Leetcode #81: Search in Rotated Sorted Array II
In this guide, we solve Leetcode #81 Search in Rotated Sorted Array 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
There is an integer array nums sorted in non-decreasing order (not necessarily with distinct values). Before being passed to your function, nums is rotated at an unknown pivot index k (0 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed).
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Binary Search
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums = [2,5,6,0,0,1,2], target = 0
Output: true
Python Solution
class Solution:
def search(self, nums: List[int], target: int) -> bool:
n = len(nums)
l, r = 0, n - 1
while l < r:
mid = (l + r) >> 1
if nums[mid] > nums[r]:
if nums[l] <= target <= nums[mid]:
r = mid
else:
l = mid + 1
elif nums[mid] < nums[r]:
if nums[mid] < target <= nums[r]:
l = mid + 1
else:
r = mid
else:
r -= 1
return nums[l] == target
Complexity
The time complexity is , where is the length of the array. The space complexity is .
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.