Question

Loop invariant allows us to understand and prove the correctness of an algorithm. Which of the following options is NOT to be proven, when we prove the correctness of any algorithm using loop invariant?

• A. Sequence
• B. Initialization
• C. Maintenance
• D. Termination

Hint:

A loop invariant is essential in proving the correctness of algorithms, especially when it comes to showing that the loop works as expected throughout.

Answer 1

The Correct Option is C

Step 1: Understanding Loop Invariants. 
A loop invariant is a condition that holds true before and after every iteration of the loop. It is used to prove the correctness of the algorithm. 

- **Sequence:** Proves that the steps or operations of the algorithm follow a logical order. 

- **Initialization:** Proves that the algorithm correctly sets up the initial values. 

- **Maintenance:** Proves that the invariant condition remains true during each iteration of the loop. 

- **Termination:** Proves that the loop will terminate, and the final condition holds after the loop ends.

Step 2: Conclusion. 
The **Maintenance** condition is used to prove the consistency of the algorithm's steps, but it is not a condition that needs to be proven when using a loop invariant. Thus, the correct answer is (3) **Maintenance**.