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This approach uses recursion combined with backtracking to generate all possible permutations of the input array. The algorithm works by swapping elements of the array and recursively building permutations by fixing one element at a time until the entire array is permutated.
Time Complexity: O(n * n!) as there are n! permutations and we copy each permutation.
Space Complexity: O(n!) for storing the permutations, plus additional space used by the recursive stack.
1function permute(nums) {
2 const result = [];
3 const backtrack = (path) => {
4 if (path.length === nums.length) {
5 result.push([...path]);
6 return;
7 }
8 for (const num of nums) {
9 if (!path.includes(num)) {
10 path.push(num);
11 backtrack(path);
12 path.pop();
13 }
14 }
15 };
16 backtrack([]);
17 return result;
18}
19
20console.log(permute([1, 2, 3]));
21This JavaScript implementation creates permutations using a recursive backtracking approach. A temporary path array is used to store current permutations, and once a complete permutation is built, it is added to the results.
An alternative iterative approach utilizes a queue to generate permutations level by level by inserting each number at every possible position within every possible permutation.
Time Complexity: O(n * n!), iterating through permutations.
Space Complexity: O(n!) for storing permutations, constant space for current permutation array.
1#
This C implementation illustrates an iterative method for generating permutations using a next permutation generator. Each permutation is based on modifying and reversing array segments to derive the next permutation sequence, iteratively processed.