Concept explainers
What is the base case of each of the recursive functions listed in Questions 12, 13, and 14?
Base case:
When the problem is solved without performing recursion is called as a base case.
- In base case, a problem gets solved during its first attempt without getting reiterated to obtain a solution or a problem’s solution could be obtained at the initial stage.
- When a recursive function solves and returns the result without performing any recursive operation is called as Base case of a problem.
Explanation of Solution
Given code:
12.
//include the necessary headers
#include <iostream>
using namespace std ;
//function prototype
int function(int);
//main method
int main()
{
//variable declaration and definition
int x = 10;
//function call to compute the sum
cout << function(x) << endl;
//return the value to be zero
return 0;
}
//function definition
int function(int num)
{
//validates the number is less than or equal to zero
if (num <= 0)
//return the value to be zero
return 0;
else
//call the function recursively
return function(num-1) + num;
}
Explanation:
The above highlighted code is the base case in the given problem, because the value of number is validated to be zero or less than zero, the function will immediately return zero after computing the result.
13.
//include the necessary headers
#include <iostream>
using namespace std;
//function prototype
void function(int);
//main method
int main()
{
//variable declaration
int x = 10 ;
//function call
function(x);
//return the value to be zero
return 0 ;
}
//method definition that displays the given character
void function(int num)
{
//validates the number is greater than zero
if (num > 0)
{
//loop that iterates for the number of times the number that is given
for (int x = 0 ; x < num; x++)
//display the character
cout << '*';
//new line
cout << endl ;
//function call that calls iteratively to display the character in the decremented order
function(num- 1);
}
}
Explanation:
The above highlighted code is the base case for the given code because the code gets executed only when the value of the number that is passed is greater than the zero or else the code will return the zero.
14.
//include the necessary headers
#include <iostream>
#include <string>
using namespace std;
//function protytype that performs the string operations
void function(string, int, int);
//main method
int main()
{
//varible declaration and definition
string mystr = "Hello";
//display the original string
cout << mystr << endl;
//function call that performs string reverse operation
function(mystr , 0 , mystr.size());
//return the value to be zero
return 0;
}
/* function definition that performs the reverse of the string */
void function(string str , int pos, int size)
{
//compares the position of the string with its size
if (pos < size)
{
//function call that performs the string reverse
function(str, pos+ 1, size);
//display the string in reverse order
cout << str[pos];
}
}
Explanation:
The above highlighted code is the base case for the given code, because the function will perform string operation only when the size and position gets validated and if the condition fails, the control will be returned to the called function.
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