Generate All Permutations of Array in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Permutations for [1, 2]

What is the output of the following Python code that generates all permutations of the array [1, 2]?

DSA Python

from itertools import permutations
arr = [1, 2]
result = list(permutations(arr))
print(result)

A [(2, 1)]

B [(2, 1), (1, 2), (1, 2)]

C [(1, 2)]

D [(1, 2), (2, 1)]

💡 Hint

Think about how many ways you can arrange two distinct numbers.

The permutations of [1, 2] are two: (1, 2) and (2, 1). itertools.permutations returns tuples of all possible orderings.

❓ Predict Output

intermediate

Number of Permutations for [1, 2, 3]

What is the length of the list generated by all permutations of the array [1, 2, 3] using itertools.permutations?

DSA Python

from itertools import permutations
arr = [1, 2, 3]
result = list(permutations(arr))
print(len(result))

A 6

B 3

C 9

D 5

💡 Hint

Number of permutations of n distinct elements is n factorial (n!).

For 3 elements, the number of permutations is 3! = 3 × 2 × 1 = 6.

🔧 Debug

advanced

Identify the Error in Permutation Generation Code

What error will this code produce when trying to generate all permutations of [1, 2, 3]?

DSA Python

def permute(arr):
    if len(arr) == 1:
        return [arr]
    result = []
    for i in range(len(arr)):
        for p in permute(arr):
            if i != p:
                result.append([arr[i]] + p)
    return result

print(permute([1, 2, 3]))

A RecursionError due to infinite recursion

B TypeError because of wrong list concatenation

C NameError due to undefined variable

D No error, prints all permutations

💡 Hint

Look at the recursive call inside the loop and what argument it uses.

The function calls permute(arr) inside the loop without reducing the input size, causing infinite recursion and eventually a RecursionError.

❓ Predict Output

advanced

Output of Custom Permutation Function

What is the output of this custom permutation function for input [1, 2]?

DSA Python

def permute(arr):
    if len(arr) == 0:
        return [[]]
    res = []
    for i in range(len(arr)):
        rest = arr[:i] + arr[i+1:]
        for p in permute(rest):
            res.append([arr[i]] + p)
    return res

print(permute([1, 2]))

A [[1], [2]]

B [[1, 2], [2, 1]]

C [[2, 1]]

D [[1, 2]]

💡 Hint

Think about how the function builds permutations by choosing each element and permuting the rest.

The function correctly generates all permutations by recursively removing one element and permuting the rest, then adding the removed element at the front.

🧠 Conceptual

expert

Time Complexity of Generating All Permutations

What is the time complexity of generating all permutations of an array of size n?

A O(2^n) because each element can be included or excluded

B O(n^2) because permutations are generated by nested loops

C O(n!) because there are n! permutations and each takes O(n) to build

D O(n) because each element is processed once

💡 Hint

Consider how many permutations exist and how much work is done per permutation.

There are n! permutations of n elements. Generating each permutation requires copying or building a list of length n, so total time is O(n × n!) = O(n!).

Practice

1. What does the function permutations from Python's itertools module do when given an array as input?

easy

A. Generates all possible orderings of the elements in the array

B. Sorts the array in ascending order

C. Removes duplicate elements from the array

D. Returns the array reversed

Solution

1. Step 1: Understand the purpose of permutations

   The permutations function creates all possible ways to arrange the elements of the input array.

2. Step 2: Compare with other options

   Sorting, removing duplicates, or reversing are different operations and not what permutations does.

3. Final Answer:

   Generates all possible orderings of the elements in the array -> Option A

4. Quick Check:

   Permutations = all orderings [OK]

Hint: Permutations = all ways to arrange elements [OK]

Common Mistakes:

• Confusing permutations with sorting
• Thinking permutations remove duplicates
• Assuming permutations reverse the array

2. Which of the following is the correct syntax to generate all permutations of the list [1, 2, 3] using itertools.permutations in Python?

easy

A. from itertools import permutation
perms = permutations([1, 2, 3])

B. from itertools import permutation
perms = permutation([1, 2, 3])

C. import itertools
perms = itertools.permutations([1, 2, 3])

D. import itertools
perms = itertools.permutation([1, 2, 3])

Solution

1. Step 1: Check correct import and function name

   The correct module is itertools and the function is permutations (plural).

2. Step 2: Verify syntax correctness

   import itertools perms = itertools.permutations([1, 2, 3]) correctly imports itertools and calls itertools.permutations with the list.

3. Final Answer:

   import itertools perms = itertools.permutations([1, 2, 3]) -> Option C

4. Quick Check:

   Correct import and function name = import itertools perms = itertools.permutations([1, 2, 3]) [OK]

Hint: Use plural 'permutations' and correct import [OK]

Common Mistakes:

• Using singular 'permutation' instead of 'permutations'
• Wrong import statement
• Calling function without module prefix when not imported directly

3. What is the output of the following code?

from itertools import permutations
for p in permutations([1, 2]):
    print(p)

medium

A. (1, 2)\n(2, 1)

B. [1, 2]\n[2, 1]

C. (1, 2)\n(1, 2)

D. [1, 2]\n[1, 2]

Solution

1. Step 1: Understand permutations output type

   itertools.permutations returns tuples representing each permutation.

2. Step 2: List all permutations of [1, 2]

   They are (1, 2) and (2, 1), printed on separate lines.

3. Final Answer:

   (1, 2)\n(2, 1) -> Option A

4. Quick Check:

   Permutations of two elements = two tuples [OK]

Hint: Permutations output tuples, not lists [OK]

Common Mistakes:

• Expecting lists instead of tuples
• Repeating same permutation twice
• Confusing output format with string or list

4. The following code is intended to print all permutations of [1, 2, 3]. What is the error?

from itertools import permutations
perms = permutations([1, 2, 3])
print(perms)

medium

A. The import statement is incorrect

B. It prints a permutations object, not the permutations themselves

C. The list should be converted to a tuple first

D. The function permutations does not exist

Solution

1. Step 1: Understand what permutations returns

   permutations returns an iterator object, not a list of permutations directly.

2. Step 2: Printing the iterator shows its object info, not permutations

   To see permutations, you must iterate or convert to list first.

3. Final Answer:

   It prints a permutations object, not the permutations themselves -> Option B

4. Quick Check:

   Printing iterator shows object info, not data [OK]

Hint: Convert iterator to list to see permutations [OK]

Common Mistakes:

• Expecting print to show permutations directly
• Thinking import is wrong
• Believing input must be tuple

5. You want to generate all permutations of the array [1, 2, 2] but only keep unique permutations (no duplicates). Which approach correctly achieves this in Python?

hard

A. Use list(permutations([1, 2, 2])) directly

B. Use permutations(set([1, 2, 2])) to generate permutations of unique elements

C. Sort the array first, then use permutations

D. Use set(permutations([1, 2, 2])) to remove duplicate tuples

Solution

1. Step 1: Understand duplicates in permutations

   Input has repeated elements, so permutations include duplicates.

2. Step 2: Remove duplicates by converting permutations to a set

   Using set() on permutations removes duplicate tuples, keeping unique permutations only.

3. Final Answer:

   Use set(permutations([1, 2, 2])) to remove duplicate tuples -> Option D

4. Quick Check:

   Set removes duplicates from permutations [OK]

Hint: Convert permutations to set to remove duplicates [OK]

Common Mistakes:

• Using set on input list before permutations (loses duplicates)
• Assuming sorting removes duplicates
• Not removing duplicates at all