LeetCode 46. Permutations

🧩 Problem Description

Given an array nums of distinct integers, return all the possible permutations.
You can return the answer in any order.

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💬 Example

Input: nums = [1,2,3]
Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]

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💡 Approach: Backtracking

We use backtracking to generate all permutations by swapping elements or by building a temporary path with used flags.

🔢 Java Code

import java.util.*;

class Solution {
    public List<List<Integer>> permute(int[] nums) {
        List<List<Integer>> result = new ArrayList<>();
        backtrack(nums, new ArrayList<>(), new boolean[nums.length], result);
        return result;
    }

    private void backtrack(int[] nums, List<Integer> path, boolean[] used, List<List<Integer>> result) {
        if (path.size() == nums.length) {
            result.add(new ArrayList<>(path));
            return;
        }
        for (int i = 0; i < nums.length; i++) {
            if (used[i]) continue;
            used[i] = true;
            path.add(nums[i]);
            backtrack(nums, path, used, result);
            path.remove(path.size() - 1);
            used[i] = false;
        }
    }
}

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⏱ Complexity Analysis

• Time: O(n × n!) → each permutation takes O(n) to build, total n! permutations
• Space: O(n) recursion depth + O(n) used flags

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✍️ Summary

• Classic backtracking problem.
• Generates all n! permutations.
• Useful in problems involving ordering, scheduling, or searching solution spaces.

Related problems:

• lc-47 — Permutations II (with duplicates)
• lc-77 — Combinations
• lc-78 — Subsets
• lc-90 — Subsets II