Given a string of binary characters, check if it is multiple of 3 or not.
Input : 1 0 1 0 Output : NO Explanation : (1 0 1 0) is 10 and hence not a multiple of 3 Input : 1 1 0 0 Output : YES Explanation : (1 1 0 0) is 12 and hence a multiple of 3
Approach : One simple method is to convert the binary number into its decimal representation and then check if it is a multiple of 3 or not. Now, when it comes to DFA (Deterministic Finite Automata), there is no concept of memory i.e. you cannot store the string when it is provided, so the above method would not be applicable. In simple terms, a DFA takes a string as input and process it. If it reaches final state, it is accepted, else rejected. As you cannot store the string, so input is taken character by character.
The DFA for given problem is :
As, when a number is divided by 3, there are only 3 possibilities. The remainder can be either 0, 1 or 2. Here, state 0 represents that the remainder when the number is divided by 3 is 0. State 1 represents that the remainder when the number is divided by 3 is 1 and similarly state 2 represents that the remainder when the number is divided by 3 is 2. So if a string reaches state 0 in the end, it is accepted otherwise rejected.
Below is the implementation of above approach :
- Check divisibility of binary string by 2^k
- Efficiently check whether n is a multiple of 4 or not
- Check if a number is multiple of 9 using bitwise operators
- Check whether a very large number of the given form is a multiple of 3.
- Write an Efficient Method to Check if a Number is Multiple of 3
- Check divisibility in a binary stream
- Check if binary representations of two numbers are anagram
- Check if binary representation of a number is palindrome
- Check if actual binary representation of a number is palindrome
- Check in binary array the number represented by a subarray is odd or even
- Check if binary representation of a given number and its complement are anagram
- Rotations of a Binary String with Odd Value
- Decimal representation of given binary string is divisible by 5 or not
- Efficient method for 2's complement of a binary string
- Decimal representation of given binary string is divisible by 10 or not
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