Permutations - Problem
Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order.
A permutation is a rearrangement of all elements in the array where each element appears exactly once in a different order.
Input & Output
Example 1 — Basic Three Elements
$
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]]
💡 Note:
All 6 possible arrangements of [1,2,3]: start with each element, then arrange the remaining two elements in all possible ways
Example 2 — Two Elements
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Input:
nums = [0,1]
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Output:
[[0,1],[1,0]]
💡 Note:
Only 2 possible arrangements: [0,1] and [1,0]. With 2 elements, we have 2! = 2 permutations
Example 3 — Single Element
$
Input:
nums = [1]
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Output:
[[1]]
💡 Note:
With only one element, there's only one possible arrangement: [1]. 1! = 1 permutation
Constraints
- 1 ≤ nums.length ≤ 6
- -10 ≤ nums[i] ≤ 10
- All the integers of nums are unique
Visualization
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Understanding the Visualization
1
Input
Array of distinct integers [1,2,3]
2
Process
Generate all possible arrangements using backtracking
3
Output
All 6 permutations in 2D array format
Key Takeaway
🎯 Key Insight: Use backtracking to systematically explore all possible arrangements by making choices and undoing them
💡
Explanation
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// Output will appear here after running code