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    Python Data Structures: Lists, Sets and Dictionaries Short Notes for GATE DA

    Python Data Structures: Lists, Sets and Dictionaries short notes for GATE DA: 1 study cards covering concepts, formulas, shortcuts and exam traps, plus solved

    python data structures lists sets and dictionaries short notes

    Final Revision: List and Set Tracing Rules

    Final Revision: List and Set Tracing Rules

    Summary Level 5 70 sec Importance 0.62 Toughness 0.25

    Lists

    RuleMeaning
    OrderedPosition matters
    MutableCan be changed in place
    appendAdds one object
    extendAdds items from an iterable
    +Creates a new list
    +=Mutates the existing list
    b = aAlias, same object
    b = a[:]Shallow copy, new outer list

    Sets

    RuleMeaning
    Unique elementsDuplicates are removed
    UnorderedDo not rely on position
    inMembership test
    A | BUnion
    A & BIntersection
    A - BElements in A but not B
    A ^ BElements in exactly one of them
    S |= TMutates S
    S = S | TRebinds S to a new set

    Tracing Method

    1. Write the current value of each variable.
    2. Decide whether the operation mutates or rebinds.
    3. For simultaneous assignment, evaluate all right-hand sides first.
    4. After a loop body, recheck the loop condition.

    Memory Hook

    Append one, extend many.
Plus new, plus-equals changes.
Sets deduplicate.
Right side first.

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    Answer it here to see how it works. Nothing is recorded until you sign in.

    Question 1
    Level 1: Warm-up

    Which of the following statements is true regarding list mutation and rebinding in Python?

    Question 2
    Level 1: Warm-up

    Given , how many of the following expressions evaluate to True?

    (i) 1 in S

    (ii) {1} in S

    (iii) {1, 2} <= S

    (iv) 4 not in S

    Question 3
    Level 1: Warm-up

    Which of the following CANNOT be an element of a Python set?

    Question 4
    Level 1: Warm-up

    Consider the following Python code:

    ```python

    x = [1, 2, 3]

    y = x

    z = x[:]

    ```

    What is the minimum number of distinct list objects present in memory after execution?

    Question 5
    Level 1: Warm-up

    For a Python list x, which of the following operations guarantees that the length of x increases by exactly 1, regardless of the contents of the added elements?

    Question 6
    Level 1: Warm-up

    Let A = {1, 2} and B = {2, 3}. After executing the simultaneous assignment A, B = B - A, A & B, what is the maximum element in the new set B?

    Question 7
    Level 1: Warm-up

    Consider the following Python code:

    ```python

    S = {1, 2, 3}

    S = S | {4}

    ```

    Assertion (A): After the above code executes, the original set object is mutated to include 4.

    Reason (R): The | operator creates a new set object, and the assignment operator = rebinds the name S to this new object.

    Question 8
    Level 1: Warm-up

    If set has 7 elements, set has 5 elements, and has 2 elements, what is the number of elements in ?

    Question 9
    Level 1: Warm-up

    Let and be sets such that , , and . What is ?

    Question 10
    Level 1: Warm-up

    Let and . Rank the following sets by size, from smallest to largest: , , .

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    Python Data Structures: Lists, Sets and Dictionaries Short Notes for GATE DA

    Python Data Structures: Lists, Sets and Dictionaries short notes for GATE DA: 1 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

    Final Revision: List and Set Tracing Rules

    Final Revision: List and Set Tracing Rules

    Summary Level 5 70 sec Importance 0.62 Toughness 0.25

    Lists

    RuleMeaning
    OrderedPosition matters
    MutableCan be changed in place
    appendAdds one object
    extendAdds items from an iterable
    +Creates a new list
    +=Mutates the existing list
    b = aAlias, same object
    b = a[:]Shallow copy, new outer list

    Sets

    RuleMeaning
    Unique elementsDuplicates are removed
    UnorderedDo not rely on position
    inMembership test
    A | BUnion
    A & BIntersection
    A - BElements in A but not B
    A ^ BElements in exactly one of them
    S |= TMutates S
    S = S | TRebinds S to a new set

    Tracing Method

    1. Write the current value of each variable.
    2. Decide whether the operation mutates or rebinds.
    3. For simultaneous assignment, evaluate all right-hand sides first.
    4. After a loop body, recheck the loop condition.

    Memory Hook

    Append one, extend many.
Plus new, plus-equals changes.
Sets deduplicate.
Right side first.

    Python Data Structures: Lists, Sets and Dictionaries: Solved Questions with Step-by-Step Explanations (10 Problems)

    Question 1 · Programming, Data Structures and Algorithms MCQ

    Which of the following statements is true regarding list mutation and rebinding in Python?

    1. A.

      x = x + [4] mutates the existing list in place.

    2. B.

      x += [4] creates a new list and leaves the original unchanged.

    3. C.

      y = x creates a separate copy of the list.

    4. D.

      x.append(4) modifies the existing list, so all aliases see the change.

    Correct Answer:

    D

    Step-by-Step Solution

    Key idea: This is a statement truth question testing the boundary between mutation and rebinding.

    Step 1: Analyze Option A

    x = x + [4] uses the + operator, which creates a new list and rebinds x. It does not mutate. (False)

    Step 2: Analyze Option B

    x += [4] uses augmented assignment. For lists, this mutates the existing list in place. It does not create a new list. (False)

    Step 3: Analyze Option C

    y = x creates an alias, not a copy. Both point to the same object. (False)

    Step 4: Analyze Option D

    x.append(4) is a mutating method. It changes the existing list, so any other variable pointing to the same list (aliases) will see the change. (True)

    Answer: Option D

    Question 2 · Programming, Data Structures and Algorithms MCQ

    Given , how many of the following expressions evaluate to True?

    (i) 1 in S

    (ii) {1} in S

    (iii) {1, 2} <= S

    (iv) 4 not in S

    1. A.

      1

    2. B.

      2

    3. C.

      3

    4. D.

      4

    Correct Answer:

    C

    Step-by-Step Solution

    Key idea: Distinguish between membership testing (in) and subset testing (<=). The in operator checks if an element is in the set, not if a set is in the set.

    Step 1: Evaluate each expression:

    (i) 1 in S: Is the integer 1 an element of S?

    S = {1, 2, 3}, so yes. True

    (ii) {1} in S: Is the set {1} an element of S?

    S contains integers 1, 2, 3, not the set {1}. False

    (iii) {1, 2} <= S: Is {1, 2} a subset of S?

    Both 1 and 2 are in S, so yes. True

    (iv) 4 not in S: Is 4 not an element of S?

    S = {1, 2, 3}, so 4 is not in S. True

    Step 2: Count the True expressions:

    (i) True, (ii) False, (iii) True, (iv) True

    Total: 3 expressions are True.

    Answer: C

    Common mistake: Thinking {1} in S is True because 1 is in S. But {1} is a set, not the integer 1.

    Question 3 · Programming, Data Structures and Algorithms MCQ

    Which of the following CANNOT be an element of a Python set?

    1. A.

      The integer 42

    2. B.

      The string "hello"

    3. C.

      The tuple (1, 2, 3)

    4. D.

      The list [1, 2, 3]

    Correct Answer:

    D

    Step-by-Step Solution

    Key idea: Set elements must be hashable (immutable). Lists are mutable and therefore not hashable.

    Step 1: Recall the requirement for set elements:

    • Elements must be hashable
    • Hashable objects are immutable

    Step 2: Check each option:

    • Integer 42: immutable → hashable → allowed
    • String "hello": immutable → hashable → allowed
    • Tuple (1, 2, 3): immutable → hashable → allowed (if all elements are hashable)
    • List [1, 2, 3]: mutable → not hashable → NOT allowed

    Step 3: Lists are mutable, so they cannot be set elements.

    Answer: D

    Common mistake: Thinking tuples are also invalid because they "look like" lists, but tuples are immutable and hashable.

    Question 4 · Programming, Data Structures and Algorithms MCQ

    Consider the following Python code:

    ```python

    x = [1, 2, 3]

    y = x

    z = x[:]

    ```

    What is the minimum number of distinct list objects present in memory after execution?

    1. A.

      1

    2. B.

      3

    3. C.

      4

    4. D.

      2

    Correct Answer:

    D

    Step-by-Step Solution

    Key idea: This is a contradiction question testing the difference between aliasing (same object) and slicing (new object).

    Step 1: Analyze x = [1, 2, 3]

    Creates 1 list object. x points to it.

    Step 2: Analyze y = x

    This is aliasing. y points to the same object as x. No new object is created.

    Step 3: Analyze z = x[:]

    This is a shallow copy using slicing. It creates 1 new list object. z points to it.

    Step 4: Count distinct objects

    Object 1: pointed to by x and y.

    Object 2: pointed to by z.

    Total = 2 distinct list objects.

    Answer: 2 (Option D)

    Question 5 · Programming, Data Structures and Algorithms MCQ

    For a Python list x, which of the following operations guarantees that the length of x increases by exactly 1, regardless of the contents of the added elements?

    1. A.

      x.append([1, 2])

    2. B.

      x.extend([1, 2])

    3. C.

      x += [1, 2]

    4. D.

      x = x + [1, 2]

    Correct Answer:

    A

    Step-by-Step Solution

    Insight: append adds its argument as a single element, while extend and + add the individual elements of the iterable.

    Exam route: x.append([1, 2]) adds the list [1, 2] as one single element. Length increases by 1. extend and + add 1 and 2 separately, increasing length by 2.

    Learning route: The append method takes its argument and inserts it as exactly one element at the end of the list, even if that argument is itself a list. Thus, x.append([1, 2]) increases the length of x by exactly 1. In contrast, extend and the + operator iterate over the argument and add each item individually, which would increase the length by 2 in this case.

    Wrong path: A student might ignore the constraint "increases by exactly 1" and simply look for an operation that adds elements, choosing extend or + (Options B, C, D). The break occurs at failing to distinguish between adding one object versus adding the contents of an object.

    Generalization: append always increases list length by 1. extend increases length by the number of elements in the iterable.

    Verification: x.append([1, 2]) results in x having one new element (the list [1, 2]). Length increases by 1. Correct.

    Question 6 · Programming, Data Structures and Algorithms MCQ

    Let A = {1, 2} and B = {2, 3}. After executing the simultaneous assignment A, B = B - A, A & B, what is the maximum element in the new set B?

    1. A.

      3

    2. B.

      1

    3. C.

      2

    4. D.

      0

    Correct Answer:

    C

    Step-by-Step Solution

    Insight: In simultaneous assignment, all right-hand side expressions are evaluated using the original values of the sets before any assignments occur.

    Exam route: Original A = {1, 2}, B = {2, 3}. B - A = {3}. A & B = {2}. B is assigned {2}. The maximum element in B is 2.

    Learning route: The right-hand sides are evaluated first. B - A using the original sets is {2, 3} - {1, 2} = {3}. A & B using the original sets is {1, 2} & {2, 3} = {2}. Then, the assignments happen: A becomes {3} and B becomes {2}. The new set B is {2}, and its maximum element is 2.

    Wrong path: A student might evaluate sequentially. A becomes B - A = {3}. Then B becomes A & B = {3} & {2, 3} = {3}. The maximum element would be 3 (Option A). This breaks because simultaneous assignment does not update variables one by one; it uses the old values for all right-hand sides.

    Generalization: In x, y = expr1, expr2, both expr1 and expr2 are computed before x or y is updated.

    Verification: The original A and B yield {3} and {2}. B receives {2}, so the max is 2.

    Question 7 · Programming, Data Structures and Algorithms MCQ

    Consider the following Python code:

    ```python

    S = {1, 2, 3}

    S = S | {4}

    ```

    Assertion (A): After the above code executes, the original set object is mutated to include 4.

    Reason (R): The | operator creates a new set object, and the assignment operator = rebinds the name S to this new object.

    1. A.

      Both A and R are true and R is the correct explanation of A

    2. B.

      Both A and R are true but R is NOT the correct explanation of A

    3. C.

      A is true but R is false

    4. D.

      A is false but R is true

    Correct Answer:

    D

    Step-by-Step Solution

    Insight: The | operator on sets creates a new set, and = rebinds the variable name; it does not mutate the original set in place.

    Exam route: S = S | {4} evaluates S | {4} to a new set {1, 2, 3, 4} and rebinds S to it. The original set object {1, 2, 3} is unchanged. Thus, A is false. R correctly describes this rebinding behavior, so R is true. Answer is D.

    Learning route: The expression S | {4} computes the union, which produces a brand new set object in memory. The assignment S = ... then points the name S to this new object. The original set object that S previously pointed to is not modified; it remains {1, 2, 3} (though it may be garbage collected if no other names reference it). Therefore, Assertion A is false because no mutation occurs. Reason R is true because it accurately describes the creation of a new object and the rebinding of the name S.

    Wrong path: A student might commit a unit mismatch error, confusing the unit of change (variable rebinding) with object mutation. They might think S = S | {4} adds 4 to the existing set object, making A true. This leads to choosing Option A or C. The break occurs at misunderstanding that | does not have an in-place effect like |= does.

    Generalization: For sets, | creates a new object (rebinding), while |= mutates the existing object in place.

    Verification: If another variable T = S was set before the operation, T would remain {1, 2, 3}, proving the original object was not mutated.

    Question 8 · Programming, Data Structures and Algorithms MCQ

    If set has 7 elements, set has 5 elements, and has 2 elements, what is the number of elements in ?

    1. A.

      9

    2. B.

      10

    3. C.

      12

    4. D.

      14

    Correct Answer:

    B

    Step-by-Step Solution

    Key idea: This is a direct application of the inclusion-exclusion principle for two sets.

    Step 1: Recall the formula for the size of a union:

    Step 2: Substitute the given values:

    Step 3: Calculate:

    Answer: 10

    Common mistake: Forgetting to subtract the intersection gives , which is option C. This overcounts the 2 elements that appear in both sets.

    Question 9 · Programming, Data Structures and Algorithms MCQ

    Let and be sets such that , , and . What is ?

    1. A.

      3

    2. B.

      5

    3. C.

      7

    4. D.

      21

    Correct Answer:

    B

    Step-by-Step Solution

    Key idea: This is a reverse application of the inclusion-exclusion principle. Instead of finding the union from the intersection, we find the intersection from the union.

    Step 1: Recall the inclusion-exclusion formula:

    Step 2: Rearrange to solve for :

    Step 3: Substitute the given values:

    Step 4: Calculate:

    Answer: 5

    Common mistake: Using the wrong formula arrangement, such as (option A if taking absolute value), or (option C), or simply adding (option D).

    Question 10 · Programming, Data Structures and Algorithms MCQ

    Let and . Rank the following sets by size, from smallest to largest: , , .

    1. A.

      , ,

    2. B.

      , ,

    3. C.

      , ,

    4. D.

      , ,

    Correct Answer:

    A

    Step-by-Step Solution

    Key idea: Calculate the size of each set operation, then rank them.

    Step 1: Calculate (elements in both A and B):

    Size: 2

    Step 2: Calculate (elements in A but not in B):

    Size: 3

    Step 3: Calculate (elements in A or B or both):

    Size: 6

    Step 4: Rank by size (smallest to largest):

    , ,

    Ranking: , ,

    Answer: A

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