Given two positive integers ‘a’ and ‘b’ that represent coefficients in equation ax + by = m. Find the minimum value of m that satisfies the equation for any positive integer values of x and y. And after this minimum value, the equation is satisfied by all (greater) values of m. If no such minimum value exists, return “-1”.
Input: a = 4, b = 7 Output: 18 Explanation: 18 is the smallest value that can can be satisfied by equation 4x + 7y. 4*1 + 7*2 = 18 And after 18 all values are satisifed 4*3 + 7*1 = 19 4*5 + 7*0 = 20 ... and so on.
This is a variation of Frobenius coin problem. In Frobenius coin problem, we need to find the largest number that can not be represented using two coins. The largest amount for coins with denominations as ‘a’ and ‘b’ is a*b – (a+b). So the smallest number such that it can be represented using two coins and all numbers after it can also be represented is, a*b – (a+b) + 1.
One important case is when GCD of ‘a’ and ‘b’ is not 1. For example if ‘a’ = 4 and ‘b’ = 6, then all values that can be represented using two coins are even (or all values of m that can stratify the equation) are even. So all values that are NOT multiple of 2, cannot satisfy the equation. In this case there is no minimum value after which all values satisfy the equation.
Below is the implementation of above idea :
This article is contributed by Rishabh Jain. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks 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.
GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details
- Program to find whether a no is power of two
- Program to find parity
- Minimum number of jumps to reach end
- Find minimum number to be divided to make a number a perfect square
- Find whether a given number is a power of 4 or not
- Find Union and Intersection of two unsorted arrays
- To find sum of two numbers without using any operator
- Find day of the week for a given date
- Given a number, find the next smallest palindrome
- Find the element that appears once
- Find the largest multiple of 2, 3 and 5
- Program to find amount of water in a given glass
- Find the maximum distance covered using n bikes
- Find if two rectangles overlap
- Find the smallest number whose digits multiply to a given number n