77 lines
1.6 KiB
C++
77 lines
1.6 KiB
C++
/*
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Find the number of continued fractions for the square roots of n <= 10000 which have an odd period
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*/
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#include <bits/stdc++.h>
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using namespace std;
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int gcd(int a, int b){
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if(b == 0){
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return a;
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}
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return gcd(b, a % b);
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}
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int gcd(int a, int b, int c){
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return gcd(a, gcd(b, c));
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}
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// Pseudocode found in the video on continued fraction of square roots of integers https://www.youtube.com/watch?v=GFJsU9QsytM
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bool check(int n){
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float x = sqrt((float)n);
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if(x != sqrt(n)){
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vector<int> cf;
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int a, b = 1, c = 1, d = 0;
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int bn, cn, dn, g;
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int b1, c1, d1;
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for(int i = 0; ; ++i){
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a = floor((floor(b * x) + d) / c);
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cf.push_back(a);
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bn = b*c;
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cn = b*b*n - d*d - a*a*c*c + 2*a*c*d;
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dn = a*c*c - c*d;
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g = gcd(bn, cn, dn);
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b = bn / g;
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c = cn / g;
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d = dn / g;
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if(i == 0){
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b1 = b;
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c1 = c;
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d1 = d;
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} else if(b1 == b && c1 == c && d1 == d){
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break;
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}
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}
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return cf.size() % 2 == 0;
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}
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return false;
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}
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int main(){
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cout << "Hello this is Patrick" << endl;
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auto start = chrono::high_resolution_clock::now();
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int result = 0;
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for(int n = 1; n <= 10000; ++n){
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result += check(n);
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}
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cout << result << endl;
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auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
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cout << (float)duration.count()/1000 << endl;
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return 0;
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}
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