number is shown, then the fouriness, then the bases in which the input is fouriest.
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int main(){
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map<int, int> distribution;
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cout << "Number, \t Fouriness, \t Possible bases" << endl;
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for(int i = 1; i < 1000; i++){
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auto bases = fourier(i);
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auto nfours = fours(i, bases.back());
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distribution[bases.front()]++;
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cout << setw(5) << i << ", \t" << setw(5) << nfours << ", \t[ ";
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copy(begin(bases), end(bases), ostream_iterator<int>(cout, " "));
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cout << "]" << endl;
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}
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cout << "\nDistribution of least bases" << endl;
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for(auto x : distribution){
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cout << x.first << ", \t" << x.second << endl;
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}
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}
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