Beautiful Arrangement II — LeetCode 667 Python Solution

The problem

Given two integers n and k, construct a list answer that contains n different positive integers ranging from 1 to n and obeys the following requirement: Suppose this list is answer = [a1, a2, a3, ... , an], then the list [|a1 - a2|, |a2 - a3|, |a3 - a4|, ...

Example

Input

n = 3, k = 1

Output

[1,2,3]

Explanation

The [1,2,3] has three different positive integers ranging from 1 to 3, and the [1,1] has exactly 1 distinct integer: 1

Python solution

class Solution:
    def constructArray(self, n: int, k: int) -> List[int]:
        l, r = 1, n
        ans = []
        for i in range(k):
            if i % 2 == 0:
                ans.append(l)
                l += 1
            else:
                ans.append(r)
                r -= 1
        for i in range(k, n):
            if k % 2 == 0:
                ans.append(r)
                r -= 1
            else:
                ans.append(l)
                l += 1
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 667. Beautiful Arrangement II 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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