Generate All Permutations of Array in DSA Java - 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 all permutations of an array?

The base case occurs when the current index reaches the length of the array, meaning a complete permutation has been formed and can be recorded or printed.

intermediate

How does swapping elements help in generating permutations?

Swapping elements allows us to fix one element at the current position and recursively generate permutations for the remaining positions, ensuring all orderings are explored.

intermediate

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

Swapping back restores the original array order before the next iteration, so that other permutations can be generated correctly without interference from previous swaps.

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 to generate and process.

What does the base case in permutation recursion usually check?

A If the array is sorted

B If the array contains duplicates

C If the current index equals the array length

D If the first element is fixed

The base case is when the current index reaches 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 the next permutation

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

How many permutations does an array of size 3 have?

A 3

B 6

C 9

D 12

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

Which technique is commonly used to generate all permutations of an array?

A Backtracking

B Divide and conquer

C Greedy algorithm

D Dynamic programming

Backtracking is used to explore all possible permutations by swapping and recursive calls.

What is the role of swapping in permutation generation?

A To fix an element at the current position

B To sort the array

C To delete elements

D To reverse the array

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

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

Think about fixing one element at a time and exploring all options for the rest.

Describe the steps to generate all permutations of [1, 2, 3] using backtracking.

Visualize swapping elements and moving forward step by step.

Practice

1. What does generating all permutations of an array mean?

easy

A. Sorting the array in ascending order

B. Listing all possible orders of the array elements

C. Finding the largest element in the array

D. Removing duplicate elements from the array

Solution

1. Step 1: Understand permutations

   Permutations are all possible ways to arrange elements in order.

2. Step 2: Apply to array

   Generating all permutations means listing every possible order of the array elements.

3. Final Answer:

   Listing all possible orders of the array elements -> Option B

4. Quick Check:

   Permutations = all orders [OK]

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

Common Mistakes:

• Confusing permutations with sorting
• Thinking permutations remove duplicates
• Mixing permutations with finding max element

2. Which Java method signature correctly defines a function to generate permutations of an integer array?

easy

A. public void generatePermutations(int[] arr, int start)

B. void generatePermutations(int arr[], int start) public

C. public int generatePermutations(int[] arr, int start)

D. public static generatePermutations(int[] arr, int start)

Solution

1. Step 1: Check method signature syntax

   In Java, method signature starts with access modifier, return type, method name, and parameters.

2. Step 2: Validate options

   public void generatePermutations(int[] arr, int start) correctly uses 'public void' and parameter types. void generatePermutations(int arr[], int start) public has wrong order. public int generatePermutations(int[] arr, int start) returns int but should be void. public static generatePermutations(int[] arr, int start) misses return type.

3. Final Answer:

   public void generatePermutations(int[] arr, int start) -> Option A

4. Quick Check:

   Correct Java method syntax = public void generatePermutations(int[] arr, int start) [OK]

Hint: Java method = access + return type + name + params [OK]

Common Mistakes:

• Missing return type in method signature
• Incorrect order of access modifier and return type
• Wrong return type for void methods

3. What is the output of the following Java code snippet?

public class PermTest {
  public static void permute(int[] arr, int start) {
    if (start == arr.length - 1) {
      for (int num : arr) System.out.print(num + " ");
      System.out.println();
      return;
    }
    for (int i = start; i < arr.length; i++) {
      int temp = arr[start];
      arr[start] = arr[i];
      arr[i] = temp;
      permute(arr, start + 1);
      temp = arr[start];
      arr[start] = arr[i];
      arr[i] = temp;
    }
  }
  public static void main(String[] args) {
    int[] arr = {1, 2};
    permute(arr, 0);
  }
}

medium

A. 1 2 \n2 1 \n

B. 1 2 \n1 2 \n

C. 2 1 \n1 2 \n

D. No output

Solution

1. Step 1: Trace recursive calls for arr = {1, 2}

   Start with start=0, swap arr[0] with arr[0] (no change), recurse with start=1, print 1 2. Then swap back, swap arr[0] with arr[1], arr becomes {2,1}, recurse start=1, print 2 1.

2. Step 2: Confirm output lines

   Two lines printed: '1 2' and '2 1', each followed by newline.

3. Final Answer:

   1 2 \n2 1 \n -> Option A

4. Quick Check:

   All permutations of [1,2] = 1 2 and 2 1 [OK]

Hint: Swap and recurse to generate permutations [OK]

Common Mistakes:

• Forgetting to swap back after recursion
• Printing before reaching last index
• Confusing order of swaps

4. Identify the error in this Java method for generating permutations:

public void permute(int[] arr, int start) {
  if (start == arr.length) {
    System.out.println(Arrays.toString(arr));
    return;
  }
  for (int i = start; i < arr.length; i++) {
    int temp = arr[start];
    arr[start] = arr[i];
    arr[i] = temp;
    permute(arr, start + 1);
  }
}

medium

A. Using Arrays.toString incorrectly

B. Incorrect base case condition

C. Missing swap back after recursive call

D. Wrong loop range in for loop

Solution

1. Step 1: Analyze swapping logic

   After swapping arr[start] and arr[i], the method calls recursion but does not swap back, so array stays changed for next iterations.

2. Step 2: Identify missing swap back

   To restore original array before next iteration, swap back is needed after recursive call.

3. Final Answer:

   Missing swap back after recursive call -> Option C

4. Quick Check:

   Swap back needed to restore array [OK]

Hint: Always swap back after recursion to restore array [OK]

Common Mistakes:

• Not swapping back after recursion
• Incorrect base case index
• Misusing Arrays.toString for printing

5. You want to generate all permutations of an array with possible duplicate elements, but avoid printing duplicate permutations. Which approach is best?

hard

A. Use a HashSet to store and print only unique permutations after generating all

B. Only swap elements if they are different values

C. Generate all permutations without any checks and print all

D. Sort the array first and skip swapping duplicate elements during recursion

Solution

1. Step 1: Understand duplicates in permutations

   Duplicates cause repeated permutations if not handled. Sorting helps group duplicates together.

2. Step 2: Skip swapping duplicates during recursion

   By sorting and skipping swaps of same values at the same recursion level, duplicates are avoided efficiently.

3. Final Answer:

   Sort the array first and skip swapping duplicate elements during recursion -> Option D

4. Quick Check:

   Sort + skip duplicates = unique permutations [OK]

Hint: Sort array and skip duplicate swaps to avoid repeats [OK]

Common Mistakes:

• Generating all then filtering duplicates (inefficient)
• Not sorting before recursion
• Only swapping if values differ misses some permutations