526. Beautiful Arrangement

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true:

perm[i] is divisible by i.
i is divisible by perm[i].

Given an integer n, return the number of the beautiful arrangements that you can construct.

Example 1:

Input: n = 2
Output: 2
Explanation: 
The first beautiful arrangement is [1,2]:
    - perm[1] = 1 is divisible by i = 1
    - perm[2] = 2 is divisible by i = 2
The second beautiful arrangement is [2,1]:
    - perm[1] = 2 is divisible by i = 1
    - i = 2 is divisible by perm[2] = 1

Example 2:

Input: n = 1
Output: 1

Constraints:

1 <= n <= 15

🧠 Thuật Toán & Kỹ Thuật

Backtracking (Quay lui)

⏱️ Thời gian O(2ⁿ)

💾 Không gian O(n)

💻 Lời Giải

Python 0526-beautiful-arrangement.py

class Solution:
    def __init__(self):
        self.cnt = 0
        self.flag = []
        
    def backTracking(self, n, i):
        if i > n:
            self.cnt += 1
            return
        
        for j in range(1, n + 1):
            if not self.flag[j] and (i % j == 0 or j % i == 0):
                self.flag[j] = True
                self.backTracking(n, i + 1)
                self.flag[j] = False
        
    def countArrangement(self, n: int) -> int:
        self.flag = [False] * (n + 1)
        self.backTracking(n, 1)
        return self.cnt