Permutation Sequence (略)

The set

[1,2,3,…,n]

contains a total of n!
unique permutations.

By listing and labeling all of the permutations in order,

We get the following sequence (ie, for n = 3):

"123"

"132"

"213"

"231"

"312"

"321"

Given n and k, return the kth permutation sequence.

public String getPermutation(int n, int k) {
        int pos = 0;
        List<Integer> numbers = new ArrayList<>();
        int[] factorial = new int[n+1];
        StringBuilder sb = new StringBuilder();
        // create an array of factorial lookup
        int sum = 1;
        factorial[0] = 1;
        for(int i=1; i<=n; i++){
            sum *= i;
            factorial[i] = sum;
        }
        // factorial[] = {1, 1, 2, 6, 24, ... n!}
    
        // create a list of numbers to get indices
        for(int i=1; i<=n; i++){
            numbers.add(i);
        }
        // numbers = {1, 2, 3, 4}
        k--;
        for(int i = 1; i <= n; i++){
            int index = k/factorial[n-i];
            sb.append(String.valueOf(numbers.get(index)));
            numbers.remove(index);
            k-=index*factorial[n-i];
        }
        return String.valueOf(sb);
    }

详细解释：
https://leetcode.com/discuss/42700/explain-like-im-five-java-solution-in-o-n