Given a positive floating point number n, the task is to find the smallest integer k, such that when we multiply k with n, we get a natural number.
Examples:
Input : 30.25 Output : 4 30.25 * 4 = 321, there is no number less than 4 which can convert 30.25 into natural number. Input : 5.5 Output : 2 5.5 * 2 = 11, there is no number less than 2 which can convert 5.5 into natural number. Input : 5.33 Output : 100
The idea is to convert given floating point number into a fraction (not necessarily in reduced form) and find the GCD of numerator and denominator. For example, if input floating point number is 30.25, we convert into fraction as 3025/100. This can be easily done by finding the position of dot.
Finally to get the answer, we divide the denominator of the converted fraction by GCD of denominator and numerator. For example, GCD of 3025 and 100 is 25. We divide 100 by 25 and get the answer as 4.
Below is implementation of this approach:
C++
// C++ program to find the smallest number to multiply // to convert a floating point number into natural number. #include<bits/stdc++.h> using namespace std; // Finding GCD of two number int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a%b); } // Returns smallest integer k such that k * str becomes // natural. str is an input floating point number int findnum(string &str) { // Find size of string representing a // floating point number. int n = str.length(); // Below is used to find denominator in // fraction form. int count_after_dot = 0; // Used to find value of count_after_dot bool dot_seen = false; // To find numerator in fraction form of // given number. For example, for 30.25, // numerator would be 3025. int num = 0; for (int i = 0; i < n; i++) { if (str[i] != '.') { num = num*10 + (str[i] - '0'); if (dot_seen == true) count_after_dot++; } else dot_seen = true; } // If there was no dot, then number // is already a natural. if (dot_seen == false) return 1; // Find denominator in fraction form. For example, // for 30.25, denominator is 100 int dem = (int)pow(10, count_after_dot); // Result is denominator divided by // GCD-of-numerator-and-denominator. For example, for // 30.25, result is 100 / GCD(3025,100) = 100/25 = 4 return (dem / gcd(num, dem)); } // Driven Program int main() { string str = "5.125"; cout << findnum(str) << endl; return 0; } |
Java
// Java program to find the smallest number to multiply// to convert a floating point number into natural number.class GFG { // Finding GCD of two number static int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } // Returns smallest integer k such that k * str becomes // natural. str is an input floating point number static int findnum(String str) { // Find size of string representing a // floating point number. int n = str.length(); // Below is used to find denominator in // fraction form. int count_after_dot = 0; // Used to find value of count_after_dot boolean dot_seen = false; // To find numerator in fraction form of // given number. For example, for 30.25, // numerator would be 3025. int num = 0; for (int i = 0; i < n; i++) { if (str.charAt(i) != '.') { num = num * 10 + (str.charAt(i) - '0'); if (dot_seen == true) count_after_dot++; } else dot_seen = true; } // If there was no dot, then number // is already a natural. if (dot_seen == false) return 1; // Find denominator in fraction form. For example, // for 30.25, denominator is 100 int dem = (int)Math.pow(10, count_after_dot); // Result is denominator divided by // GCD-of-numerator-and-denominator. For example, for // 30.25, result is 100 / GCD(3025, 100) = 100/25 = 4 return (dem / gcd(num, dem)); } // Driver code public static void main(String[] args) { String str = "5.125"; System.out.print(findnum(str)); }}// This code is contributed by Anant Agarwal. |
Python3
# Python program to find the smallest number to multiply# to convert a floating point number into natural number.# Finding GCD of two numberimport mathdef gcd(a, b): if (b == 0): return a return gcd(b, a%b) # Returns smallest integer k such that k * str becomes# natural. str is an input floating point numberdef findnum(str): # Find size of string representing a # floating point number. n = len(str) # Below is used to find denominator in # fraction form. count_after_dot = 0 # Used to find value of count_after_dot dot_seen = 0 # To find numerator in fraction form of # given number. For example, for 30.25, # numerator would be 3025. num = 0 for i in range(n): if (str[i] != '.'): num = num*10 + int(str[i]) if (dot_seen == 1): count_after_dot += 1 else: dot_seen = 1 # If there was no dot, then number # is already a natural. if (dot_seen == 0): return 1 # Find denominator in fraction form. For example, # for 30.25, denominator is 100 dem = int(math.pow(10, count_after_dot)) # Result is denominator divided by # GCD-of-numerator-and-denominator. For example, for # 30.25, result is 100 / GCD(3025,100) = 100/25 = 4 return (dem // gcd(num, dem)) # Driver Programstr = "5.125"print (findnum(str))# Contributed by: Afzal Ansari |
C#
// C# program to find the smallest// number to multiply to convert a // floating point number into// natural number.using System;class GFG { // Finding GCD of two numberstatic int gcd(int a, int b){ if (b == 0) return a; return gcd(b, a % b);}// Returns smallest integer k// such that k * str becomes// natural. str is an input // floating point numberstatic int findnum(String str) { // Find size of string representing // a floating point number. int n = str.Length; // Below is used to find denominator // in fraction form. int count_after_dot = 0; // Used to find value of count_after_dot bool dot_seen = false; // To find numerator in fraction form of // given number. For example, for 30.25, // numerator would be 3025. int num = 0; for (int i = 0; i < n; i++) { if (str[i] != '.') { num = num * 10 + (str[i] - '0'); if (dot_seen == true) count_after_dot++; } else dot_seen = true; } // If there was no dot, then // number is already a natural. if (dot_seen == false) return 1; // Find denominator in fraction form. // For example, for 30.25, // denominator is 100 int dem = (int)Math.Pow(10, count_after_dot); // Result is denominator divided by // GCD-of-numerator-and-denominator. // For example, for 30.25, result is // 100 / GCD(3025, 100) = 100/25 = 4 return (dem / gcd(num, dem));}// Driver codepublic static void Main() { String str = "5.125"; Console.Write(findnum(str));}}// This code is contributed by Nitin Mittal. |
PHP
<?php// PHP program to find the smallest// number to multiply to convert a // floating point number into // natural number.// Finding GCD of two numberfunction gcd($a, $b){ if ($b == 0) return $a; return gcd($b, $a % $b);}// Returns smallest integer k // such that k * str becomes// natural. str is an input // floating point numberfunction findnum( $str){ // Find size of string // representing a floating // point number. $n = strlen($str); // Below is used to // find denominator in // fraction form. $count_after_dot = 0; // Used to find value // of count_after_dot $dot_seen = false; // To find numerator in // fraction form of // given number. For // example, for 30.25, // numerator would be 3025. $num = 0; for($i = 0; $i < $n; $i++) { if ($str[$i] != '.') { $num = $num*10 + ($str[$i] - '0'); if ($dot_seen == true) $count_after_dot++; } else $dot_seen = true; } // If there was no dot, // then number is // already a natural. if ($dot_seen == false) return 1; // Find denominator in // fraction form. For // example, for 30.25, // denominator is 100 $dem = pow(10, $count_after_dot); // Result is denominator // divided by GCD-of- // numerator-and-denominator. // For example, for 30.25, // result is 100 / GCD(3025,100) // = 100/25 = 4 return ($dem / gcd($num, $dem));}// Driver Code{ $str = "5.125"; echo findnum($str) ; return 0;}// This code is contributed by nitin mittal?> |
Javascript
<script>// javascript program to find the smallest number to multiply// to convert a floating point number into natural number. // Finding GCD of two number function gcd(a , b) { if (b == 0) return a; return gcd(b, a % b); } // Returns smallest integer k such that k * str becomes // natural. str is an input floating point number function findnum( str) { // Find size of string representing a // floating point number. var n = str.length; // Below is used to find denominator in // fraction form. var count_after_dot = 0; // Used to find value of count_after_dot let dot_seen = false; // To find numerator in fraction form of // given number. For example, for 30.25, // numerator would be 3025. var num = 0; for (i = 0; i < n; i++) { if (str.charAt(i) != '.') { num = num * 10 + (str.charAt(i) - '0'); if (dot_seen == true) count_after_dot++; } else dot_seen = true; } // If there was no dot, then number // is already a natural. if (dot_seen == false) return 1; // Find denominator in fraction form. For example, // for 30.25, denominator is 100 var dem = parseInt( Math.pow(10, count_after_dot)); // Result is denominator divided by // GCD-of-numerator-and-denominator. For example, for // 30.25, result is 100 / GCD(3025, 100) = 100/25 = 4 return (dem / gcd(num, dem)); } // Driver code let str = "5.125"; document.write(findnum(str));// This code is contributed by todaysgaurav</script> |
Output:
8
Time Complexity: O(n)
Auxiliary Space: O(log(min(a,b)))
This article is contributed by Aarti_Rathi and Anuj Chauhan(anuj0503). If you like neveropen and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the neveropen main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
