Generate All Permutations of Array in DSA Python - Build from Scratch

Generate All Permutations of Array

📖 Scenario: You are organizing a small event and want to find all possible ways to arrange 3 different colored flags in a row. Each arrangement is a unique order of the flags.

🎯 Goal: Build a program that generates and prints all possible permutations (arrangements) of a list of 3 colors.

📋 What You'll Learn

Create a list called colors with the exact values 'Red', 'Green', and 'Blue'

Create a variable called result to store all permutations as a list

Write a recursive function called permute that generates all permutations of the colors list

Call the permute function with the initial parameters

Print the result list showing all permutations

💡 Why This Matters

🌍 Real World

Generating all possible arrangements is useful in planning, scheduling, and testing different orderings in real life.

💼 Career

Understanding permutations helps in algorithm design, problem solving, and coding interviews.

1

Create the list of colors

Create a list called colors with these exact values in order: 'Red', 'Green', 'Blue'

DSA Python

# Create the list of colors
# Your code here

Hint

Use square brackets to create a list and separate the colors with commas.

2

Create a list to store permutations

Create an empty list called result to store all permutations

DSA Python

colors = ['Red', 'Green', 'Blue']
# Create an empty list called result
# Your code here

Hint

Use empty square brackets to create an empty list.

3

Write the recursive function to generate permutations

Write a recursive function called permute that takes two parameters: current (a list) and remaining (a list). The function should do the following:
1. If remaining is empty, append current to result.
2. Otherwise, for each element in remaining, call permute with current plus that element, and remaining without that element.

DSA Python

colors = ['Red', 'Green', 'Blue']
result = []
# Write the recursive function permute(current, remaining) below
# Your code here

Hint

Use recursion to build permutations by choosing each element in turn and removing it from the remaining list.

4

Call the function and print all permutations

Call the permute function with an empty list for current and the colors list for remaining. Then print the result list.

DSA Python

colors = ['Red', 'Green', 'Blue']
result = []

def permute(current, remaining):
    if not remaining:
        result.append(current)
    else:
        for i in range(len(remaining)):
            permute(current + [remaining[i]], remaining[:i] + remaining[i+1:])

# Call permute and print result
# Your code here

Hint

Start with an empty current list and the full colors list as remaining. Then print the result list after generating permutations.

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