Lecture 119:-  Permutation - II

The "Permutations II" problem involves finding all unique permutations of a given array that might contain duplicate elements. Each unique permutation is a rearrangement of the elements in the array. It's important to ensure that duplicate permutations are not included in the result.

Here's how you can approach the "Permutations II" problem using a recursive backtracking approach in Python:

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def permute_unique(nums): def backtrack(start): if start == len(nums) - 1: result.append(nums[:]) return used = set() for i in range(start, len(nums)): if nums[i] in used: continue used.add(nums[i]) nums[start], nums[i] = nums[i], nums[start] backtrack(start + 1) nums[start], nums[i] = nums[i], nums[start] result = [] backtrack(0) return result # Example usage nums = [1, 1, 2] permutations = permute_unique(nums) print(permutations)

In this example, the permute_unique function takes a list of integers as input and returns a list of all unique permutations of the input array.

The backtrack function generates permutations by iterating through the array and swapping elements. It uses a used set to keep track of elements that have already been used at the current position to avoid generating duplicate permutations.

For each position, the backtrack function iterates through the remaining elements and checks whether the element has already been used at that position. If not, it swaps the current element with the element at the current position and recurses to the next position. After recursion, the elements are swapped back to their original positions to backtrack and explore other possibilities.

The time complexity of this solution can vary based on the input and the number of unique permutations. In the worst case, it can be exponential due to the branching factor of the recursion. However, by avoiding duplicate permutations, the actual number of recursive calls and permutations generated is reduced, improving the overall performance.

This solution ensures that only unique permutations are generated, even if the input array contains duplicate elements.