Question

In: Computer Science

Answer the following Discrete Structures Suppose string s = (s1 s2 ..sn). Give a recursive definition...

Answer the following Discrete Structures

Suppose string s = (s₁ s₂ ..s_n). Give a recursive definition of the function numOnes(n), which counts the number of 1s in bit-string of length n, Make sure to define the function for the base case, numOnes(0).

Expert Solution

Explanation :

String :

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation).
A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding.
String may also denote more general arrays or other sequence (or list) data types and structures.
Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements.
When a string appears literally in source code, it is known as a string literal or an anonymous string.
In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set called an alphabet.

In the light of the above discussions, the solution to the given set of question is as follows:

The Solution :

INPUT :The given bit string s = ( s1 s2 ... sn )

OUTPUT : The number of 1s in the string s counted by the recursive function numOnes(n).

Note : The function should define the base case numOnes( 0 ) .

Definition of the recursive function numOnes(n) :

numOnes ( n )

{

int number = 0; // define variable to store the number of 1s, initialised to 0

int i = 0 ; // define loop variable

int length = n; // define variable length to denote the length of the string passed as argument in the function call

string s = ( s1 s2 ... sn ) ; // the given string of bits consisting a series of 0 or 1, may be blank string as well

for ( i = 0, i < length, i++ )

{

if s [ i ] = =1,

{

number = number + 1;

} // end if

return number;

} // end for loop

} // end function

Note : For the base case numOnes ( 0 ), the function returns number = 0 as it was initialised to 0.

This concludes the answer to all parts of the question along with the necessary explanations.

Please do not forget to like the answer if it helps you. Thank you.

venereology answered 1 year ago

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