Permutation Sequence — LeetCode 60 Python Solution

The problem

The set [1, 2, 3, ..., n] contains a total of n! unique permutations.

Example

Input

n = 3, k = 3

Output

"213"

Python solution

class Solution:
    def getPermutation(self, n: int, k: int) -> str:
        ans = []
        vis = [False] * (n + 1)
        for i in range(n):
            fact = 1
            for j in range(1, n - i):
                fact *= j
            for j in range(1, n + 1):
                if not vis[j]:
                    if k > fact:
                        k -= fact
                    else:
                        ans.append(str(j))
                        vis[j] = True
                        break
        return ''.join(ans)

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 60. Permutation Sequence is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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