Leetcode #912: Sort an Array
In this guide, we solve Leetcode #912 Sort an Array 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 an array of integers nums, sort the array in ascending order and return it. You must solve the problem without using any built-in functions in O(nlog(n)) time complexity and with the smallest space complexity possible.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Divide and Conquer, Bucket Sort, Counting Sort, Radix Sort, Sorting, Heap (Priority Queue), Merge Sort
Intuition
We need to repeatedly access the smallest or largest element as the input changes.
A heap provides fast insertions and removals while keeping order.
Approach
Push candidates into the heap as you scan, and pop when you need the best element.
Keep the heap size bounded if the problem requires a top-k structure.
Steps:
- Push candidates into a heap.
- Pop the best candidate when needed.
- Maintain heap size or invariants.
Example
Input: nums = [5,2,3,1]
Output: [1,2,3,5]
Explanation: After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5).
Python Solution
class Solution:
def sortArray(self, nums: List[int]) -> List[int]:
def quick_sort(l, r):
if l >= r:
return
x = nums[randint(l, r)]
i, j, k = l - 1, r + 1, l
while k < j:
if nums[k] < x:
nums[i + 1], nums[k] = nums[k], nums[i + 1]
i, k = i + 1, k + 1
elif nums[k] > x:
j -= 1
nums[j], nums[k] = nums[k], nums[j]
else:
k = k + 1
quick_sort(l, i)
quick_sort(j, r)
quick_sort(0, len(nums) - 1)
return nums
Complexity
The time complexity is O(n log n). The space complexity is O(n).
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.