The loop invariant for the factorial calculation function is `f = (j - 1)!`.
Understand the Problem
The question is discussing a loop invariant used in the context of calculating the factorial of a number. It states that the invariant holds that f equals (j - 1)!, which indicates that at each step of the loop, the factorial of j-1 is maintained as a correct value in f. To understand this further, we would analyze how the loop invariant helps in proving the correctness of the factorial function.
Answer
The correct loop invariant for the factorial function is `f = j!`.
The loop invariant for the factorial calculation function is not f = (j - 1)! but rather that the partial product f = j! after each iteration where j is the loop counter. This invariant states the factorial is correctly computed up to the current iteration value.
Answer for screen readers
The loop invariant for the factorial calculation function is not f = (j - 1)! but rather that the partial product f = j! after each iteration where j is the loop counter. This invariant states the factorial is correctly computed up to the current iteration value.
More Information
A loop invariant is what remains true throughout a loop's execution. In this case, the product f reflects the correct factorial value up to j, not (j - 1)!.
Tips
Common mistakes include incorrectly identifying the invariant as the starting or ending condition instead of what is maintained throughout the loop.
Sources
- Loop Invariant Condition with Examples - GeeksforGeeks - geeksforgeeks.org
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