Here is what each function in your code does: 1. **`bool...

Here is what each function in your code does:

1. bool isPowerOfTwo(long n):

   • This function determines if the integer n is a power of two.
   • It works by checking two conditions:
     1. n > 0: Ensures the number is positive.
     2. (n & (n - 1)) == 0: Uses bitwise AND to verify that n has only a single bit set (a property of powers of two).
   • Example:
     • isPowerOfTwo(4) → true (4 is (2^2)).
     • isPowerOfTwo(6) → false.

2. long lowerPowerOfTwo(const long &n):

   • This function finds the largest power of two less than or equal to the input n.
   • It iteratively doubles currentPower (starting at 1) until it exceeds n, then returns the previous value (currentPower / 2).
   • Example:
     • lowerPowerOfTwo(15) → 8 (largest power of two ≤ 15).
     • lowerPowerOfTwo(20) → 16.

3. int findMedian(std::vector<int> numbers):

   • This function calculates the median of a vector of integers.
   • Steps:
     1. Sorts the vector in ascending order.
     2. Finds the median using the size of the vector:
        • If the size is odd, returns the middle element.
        • If the size is even, returns the average of the two middle elements.
   • Example:
     • findMedian({1, 3, 2}) → 2 (sorted: {1, 2, 3}, median is 2).
     • findMedian({4, 2, 1, 3}) → 2.5 (sorted: {1, 2, 3, 4}, median is (2 + 3) / 2).

4. int intSize(int x):

   • This function calculates the number of digits in a positive integer x.
   • It does so by repeatedly dividing x by 10 and incrementing size until x becomes less than 1.
   • Example:
     • intSize(1) → 1 (1 has 1 digit).
     • intSize(1234) → 4 (1234 has 4 digits).
     • Note: Negative numbers are not explicitly handled, so for negatives, the behavior may not be as intended.