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Square Root Function

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

Write a Java program to compute and return the square root of a non-negative integer x, rounded down to the nearest integer (the floor value). You are not allowed to use any built-in square root function or operator.

Example 1
     
  • Input: x = 4
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  • Output: 2
    •  
  • Explanation: 
       
    • Step 1: Use binary search approach to find the square root of the integer.
      •  
    • Step 2: The search range is initially from 1 to x.
      •  
    • Step 3: For x = 4, the middle value is 2.
      •  
    • Step 4: Since 2 * 2 = 4, which equals x, return 2 as the answer.
      •  
    •
Example 2
     
  • Input: x = 8
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  • Output: 2
    •  
  • Explanation: 
       
    • Step 1: Use binary search approach to find the square root of the integer.
      •  
    • Step 2: The search range is initially from 1 to 8.
      •  
    • Step 3: For x = 8, we need to find the largest integer whose square is less than or equal to 8.
      •  
    • Step 4: Check 2: 2 * 2 = 4, which is less than 8.
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    • Step 5: Check 3: 3 * 3 = 9, which is greater than 8.
      •  
    • Step 6: Return 2 as the floor value of the square root of 8.
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    •
Constraints
     
  • 0 ≤ x ≤ 2^31 - 1
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  • You cannot use any built-in library function like Math.sqrt()
    •  
  • Time Complexity: O(log x)
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  • Space Complexity: O(1)
    •
NumberGoldman SachsSamsung
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Hint
Solution

Solution Hints

    
  
  • Use binary search to find the square root
    • 
  
  • Start with a search range from 1 to x
    • 
  
  • For each mid value, check if mid * mid is less than or equal to x
    • 
  
  • Be careful with integer overflow when calculating mid * mid
    • 
  
  • Return the largest integer whose square is less than or equal to x
    •

Steps to solve by this approach:

 Step 1: Handle the edge case where x is 0, return 0.
 Step 2: Use binary search with left = 1 and right = x to find the square root.
 Step 3: For each middle point (mid), compute mid * mid and compare it with x.
 Step 4: Use long type to avoid integer overflow when calculating mid * mid.
 Step 5: If mid * mid equals x, return mid as the exact square root.
 Step 6: If mid * mid is less than x, update left = mid + 1 and save mid as a potential result.
 Step 7: If mid * mid is greater than x, update right = mid - 1.

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