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Search in Rotated Sorted Array

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C program to search for a target value in a rotated sorted array. A rotated sorted array is an array that was once sorted in ascending order but has been rotated at some pivot point. For example, [0,1,2,4,5,6,7] might become [4,5,6,7,0,1,2]. You need to find the index of the target value in the array, or -1 if it's not found. Your algorithm should have a time complexity of O(log n).

Example 1
    
  
  • Input: nums = [4,5,6,7,0,1,2], target = 0
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  • Output: 4
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  • Explanation: The original sorted array [0,1,2,4,5,6,7] was rotated at pivot point 4. The resulting array is [4,5,6,7,0,1,2]. We find that 0 is at index 4.
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Example 2
    
  
  • Input: nums = [4,5,6,7,0,1,2], target = 3
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  • Output: -1
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  • Explanation: The array [4,5,6,7,0,1,2] does not contain the value 3. After searching through the entire array, we don't find the target.
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Constraints
    
  
  • 1 <= nums.length <= 5000
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  • -10^4 <= nums[i] <= 10^4
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  • All values in nums are unique
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  • nums is guaranteed to be rotated at some pivot
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  • -10^4 <= target <= 10^4
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  • Time Complexity: O(log n)
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  • Space Complexity: O(1)
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Hint
Solution

Solution Hints

    
  
  • Use a modified binary search algorithm
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  • In a standard binary search, we check if the middle element equals the target
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  • In a rotated array, we first need to determine which half is sorted
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  • If the left half is sorted, check if the target is within that range, otherwise search the right half
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  • If the right half is sorted, check if the target is within that range, otherwise search the left half
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  • Continue until you find the target or determine it doesn't exist
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Steps to solve by this approach:

 Step 1: Use binary search but modify it to handle the rotation aspect of the array.

 Step 2: Find the middle element and check if it matches the target value.

 Step 3: Determine which half of the array is sorted (either left half or right half must be sorted).

 Step 4: If the left half is sorted (nums[left] <= nums[mid]), check if the target lies in this sorted range.

 Step 5: If the target is in the sorted range, narrow the search to that half; otherwise, search the other half.

 Step 6: If the right half is sorted (nums[mid] < nums[right]), apply similar logic to check if the target is in this range.

 Step 7: Continue narrowing the search range until we either find the target or determine it's not in the array.

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