heyyy can you give the algorithm of power function O(logN) with space complexity, bestcase complexity and worstcase complexity ???

Sure, here is the algorithm for the power function with time complexity O(logN). This is also known as the "Exponentiation by Squaring" method.

Algorithm:

1. If the power is zero, return 1 because any number raised to the power of 0 is 1.
2. If the power is even, recursively calculate the power of half of the power and multiply it by itself.
3. If the power is odd, recursively calculate the power of half of the power, multiply it by itself and then multiply it by the base.

Here is a Python implementation of the algorithm:

def power(base, exponent):
    if exponent == 0:
        return 1
    elif exponent % 2 == 0:
        half_power = power(base, exponent // 2)
        return half_power * half_power
    else:
        half_power = power(base, exponent // 2)
        return base * half_power * half_power

Time Complexity:

• Best Case: O(1) when the power is 0.
• Worst Case: O(logN) where N is the power. This is because we are dividing the problem size by 2 in each recursive call.

Space Complexity:

• The space complexity is O(logN) because in the worst case, if the power is N, there will be logN recursive calls, and each call adds a level to the system stack.