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Permutations

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C program to generate all possible permutations of a given array of distinct integers. A permutation is a rearrangement of the elements of the array where each element appears exactly once. The order of the permutations in the output doesn't matter.

Example 1
    
  
  • Input: nums = [1,2,3]
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  • Output: [[1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], [3,2,1]]
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  • Explanation: 
    • For the array [1,2,3], we need to generate all possible arrangements. 
    • There are 3! = 6 possible permutations. 
    • We use backtracking to systematically generate each permutation.
    •
Example 2
    
  
  • Input: nums = [0,1]
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  • Output: [[0,1], [1,0]]
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  • Explanation: 
    • For the array [0,1], we need to generate all possible arrangements. 
    • There are 2! = 2 possible permutations. 
    • The permutations are [0,1] and [1,0].
    •
Constraints
    
  
  • 1 <= nums.length <= 6
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  • -10 <= nums[i] <= 10
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  • All the integers of nums are unique
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  • Time Complexity: O(n * n!), where n is the length of the array
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  • Space Complexity: O(n * n!) for storing all permutations
    •
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Hint
Solution

Solution Hints

    
  
  • Use backtracking to systematically generate all permutations
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  • For each position in the permutation, try placing each unused number
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  • Keep track of which numbers have been used in the current permutation
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  • When you've placed all numbers, you've found a complete permutation
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  • Use recursion to build permutations element by element
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  • You can use a boolean array or set to track which elements have been used
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  • You can also swap elements in the array to generate permutations without extra space
    •

Steps to solve by this approach:

 Step 1: Create a backtracking function that builds permutations one element at a time.

 Step 2: Use an array or bit mask to keep track of which elements have been used in the current permutation.

 Step 3: For each position in the permutation, try placing each unused number.

 Step 4: After placing a number, mark it as used before moving to the next position.

 Step 5: When we've filled all positions, we've found a complete permutation.

 Step 6: After adding a permutation to our result, backtrack by marking the last placed number as unused.

 Step 7: Continue this process until all possible permutations have been generated.

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