How to Find the Kth Permutation Sequence of a Given Set of Numbers?

How can I calculate the kth permutation sequence for a set of numbers from 1 to n?

int factorial(int n) { return (n == 0) ? 1 : n * factorial(n - 1); }

The kth permutation sequence of a set of numbers is a specific arrangement of those numbers based on the lexicographical ordering of all possible permutations. To derive this sequence, we can use a mathematical approach that relies on factorials to determine the indexes of the numbers to be used for each position in the permutation sequence.

class Solution {
    public String getPermutation(int n, int k) {
        List<Integer> numbers = new ArrayList<>();
        for (int i = 1; i <= n; i++) {
            numbers.add(i);
        }
        StringBuilder permutation = new StringBuilder();
        k--; // Convert k to 0-based index
        int[] factorials = new int[n];
        factorials[0] = 1;
        for (int i = 1; i < n; i++) {
            factorials[i] = factorials[i - 1] * i;
        }
        for (int i = n; i > 0; i--) {
            int index = k / factorials[i - 1];
            permutation.append(numbers.get(index));
            numbers.remove(index);
            k -= index * factorials[i - 1];
        }
        return permutation.toString();
    }
}

Causes

• Understanding permutations and their lexicographical order is essential.
• The problem involves mathematical reasoning based on permutations.

Solutions

• Calculate the factorial of the numbers to determine how many permutations can be formed with the remaining numbers.
• Use the factorial values to determine the index of the next number in the permutation sequence.

Mistake: Not adjusting k to be zero-based indexing.

Solution: Always subtract 1 from k to convert it to zero-based indexing before proceeding.

Mistake: Incorrectly calculating factorial values or using them inadequately.

Solution: Ensure that factorials are pre-computed and used for indexing correctly.