The given `myPow` function is an implementation of a recursive...

The given myPow function is an implementation of a recursive algorithm to calculate (x^n) (x raised to the power n). Here is an explanation of what the code does and a potential issue:

Code Explanation:

1. Base Cases:

   • If (x = 1) or (n = 0), the result is (1) because any number raised to the power of 0 is 1, and 1 raised to any power is 1.
   • If (n = 1), the function directly returns (x) because any number to the power of 1 is itself.

2. Handling Negative Powers:

   • If (n < 0), the function computes the reciprocal of (x^n) (i.e., (1 / x^{-n})).
   • Note that the absolute value of (n) ((-n)) is passed recursively.

3. Recursive Case for Even (n):

   • If (n) is even ((n % 2 == 0)), the function reduces the problem by computing (x^{n/2}) instead of multiplying (x) (n) times. This optimization reduces the work to logarithmic levels.

4. Recursive Case for Odd (n):

   • If (n) is odd, the function computes (x) times (x^{n-1}) recursively.

This algorithm reduces the complexity to (O(\log n)), which is efficient compared to a naive (O(n)) approach.

Problem in the Code:

1. Integer Overflow for n with Large Negative Values:

   • If (n = \text{INT_MIN}) (the smallest possible 32-bit integer, -2,147,483,648), the expression (-n) will cause an integer overflow because (-(-2,147,483,648)) is (2,147,483,648), which cannot be stored in a 32-bit signed integer.
   • This will lead to undefined behavior or incorrect results.

   Fix for this issue: Before negating (n), you can handle the case when (n = \text{INT_MIN}) explicitly:

   if (n < 0) {
       if (n == INT_MIN) {
           return 1 / (myPow(x, INT_MAX) * x);
       }
       return 1 / myPow(x, -n);
   }
   

2. Precision Issues for Large (n):

   • For very large (n), repeated multiplications (even optimized) can result in floating-point precision errors.

Correctness in Edge Cases:

To ensure the code works well for all cases:

• Explicitly handle cases like (x = 0, n < 0) (division by zero error).
• Handle (n = \text{INT_MIN}) as described above.