Generate All Permutations of Array in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a permutation of an array?

A permutation of an array is a rearrangement of its elements in any possible order. For example, for [1, 2], the permutations are [1, 2] and [2, 1].

beginner

What is the base case in a recursive function to generate permutations?

The base case occurs when the current index reaches the length of the array, meaning all positions are fixed and one complete permutation is formed.

intermediate

Why do we swap elements during permutation generation?

Swapping elements helps to fix one element at the current position and then recursively generate permutations for the rest of the array, ensuring all unique orders are explored.

intermediate

How does backtracking help in generating all permutations?

Backtracking restores the array to its original state after exploring one branch of permutations by swapping back the elements, allowing exploration of other permutations without side effects.

intermediate

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

The time complexity is O(n!), because there are n! (factorial of n) possible permutations, and each permutation takes O(n) time to process or print.

What does the base case in permutation recursion usually check?

A If the current index equals the array length

B If the array is sorted

C If the array contains duplicates

D If the first element is fixed

The base case checks if the current index has reached the array length, meaning a full permutation is formed.

Why do we swap elements back after recursive calls in permutation generation?

A To increase recursion depth

B To sort the array

C To remove duplicates

D To restore the original array for other permutations

Swapping back restores the array to its original state so other permutations can be generated correctly.

How many permutations does an array of 3 elements have?

A 3

B 6

C 9

D 12

An array of 3 elements has 3! = 6 permutations.

Which technique is commonly used to generate all permutations?

A Dynamic programming

B Greedy algorithm

C Backtracking

D Divide and conquer

Backtracking is used to explore all possible permutations by swapping and restoring elements.

What is the main purpose of swapping elements in permutation generation?

A To fix an element at the current position

B To sort the array

C To remove duplicates

D To reduce array size

Swapping fixes one element at the current position to generate permutations of the remaining elements.

Explain how recursion and swapping work together to generate all permutations of an array.

Think about how you pick one element and then permute the rest.

Describe the role of the base case in a recursive permutation function and what happens when it is reached.

What tells the function it has a full answer?

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