Table of Contents
- 1 How do you prove an algorithm is correct by induction?
- 2 What do you mean by correctness of an algorithm?
- 3 Which of the following is incorrect about an algorithm?
- 4 Which of these is not a good characteristic of good algorithm?
- 5 How to design a completely new algorithm?
- 6 How do you prove a rule is valid?
How do you prove an algorithm is correct by induction?
The proof consists of three steps: first prove that insert is correct, then prove that isort’ is correct, and finally prove that isort is correct. Each step relies on the result from the previous step. The first two steps require proofs by induction (because the functions in question are recursive).
What do you mean by correctness of an algorithm?
In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness, which refers to the input-output behavior of the algorithm (i.e., for each input it produces an output satisfying the specification).
Which of the following is not the characteristics of an algorithm?
Answer: The algorithm doesn’t stop in a finite number of times. The algorithm doesn’t display the output. The algorithm obtains the input but doesn’t apply it .
How do you identify a loop invariant?
A loop invariant is a condition [among program variables] that is necessarily true immediately before and immediately after each iteration of a loop….The loop invariant must be true:
- before the loop starts.
- before each iteration of the loop.
- after the loop terminates.
Which of the following is incorrect about an algorithm?
Which of the following is incorrect? -As pseudo codes. Explanation: An algorithm becomes a program when it is written in the form of a programming language. Any program is an algorithm but the reverse is not true.
Which of these is not a good characteristic of good algorithm?
Presence of ambiguity. The algorithm does not produce a valid output. The algorithm has a logical problem. The algorithm is not optimized to work efficiently.
How do you prove an algorithm in C++?
1 Answer. In practice, to prove an algorithm you should search a good invariant property for each loop. For example, if you compute in a given order the sum of integers with a for loop (indexed by ), the invariant could be : “At the end of an iteration, the variable contains the sum of the first values”.
Why do we use literals to prove an algorithm’s correctness?
Example with literals: Because the method we are using to prove an algorithm’s correctness is math based, or rather function based, the more the solution is similar to a real mathematic function, the easier the proof. Why is this you may ask?
How to design a completely new algorithm?
When designing a completely new algorithm, a very thorough analysis of its correctness and efficiency is needed. The last thing you would want is your solution not being adequate for a problem it was designed to solve in the first place.
How do you prove a rule is valid?
Induction Base: Proving the rule is valid for an initial value, or rather a starting point – this is often proven by solving the Induction Hypothesis F (n) for n=1 or whatever initial value is appropriate Induction Step: Proving that if we know that F (n) is true, we can step one step forward and assume F (n+1) is correct