#### Programming, Data Structures And Algorithms Using Python - Week 6 Quiz | NPTEL Jan 2023 | Answer with Explanation

## Suppose u and v both denote sets in Python. Under what condition can we guarantee that u-(u-v) == v?

a. The sets u and v should be disjoint.b. The set u should be a subset of the set v

c. The set v should be a subset of the set u

d. This is true for any u and v.

## Answer

c. The set v should be a subset of the set u

Here's the Python code to demonstrate this:

# Example sets u = {1, 2, 3, 4, 5} v = {3, 4, 5} # Calculate u - (u - v) result = u - (u - v) # Check if result is equal to v if result == v: print("u - (u - v) is equal to v") else: print("u - (u - v) is not equal to v") Output: u - (u - v) is equal to v

Explanation:

u - v gives a set of elements in u that are not in v. This will be {1, 2} in this example.

u - (u - v) gives a set of elements in u that are not in the set {1, 2}. Since {1, 2} is a subset of u, this will be {3, 4, 5}.

Therefore, u - (u - v) gives the same set as v if and only if v is a subset of u.

## Suppose u and v both denote sets in Python. Under what condition can we guarantee that u|v == u^v?

a. The sets u and v should be disjoint.b. The set v should be a subset of the set u.

c. The set u should be a subset of the set v.

d. This is true for any u and v.

## Answer

a. The sets u and v should be disjoint.

Here is the python code to demonstrate this:

u = {1, 2, 3} v = {4, 5, 6} # Union of u and v union = u | v # Symmetric difference of u and v symmetric_diff = u ^ v if union == symmetric_diff: print("u|v == u^v") else: print("u|v != u^v")

Output:

u|v == u^v

In this example, u and v are disjoint sets, meaning they have no common elements. The union of u and v is the set of all elements in u and v, while the symmetric difference of u and v is the set of elements that are in u or v, but not in both. Since u and v have no common elements, their union and symmetric difference are the same, and the condition u|v == u^v is satisfied.

## Which of the following does not correspond to a max-heap on the list of values [19, 28, 29, 31, 31, 45, 55, 72, 83, 97]?

a. [97, 83, 45, 55, 72, 28, 31, 19, 31, 29]b. [97, 55, 83, 29, 45, 72, 31, 19, 31, 28]

c. [97, 83, 55, 72, 31, 45, 29, 19, 31, 28]

d. [97, 55, 83, 45, 29, 72, 31, 19, 31, 28]

## Answer

b. [97, 55, 83, 29, 45, 72, 31, 19, 31, 28]

## Consider the max-heap [96, 96, 55, 74, 37, 42, 29, 18, 31, 19]. Suppose we apply the operation delete_max() twice to this max-heap. The resulting max-heap is:

a. [74, 37, 55, 19, 31, 42, 29, 18]b. [74, 37, 55, 31, 19, 29, 42, 18]

c. [74, 37, 55, 31, 18, 42, 29, 19]

d. [74, 37, 55, 31, 19, 42, 29, 18]

## Answer

d. [74, 37, 55, 31, 19, 42, 29, 18]

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