InsertionSort Algorithm Quiz

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Questions and Answers

The InsertionSort algorithm starts with all cards in the left hand and moves them to the right hand.

False (B)

The ______ ensures that the cards in the left hand are always kept in sorted order during InsertionSort.

invariant

What is the primary logic behind the InsertionSort algorithm?

The InsertionSort algorithm works by iteratively taking a card from the right hand and placing it in its correct position within the sorted sequence of cards in the left hand.

Which of these statements accurately describes the InsertionSort algorithm?

An algorithm that iteratively inserts elements from an unsorted array into their correct position in a sorted array. (D) Signup and view all the answers

Match the following terms with their descriptions:

Invariant = A condition that remains true throughout the execution of an algorithm. Incremental Algorithm = An algorithm that processes the input one element at a time. InsertionSort = An algorithm that sorts an array by iteratively inserting elements into their correct positions in a sorted array. Signup and view all the answers

The InsertionSort algorithm is a recursive algorithm.

False (B) Signup and view all the answers

What is the ultimate goal of the InsertionSort algorithm?

The ultimate goal of the InsertionSort algorithm is to arrange all the cards in the left hand in sorted order. Signup and view all the answers

The InsertionSort algorithm is an example of an ______ algorithm.

incremental Signup and view all the answers

The algorithm `InsertionSort(int[ ] A)` starts the `for` loop from `j =` ______ to `A.length`.

2 Signup and view all the answers

What is the purpose of the inner `while` loop in the `InsertionSort` algorithm?

To find the correct position for the <code>key</code> element in the sorted subarray (D) Signup and view all the answers

The `InsertionSort` algorithm is an in-place sorting algorithm, meaning it sorts the array without using additional memory.

True (A) Signup and view all the answers

What is the name of the variable used to store the element to be inserted in its correct position in the sorted subarray?

key Signup and view all the answers

Match the following code snippets with their corresponding functions in the `InsertionSort` algorithm:

<code>key = A[j]</code> = Storing the element to be inserted <code>i = j - 1</code> = Initializing the index to iterate through the sorted subarray <code>A[i + 1] = A[i]</code> = Shifting elements to the right <code>A[i + 1] = key</code> = Inserting the <code>key</code> element into its correct position Signup and view all the answers

The loop invariant for the InsertionSort algorithm is established ______ of every iteration of the `for` loop.

at the beginning Signup and view all the answers

What is the purpose of the loop invariant in proving the correctness of the `InsertionSort` algorithm?

It shows that the subarray <code>A[1..j-1]</code> is always sorted, and that the element <code>A[j]</code> will be placed in its correct position in the sorted subarray at the end of each iteration. Signup and view all the answers

The `InsertionSort` algorithm has a time complexity of O(n^2) in the worst case.

True (A) Signup and view all the answers

The loop invariant for the Factorial function is: f = (j - ______)!

1 Signup and view all the answers

The loop invariant for the factorial calculation function is `f = (j - 1)!`.

f = 1 Signup and view all the answers

What is the violated loop condition for the factorial calculation function?

j > k Signup and view all the answers

The Factorial function calculates the factorial of a given number using a loop.

True (A) Signup and view all the answers

What is the value of `j` when the loop condition is violated?

j = k + 1 (C) Signup and view all the answers

Which of the following expressions correctly represents the value of f after the first iteration of the loop in the Factorial function?

f = 2 (A) Signup and view all the answers

What is the purpose of the if statement `if k < 0 then error(...)` in the Factorial function?

To handle negative input values. Factorial is not defined for negative numbers. Signup and view all the answers

Inserting the violated loop condition `j = k + 1` into the loop invariant `f = (j - 1)!` results in `f = (k + 1 - 1)!` which simplifies to `f = k!`.

True (A) Signup and view all the answers

The loop invariant in the factorial calculation function is always true before and after every iteration of the loop.

True (A) Signup and view all the answers

The loop invariant is used to prove the correctness of a ______

loop Signup and view all the answers

Match the following stages of the loop with their descriptions:

1.) Initialisation = Establishes the initial values for the variables involved 2.) Maintenance = Ensures that the invariant remains true after each iteration 3.) Termination = Shows that the invariant and the violated loop condition together imply the desired result Violated loop condition = The condition that causes the loop to terminate Signup and view all the answers

Match the following steps in the loop invariant proof with their descriptions:

Initialisation = Show that the invariant holds before the loop starts. Maintenance = Show that if the invariant holds at the beginning of an iteration, it also holds at the end of the iteration. Termination = Show that the invariant combined with the loop termination condition implies the correctness of the algorithm. Signup and view all the answers

Why is the loop invariant important in program correctness?

The loop invariant provides a way to prove that the loop behaves correctly. It ensures that the relationship between variables remains consistent throughout the loop's execution, leading to a desired outcome when the loop terminates. Signup and view all the answers

In the Factorial function, what is the initial value of j?

2 Signup and view all the answers

What is the final value of f returned by the Factorial function?

k! (C) Signup and view all the answers

In the factorial calculation function, the loop invariant `f = (j - 1)!` and the violated loop condition `j > k` together imply that `f = ______`, thus proving the correctness of the function.

k! Signup and view all the answers

In the provided code snippet, the variable `f` is initialized to the value of ______.

1 Signup and view all the answers

If the loop in the code snippet does not execute, the return value of the `Factorial(int k)` function is 1.

True (A) Signup and view all the answers

What is the purpose of the `error(...)` function call within the code snippet?

To handle invalid input (k < 0) by raising an error. Signup and view all the answers

What is the variable `j` used to represent in the code snippet?

The starting point of the loop counter (B) Signup and view all the answers

Match the following code snippets with their explanations:

<code>if k < 0 then error(...)</code> = Handles invalid input conditions <code>f = f · j</code> = Multiplies the current factor into the accumulating result <code>j = j + 1</code> = Increments the loop counter <code>return f</code> = Returns the calculated factorial result Signup and view all the answers

What condition needs to be met for the loop to continue executing?

<code>j ≤ k</code> (j is less than or equal to k) Signup and view all the answers

If `j` is greater than `k`, the loop ______ execute.

will not Signup and view all the answers

The loop invariant for the code snippet is: `f` is the product of all integers from 1 to `j-1` inclusive.

True (A) Signup and view all the answers

What is the desired output of the sorting problem described?

An array of numbers in ascending order (B) Signup and view all the answers

The internal representation of numbers is crucial for solving the sorting problem.

False (B) Signup and view all the answers

What is the main objective when given an array of numbers in the sorting problem?

To obtain a permutation of the array such that the numbers are in ascending order. Signup and view all the answers

Given an array A = ⟨a1, a2, ..., an⟩ of n numbers, a sorted output is a permutation ⟨a1′, a2′, ..., an′⟩ where a1′ ≤ a2′ ≤ ... ≤ an′.

ascending order Signup and view all the answers

Match the components of the sorting problem with their descriptions:

Input = An array of n numbers Output = A sorted permutation of the array Algorithm = The method used to sort the array Observation = Internal representation of numbers is unimportant Signup and view all the answers

When sorting the array A = ⟨5, 2, 8, 1⟩, which of the following would be the first element in the sorted output?

1 (C) Signup and view all the answers

A permutation in the context of sorting can include the same number appearing multiple times.

True (A) Signup and view all the answers

What is meant by the term 'permutation' in the sorting problem?

A rearrangement of the elements in the array. Signup and view all the answers

The sorting problem seeks a ________ of an array, meaning its elements are arranged in a specific order.

permutation Signup and view all the answers

Signup and view all the answers

Flashcards

Sorting Problem

Rearranging an array into non-decreasing order.

Array

A collection of numbers stored in a sequential manner.