Explain with example how the count variable is introduced in the program to find the number of steps required by a program to solve the problems

In this post we are discussing about Explain with example how the count variable is introduced in the program to find the number of steps required by a program to solve the problems

we introduce a new variable count to the program which is initialized to zero. We also introduce statements to increment count by an appropriate amount into the program. So when each time original program executes, the count also incremented by the step count.

Consider the algorithm sum( ). After the introduction of the count the program will be as follows.

float Sum (float a [J , int n)
{ 
       float s = 0.0;
       count++; // count is global
       for (int i=l; i<=n ; i++) {
            count++; // For 'for'
            s += a[i] ; 
            count++; // For assignment
       }
count++; // For last time of C for'
count++; // For the return
return s;
}

From the above we can estimate that invocation of sum( ) executes total number of 2n+3 steps.

how the count variable is used in the program:

1. float Sum(float a[], int n) is a function that takes an array a and an integer n as its parameters and returns a float. Its purpose is to calculate the sum of elements in the array.
2. Inside the function, a local variable s of type float is declared and initialized to 0.0. This initialization doesn’t count as a step, so it’s not incremented in count.
3. count++ is used immediately after the declaration of s. This is done to increment the count variable to account for the operation of initializing s. This is a common practice when analyzing the time complexity of algorithms to count basic operations.
4. Next, there is a for loop that iterates from i equals 1 to n, inclusive. a. count++ is incremented at the beginning of the for loop to count the operation of entering the loop. b. Inside the loop, there’s an addition operation s += a[i], which calculates the sum of the elements in the array. count++ is incremented to count this addition operation. c. After the addition operation, count++ is again incremented to count the assignment operation associated with updating the value of s.
5. After the for loop, there is one more count++ operation to account for the operation that occurs after the loop exits.
6. Finally, there is one more count++ operation to account for the return s statement at the end of the function.