MediumLeetCode #33Binary Search

Search in Rotated Sorted Array

There is an integer array nums sorted in ascending order (with distinct values). Prior to being passed to your function, nums is possibly rotated at an unknown pivot. Given the array nums after rotation and an integer target, return the index of target if it is in nums, or -1 if it is not in nums.

Constraints

1 <= nums.length <= 5000, -10^4 <= nums[i] <= 10^4, All values of nums are unique

Examples

Input: nums = [4,5,6,7,0,1,2], target = 0

Output: 4

Solution Approach

Divide problem into subproblems, solve each recursively, combine results. Classic examples: merge sort, quick sort, binary tree problems.

Implementation

def mergeSort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = mergeSort(arr[:mid])
    right = mergeSort(arr[mid:])
    return merge(left, right)

def merge(left, right):
    result = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1
    return result + left[i:] + right[j:]

Complexity Analysis

Time Complexity

O(n log n)

Space Complexity

O(n)

Key Learning Points

Divide into subproblemsRecursive solutionCombine subresults