How Can We Generate All Unique Permutations of an Integer Array?

Permutations of an array can be achieved by generating every possible combination while ensuring that each combination is unique. To explore this concept further, let's consider the given array:

int[] a = {3, 4, 6, 2, 1};

The goal is to list all distinct permutations of this array. Here's the pseudocode algorithm:

for (int i = 0; i < a.length; i++) {
  // Perform actions for each element of the array
  for (int j = i + 1; j < a.length; j++) {
    // Swap elements at indices i and j to generate a permutation
    int temp = a[i];
    a[i] = a[j];
    a[j] = temp;

    // Check if the current permutation has already been generated
    if (!hasBeenGenerated(a)) {
      // If the permutation is new, add it to the list of permutations
      addPermutationToList(a);
    }

    // Swap the elements back to restore the original array
    temp = a[i];
    a[i] = a[j];
    a[j] = temp;
  }
}

In this algorithm, we iterate through each element of the array (represented by the index i) and compare it with every other element (represented by the index j). If the elements have not been swapped before (indicated by the hasBeenGenerated() check), we create a new permutation by swapping them and add it to the list. We then swap the elements back to maintain the original array. By considering all possible pairings of elements, we generate a comprehensive list of permutations.

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