How many elementary operations are used in the following algorithm?
Step 1 Set S = a, k = 0 , and t = a
Step 2 while k < n
(a) Replace t with t+d
(b) Replace S with S+t
(c) Replace k with k+1
endwhile
Step 2 Print S
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My answer was: 4*n+1
I don't know if it is right :(
if k=>n, there is only one operation, the test.
If k<n, then each time the test occurs, there are four operations(test, replace, replace, replace), and one final operation the test.
4n+1 is correct.
Step 1 Set a=1, b=1, c=2,and k=0
Step 2 while k < n
(a) Replace c with a+b
(b) Replace a with b
(c) Replace k with k+1
endwhile
Step 3 Print b
To determine the number of elementary operations used in the given algorithm, we need to consider each step and determine how many operations are performed in each iteration of the loop.
Step 1: Setting variables (1 operation)
- Set S = a (1 operation)
- Set k = 0 (1 operation)
- Set t = a (1 operation)
Step 2: Loop (3 operations per iteration)
- Check if k < n (1 operation)
- If the condition is true, then perform the following operations in each iteration:
(a) Replace t with t + d (1 operation)
(b) Replace S with S + t (1 operation)
(c) Replace k with k + 1 (1 operation)
So, in each iteration of the loop, there are a total of 3 operations.
The loop iterates n times, as indicated by the condition "k < n", and each iteration has 3 operations.
Additionally, we have the operation of printing S (1 operation).
Therefore, the total number of elementary operations involved in the algorithm can be calculated as:
3 * n (operations in the loop) + 1 (operation of printing S)
Hence, the correct answer would be 3n + 1, which is the same as 4n + 1 as you have mentioned.