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Binary Search

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C++ program that implements the binary search algorithm. The program should take a sorted array of integers and a target value as input, and return the index of the target value in the array. If the target value is not found, return -1.

Example 1
    

  • Input: 
  
      
    
    • array = [1, 3, 5, 7, 9, 11, 13]
      • 
    
    • target = 7
      • 
  
    

    • 

  • Output: 3
    • 

  • Explanation: 
  
      
    
    • Step 1: Initialize low = 0 and high = 6 (array length - 1).
      • 
    
    • Step 2: Calculate mid = (low + high) / 2 = 3.
      • 
    
    • Step 3: Compare array[mid] = 7 with target = 7. They are equal.
      • 
    
    • Step 4: Return mid = 3 as the index of the target element.
      • 
  
    

    •
Example 2
    

  • Input: 
  
      
    
    • array = [2, 4, 6, 8, 10]
      • 
    
    • target = 5
      • 
  
    

    • 

  • Output: -1
    • 

  • Explanation: 
  
      
    
    • Step 1: Initialize low = 0 and high = 4 (array length - 1).
      • 
    
    • Step 2: Calculate mid = (low + high) / 2 = 2.
      • 
    
    • Step 3: Compare array[mid] = 6 with target = 5. array[mid] > target.
      • 
    
    • Step 4: Set high = mid - 1 = 1.
      • 
    
    • Step 5: Calculate mid = (low + high) / 2 = 0.
      • 
    
    • Step 6: Compare array[mid] = 2 with target = 5. array[mid] < target.
      • 
    
    • Step 7: Set low = mid + 1 = 1.
      • 
    
    • Step 8: Calculate mid = (low + high) / 2 = 1.
      • 
    
    • Step 9: Compare array[mid] = 4 with target = 5. array[mid] < target.
      • 
    
    • Step 10: Set low = mid + 1 = 2.
      • 
    
    • Step 11: Now low > high, so target is not found.
      • 
    
    • Step 12: Return -1.
      • 
  
    

    •
Constraints
    

  • 1 ≤ array.length ≤ 10^6
    • 

  • The array is sorted in ascending order
    • 

  • -10^9 ≤ array[i] ≤ 10^9
    • 

  • Time Complexity: O(log n), where n is the length of the array
    • 

  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
  
  • Use two pointers (left and right) to keep track of the search range.
    • 
  
  • Calculate the middle index and compare the middle element with the target value.
    • 
  
  • If the middle element is equal to the target, return the middle index.
    • 
  
  • If the middle element is greater than the target, search in the left half.
    • 
  
  • If the middle element is less than the target, search in the right half.
    • 
  
  • Repeat the process until the target is found or the search range is empty.
    •

Steps to solve by this approach:

 Step 1: Initialize search boundaries to the full array.

 Step 2: Find the middle element of the current search space.

 Step 3: If the target equals the middle element, return its index.

 Step 4: If the target is greater, search in the right half.

 Step 5: If the target is smaller, search in the left half.

 Step 6: Repeat until the target is found or the search space is empty.

 Step 7: Return -1 if the target is not found in the array.

Submitted Code :