Generate All Permutations of Array in DSA C++ - Build from Scratch

Generate All Permutations of Array

📖 Scenario: You are helping a friend organize a small photo album. They want to see all possible ways to arrange 3 photos in a row. This means finding every order the photos can be placed.

🎯 Goal: Build a program that generates and prints all possible orders (permutations) of a list of 3 numbers representing photos.

📋 What You'll Learn

Create an array called photos with the values 1, 2, and 3

Create a helper function called swap that swaps two elements in the array

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

Print each permutation on its own line with elements separated by spaces

💡 Why This Matters

🌍 Real World

Generating all permutations is useful in tasks like arranging photos, scheduling, or solving puzzles where all possible orders matter.

💼 Career

Understanding permutations and recursion is important for software roles involving algorithms, problem solving, and optimization.

1

Create the initial array

Create an integer array called photos with exactly these values: 1, 2, and 3.

DSA C++

// Your code here

Hint

Use C++ array syntax with curly braces to list the values.

2

Create a swap helper function

Write a function called swap that takes two integer references a and b and swaps their values.

DSA C++

int photos[] = {1, 2, 3};
// Your code here

Hint

Use a temporary variable to hold one value while swapping.

3

Write the recursive permutation function

Write a recursive function called permute that takes the array photos, an integer start, and an integer end. It should generate all permutations by swapping elements and recursively calling itself.

DSA C++

int photos[] = {1, 2, 3};

void swap(int &a, int &b) {
    int temp = a;
    a = b;
    b = temp;
}

// Your code here

Hint

Use a base case when start == end to print the array. Use a loop to swap and recurse.

4

Call the permutation function and print results

Call the permute function with photos, 0 as start, and 2 as end to print all permutations.

DSA C++

int photos[] = {1, 2, 3};

void swap(int &a, int &b) {
    int temp = a;
    a = b;
    b = temp;
}

void permute(int arr[], int start, int end) {
    if (start == end) {
        for (int i = 0; i <= end; i++) {
            std::cout << arr[i] << " ";
        }
        std::cout << std::endl;
    } else {
        for (int i = start; i <= end; i++) {
            swap(arr[start], arr[i]);
            permute(arr, start + 1, end);
            swap(arr[start], arr[i]);
        }
    }
}

// Your code here

Hint

Call permute(photos, 0, 2); inside main() to start printing all permutations.

Practice

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

easy

A. Listing all possible orders of the array elements

B. Sorting the array in ascending order

C. Finding the maximum 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 elements

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

3. Final Answer:

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

4. Quick Check:

   Permutations = all orders [OK]

Hint: Permutations = all possible orders of elements [OK]

Common Mistakes:

• Confusing permutations with sorting
• Thinking permutations remove duplicates
• Assuming permutations find max or min

2. Which of the following C++ function signatures is correct for a recursive function generating all permutations of an integer array arr with size n</> and current index start?

easy

A. void permute(int arr[], int start, int n)

B. int permute(int arr[], int n, int start)

C. void permute(int arr[], int n)

D. int permute(int arr[], int start)

Solution

1. Step 1: Check parameter order and types

   The function needs the array, current index (start), and total size (n) to generate permutations recursively.

2. Step 2: Validate return type and parameters

   It should return void (no value) and have parameters (int arr[], int start, int n) in that order.

3. Final Answer:

   void permute(int arr[], int start, int n) -> Option A

4. Quick Check:

   Correct signature = void permute(arr, start, n) [OK]

Hint: Recursive permute needs array, start index, and size [OK]

Common Mistakes:

• Wrong parameter order
• Incorrect return type
• Missing current index parameter

3. What will be the output of the following C++ code snippet?

void permute(int arr[], int start, int n) {
  if (start == n) {
    for (int i = 0; i < n; i++) std::cout << arr[i] << ' ';
    std::cout << '\n';
    return;
  }
  for (int i = start; i < n; i++) {
    std::swap(arr[start], arr[i]);
    permute(arr, start + 1, n);
    std::swap(arr[start], arr[i]);
  }
}

int main() {
  int arr[] = {1, 2};
  permute(arr, 0, 2);
  return 0;
}

medium

A. 2 1 \n 1 2 \n

B. 1 2 \n 2 1 \n

C. 1 2 \n 1 2 \n

D. No output

Solution

1. Step 1: Trace first call with arr = {1, 2}

   Start = 0, n = 2. Swap arr[0] with arr[0] (no change), call permute with start=1.

2. Step 2: Trace second call with start=1

   Swap arr[1] with arr[1] (no change), call permute with start=2 which prints "1 2".

3. Step 3: Backtrack and swap arr[0] with arr[1]

   Array becomes {2, 1}, call permute with start=1 again.

4. Step 4: At start=1 again, swap arr[1] with arr[1], call permute with start=2 prints "2 1".

5. Final Answer:

   1 2 \n 2 1 \n -> Option B

6. Quick Check:

   All permutations of {1,2} printed [OK]

Hint: Swap and backtrack to print all orders [OK]

Common Mistakes:

• Not swapping back after recursion
• Printing before base case
• Incorrect loop range

4. Identify the error in the following code snippet for generating permutations of array arr of size n:

void permute(int arr[], int start, int n) {
  if (start == n) {
    for (int i = 0; i < n; i++) std::cout << arr[i] << ' ';
    std::cout << '\n';
    return;
  }
  for (int i = 0; i < n; i++) {
    std::swap(arr[start], arr[i]);
    permute(arr, start + 1, n);
    std::swap(arr[start], arr[i]);
  }
}

medium

A. Function should return int, not void

B. Base case condition should be start == n - 1

C. Swap should be done only once outside the loop

D. Loop should start from i = start, not 0

Solution

1. Step 1: Analyze the for loop range

   The loop swaps arr[start] with arr[i]. If i starts at 0 always, it swaps elements already fixed in previous recursion steps.

2. Step 2: Correct loop start index

   Loop should start from i = start to avoid repeating swaps and ensure correct permutations.

3. Final Answer:

   Loop should start from i = start, not 0 -> Option D

4. Quick Check:

   Loop from start to n fixes correct elements [OK]

Hint: Start loop from current index to avoid duplicate swaps [OK]

Common Mistakes:

• Starting loop from 0 causes repeated permutations
• Changing base case incorrectly
• Misplacing swap calls

5. Given an array arr = {1, 2, 2}, how many unique permutations will a correct C++ program generate if it avoids duplicates?

hard

A. 2

B. 6

C. 3

D. 4

Solution

1. Step 1: Calculate total permutations without duplicates

   For 3 elements with two 2's, total permutations = 3! / 2! = 3.

2. Step 2: List unique permutations

   They are {1,2,2}, {2,1,2}, {2,2,1} -- total 3 unique permutations.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   3! / 2! = 3 unique permutations [OK]

Hint: Divide factorial by duplicates factorial for unique count [OK]

Common Mistakes:

• Counting duplicates as unique permutations
• Using 3! = 6 without division
• Ignoring repeated elements