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First and Last Position in Sorted Array

Certification: Basic Level Accuracy: 100% Submissions: 2 Points: 5

Write a Java program to find the first and last position of a given target value in a sorted array of integers. If the target is not found in the array, return [-1, -1]. You must write an algorithm with O(log n) runtime complexity.

Example 1
     
  • Input: nums = [5,7,7,8,8,10], target = 8
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  • Output: [3, 4]
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  • Explanation: 
       
    • Step 1: Use binary search to find the first occurrence of the target value.
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    • Step 2: When found, continue searching in the left subarray to find the leftmost position.
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    • Step 3: Use another binary search to find the last occurrence of the target value.
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    • Step 4: When found, continue searching in the right subarray to find the rightmost position.
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    • Step 5: For target 8, the first position is at index 3 and the last position is at index 4.
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    •
Example 2
     
  • Input: nums = [5,7,7,8,8,10], target = 6
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  • Output: [-1, -1]
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  • Explanation: 
       
    • Step 1: Apply binary search to find the target value 6.
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    • Step 2: After the binary search completes, determine that 6 does not exist in the array.
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    • Step 3: Since the target is not found, we cannot determine first or last positions.
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    • Step 4: Return [-1, -1] to indicate the target is not present in the array.
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Constraints
     
  • 0 ≤ nums.length ≤ 10^5
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  • -10^9 ≤ nums[i] ≤ 10^9
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  • nums is a non-decreasing array
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  • -10^9 ≤ target ≤ 10^9
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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 binary search twice: once to find the first occurrence and once to find the last occurrence
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  • For finding the first occurrence, when the middle element equals the target, check if it's the first element or if the previous element is different
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  • For finding the last occurrence, when the middle element equals the target, check if it's the last element or if the next element is different
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  • Modify the binary search to handle the case where the target doesn't exist in the array
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  • Be careful with the boundary conditions during binary search
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Steps to solve by this approach:

 Step 1: Handle the edge case where the input array is empty or null.
 Step 2: Perform a binary search to find the first occurrence of the target.
 Step 3: If the target is found and it's either at index 0 or the previous element is different, mark it as the first occurrence.
 Step 4: If the target is not found during the first binary search, return [-1, -1].
 Step 5: Perform another binary search starting from the first occurrence to find the last occurrence.
 Step 6: If the target is found and it's either at the last index or the next element is different, mark it as the last occurrence.
 Step 7: Return the array containing the first and last positions of the target.

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