Given a fraction in form of a/b where a & b are positive integers. Find ?X such that when it is added to numerator as well as denominator of given fraction it will result into a new Ir-reducible fraction c/d.
Examples:
Input : a = 4, b = 10, c = 1, d = 2 Output : ?X = 2 Explanation : (a + ?X)/(b + ?X) = (4 + 2) / (10 + 2) = 6/12 = 1/2 = c/d Input : a = 4, b = 10, c = 2, d = 5 Output : ?X = 0 Explanation : (a + ?X) / (b + ?X) = (4) / (10) = 2 / 5 = c/d
To solve this type of problem rather than implementing just a programming approach we have to do a little of mathematics. mathematics just necessary is as:
As per question we have to find ?X such that: => (a + ?X) / (b + ?X) = c / d => ad + d?X = bc + c?X => d?X - c?X = bc - ad => ?X (d - c) = bc -ad => ?X = (bc - ad) / (d - c)
So, in a way to finding ?X we have to only calculate 
.
C++
// C++ Program to find deltaX #include <bits/stdc++.h> using namespace std; // function to find delta X int findDelta(int a, int b, int c, int d) { return (b * c - a * d) / (d - c); } // driver program int main() { int a = 3, b = 9, c = 3, d = 5; // u0394X is code for delta sign cout << "\u0394X = " << findDelta(a, b, c, d); return 0; } |
Java
// Java Program to // find deltaX import java.io.*; class GFG { // function to find delta X static int findDelta(int a, int b, int c, int d) { return (b * c - a * d) / (d - c); } // Driver Code public static void main(String args[]) { int a = 3, b = 9, c = 3, d = 5; // u0394X is code // for delta sign System.out.print("\u0394X = " + findDelta(a, b, c, d)); } } // This code is contributed // by Manish Shaw(manishshaw1) |
Python3
# Python Program to find deltaX # !/usr/bin/python # coding=utf-8 # function to find delta X def findDelta(a, b, c, d) : return int((b * c - a * d) / (d - c)); # Driver Code a = 3; b = 9; c = 3; d = 5; # u0394X is code # for delta sign print ("X = {}" . format(findDelta(a, b, c, d))); # This code is contributed by # Manish Shaw(manishshaw1) |
C#
// C# Program to // find deltaX using System; class GFG { // function to find delta X static int findDelta(int a, int b, int c, int d) { return (b * c - a * d) / (d - c); } // Driver Code static void Main() { int a = 3, b = 9, c = 3, d = 5; // u0394X is code // for delta sign Console.Write("\u0394X = " + findDelta(a, b, c, d)); } } // This code is contributed // by Manish Shaw(manishshaw1) |
PHP
<?php // PHP Program to find deltaX // function to find delta X function findDelta($a, $b, $c, $d) { return ($b * $c - $a * $d) / ($d - $c); } // Driver Code $a = 3; $b = 9; $c = 3; $d = 5; // u0394X is code for delta sign echo "?X = ".findDelta($a, $b, $c, $d); // This code is contributed by // Manish Shaw(manishshaw1) ?> |
Javascript
<script> // JavaScript Program to // find deltaX // function to find delta X function findDelta(a, b, c, d) { return (b * c - a * d) / (d - c); } // Driver Code let a = 3, b = 9, c = 3, d = 5; // u0394X is code // for delta sign document.write("\u0394X = " + findDelta(a, b, c, d)); // This code is contributed by splevel62. </script> |
Output:
?X = 6
Time Complexity: O(1)
Auxiliary Space: O(1)
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