Given an integer N, the task is to print all proper fractions such that the denominator is less than or equal to N.
Proper Fractions: A fraction is said to be a proper fraction if the numerator is less than the denominator.
Examples:
Input: N = 3
Output: 1/2, 1/3, 2/3Input: N = 4
Output: 1/2, 1/3, 1/4, 2/3, 3/4
Approach:
Traverse all numerators over [1, N-1] and, for each of them, traverse over all denominators in the range [numerator+1, N] and check if the numerator and denominator are coprime or not. If found to be coprime, then print the fraction.
Below is the implementation of the above approach:
C++14
// C++ program to implement the// above approach#include <bits/stdc++.h> using namespace std;// Function to print all// proper fractionsvoid printFractions(int n){ for (int i = 1; i < n; i++) { for (int j = i + 1; j <= n; j++) { // If the numerator and the // denominator are coprime if (__gcd(i, j) == 1) { string a = to_string(i); string b = to_string(j); cout << a + "/" + b << ", "; } } }}// Driver Codeint main(){ int n = 3; printFractions(n); return 0;} |
Java
// Java program to implement the// above approachclass GFG{// Function to print all// proper fractionsstatic void printFractions(int n){ for(int i = 1; i < n; i++) { for(int j = i + 1; j <= n; j++) { // If the numerator and the // denominator are coprime if (__gcd(i, j) == 1) { String a = String.valueOf(i); String b = String.valueOf(j); System.out.print(a + "/" + b + ", "); } } }}static int __gcd(int a, int b) { return b == 0 ? a : __gcd(b, a % b); } // Driver codepublic static void main(String[] args){ int n = 3; printFractions(n);}}// This code is contributed by 29AjayKumar |
Python3
# Python3 program for the# above approach# Function to print# all proper functionsdef printfractions(n): for i in range(1, n): for j in range(i + 1, n + 1): # If the numerator and # denominator are coprime if __gcd(i, j) == 1: a = str(i) b = str(j) print(a + '/' + b, end = ", ") def __gcd(a, b): if b == 0: return a else: return __gcd(b, a % b)# Driver codeif __name__=='__main__': n = 3 printfractions(n)# This code is contributed by virusbuddah_ |
C#
// C# program to implement the// above approachusing System;class GFG{// Function to print all// proper fractionsstatic void printFractions(int n){ for(int i = 1; i < n; i++) { for(int j = i + 1; j <= n; j++) { // If the numerator and the // denominator are coprime if (__gcd(i, j) == 1) { string a = i.ToString(); string b = j.ToString(); Console.Write(a + "/" + b + ", "); } } }}static int __gcd(int a, int b) { return b == 0 ? a : __gcd(b, a % b); } // Driver codepublic static void Main(string[] args){ int n = 3; printFractions(n);}}// This code is contributed by rutvik_56 |
Javascript
<script>// Javascript program for the above approach // Function to print all proper functionsconst printFractions = (n) => { for (var i = 1; i < n; i++) { for (var j = i + 1; j <= n; j++) { // If the numerator and denominator are coprime if(__gcd(i, j) == 1){ let a = `${i}`; let b = `${j}`; document.write(`${a}/${b}, `) } } }}const __gcd = (a, b) => { if(b == 0){ return a; }else{ return __gcd(b, a % b); }}// Driver codelet n = 3;printFractions(n);// This article is contributed by _saurabh_jaiswal</script> |
Output:
1/2, 1/3, 2/3,
Time Complexity: O(N2 log N)
Auxiliary Space: O(1)
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