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# 31. Next Permutation

I did't know what next permutation really is but I have found some explanations on Wikipedia, and it helped.

## Quick Explanation

The explanation below is grab from next permutation section on Wikipedia.

1. Find the largest index `k` such that `a[k]` < `a[k+1]`. If no such index exist, the permutation is the last permutation.
2. Find the largest index `l` greater than `k` such that `a[k]` < `a[l]`.
3. Swap the value of `a[k]` with that of `a[l]`.
4. Reverse the sequence from `a[k+1]` up to and including th final element `a[n]`.

## Code

```class Solution {
func nextPermutation(_ nums: inout [Int]) {
// I have created methods for each step
let k = findLargestK(&nums) // ①
if k >= 0 {
let l = findLargestL(&nums, k) // ②
swap(&nums, k, l) // ③
}
reverse(&nums, k + 1) // ④
}

/// Find the largest index k such that a[k] < a[k+1].
/// If no such index exist, the permutation is the last permutation.
private func findLargestK(_ nums: inout [Int]) -> Int {
// We start from the back because we need to find a largest index.
// -2 for we need an extra space for k+1
var k = nums.count - 2

while k >= 0 && nums[k] >= nums[k+1] {
k -= 1
}

return k
}

/// Find the largest index l greater than k such that a[k] < a[l].
private func findLargestL(_ nums: inout [Int], _ k: Int) -> Int {
// We start from the back because we need to find a largest index.
var l = nums.count - 1

while l >= 0 && nums[k] >= nums[l] {
l -= 1
}

return l
}

private func swap(_ nums: inout [Int], _ a: Int, _ b: Int) {
let temp = nums[a]
nums[a] = nums[b]
nums[b] = temp
}

private func reverse(_ nums: inout [Int], _ start: Int) {
var lower = start
var upper = nums.count - 1

while lower < upper {
swap(&nums, lower, upper)
lower += 1
upper -= 1
}
}
}
```
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