Given three integers a, b and c, find the first occurrence of c in a/b after the decimal point. If it does not exists, print -1.
Input : a = 2 b = 3 c = 6 Output : 1 Explanation: 0.666666.. so 6 occurs at first place of a/b after decimal point Input : a = 1 b = 4 c = 5 Output : 2 Explanation: 1 / 4 = 0.25 which gives 5's position to be 2.
A naive approach will be to perform the division and keep the decimal part and iterate and check if the given number exists or not. This will not work well when divisions such as 2/3 is done as it yields 0.666666666, but in programming language it will round it off to 0.666667 so we get a 7 also which does not exists in the original a/b
An efficient approach will be the mathematical one, if we modulate every-time a by b and multiply it with 10 we get the integers after the decimal part every-time. The number of modulations required will be b as it will have a maximum of b integers after decimal point. So, we compare it with c and get our desired value if it is present.
Below is the implementation of the above approach :
- Find ΔX which is added to numerator and denominator both of fraction (a/b) to convert it to another fraction (c/d)
- Fraction module in Python
- Count of Numbers in Range where first digit is equal to last digit of the number
- Convert Binary fraction to Decimal
- Greedy Algorithm for Egyptian Fraction
- Reduce the fraction to its lowest form
- Find Recurring Sequence in a Fraction
- Find the remainder when First digit of a number is divided by its Last digit
- as_integer_ratio() in Python for reduced fraction of a given rational
- Maximum rational number (or fraction) from an array
- Expressing a fraction as a natural number under modulo 'm'
- Print first N terms of series (0.25, 0.5, 0.75, ...) in fraction representation
- Represent the fraction of two numbers in the string format
- Convert decimal fraction to binary number
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Improved By : vt_m