884385. Implement Pow
Implement Pow
Slug: powx-n
Difficulty: Medium
Id: 884385
Summary
The problem is about implementing the pow function, which calculates the power of a given number to a specified exponent. The key concept involved is exponentiation.
Detailed Explanation
To solve this problem, we can use the property of exponentiation that states a^(b+c) = (a^b) * (a^c). This allows us to break down the calculation into smaller sub-problems and avoid calculating the same intermediate values multiple times. We can also take advantage of the fact that 0^x is always 0 and 1^x is always 1.
Here's a step-by-step breakdown of the solution:
- If the exponent is even, calculate
(x^(exponent/2))^2. This reduces the problem size by half. - If the exponent is odd, calculate
x * (x^(exponent-1)). - Repeat steps 1 and 2 until the exponent is reduced to 0 or 1.
The time complexity of this solution is O(log n), where n is the exponent. This is because we divide the problem size by half in each step, effectively reducing it logarithmically.
The space complexity is O(1), as we only use a constant amount of space to store intermediate results.
Optimized Solutions
Java
public double myPow(double x, int y) {
if (y < 0) {
return 1 / myPow(x, -y);
}
if (y == 0) {
return 1;
}
if (y % 2 == 0) {
return myPow(x * x, y / 2);
} else {
return x * myPow(x, y - 1);
}
}