Leetcode #667: Beautiful Arrangement II
In this guide, we solve Leetcode #667 Beautiful Arrangement II in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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|, ...
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Math
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
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
The time complexity is O(n) or O(1). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.