Pow Recursion Algorithm
The Pow Recursion Algorithm is an efficient method for calculating the power of a number using a divide-and-conquer strategy. This algorithm takes two input parameters: a base number (x) and an exponent (n) and computes the result of raising the base number to the power of the exponent (x^n). The key insight behind the Pow Recursion Algorithm is that the problem of computing x^n can be broken down into smaller subproblems, which can be solved recursively. This allows the algorithm to reduce the number of multiplications required to compute the result, resulting in improved performance compared to the naive approach of performing n-1 multiplications.
To compute x^n using the Pow Recursion Algorithm, the algorithm first checks if the exponent n is even or odd. If n is even, the algorithm computes the result of x^(n/2) and multiplies this result by itself, effectively computing x^n = (x^(n/2))^2. If n is odd, the algorithm computes the result of x^((n-1)/2) and multiplies this result by itself and then by x, effectively computing x^n = x * (x^((n-1)/2))^2. By dividing the exponent by 2 at each step, the Pow Recursion Algorithm drastically reduces the number of multiplications required to compute the final result, resulting in a more efficient algorithm with a time complexity of O(log n).
package Maths;
public class PowRecursion {
public static void main(String[] args) {
assert pow(2, 0) == Math.pow(2, 0);
assert pow(0, 2) == Math.pow(0, 2);
assert pow(2, 10) == Math.pow(2, 10);
assert pow(10, 2) == Math.pow(10, 2);
}
/**
* Returns the value of the first argument raised to the power of the
* second argument
*
* @param a the base.
* @param b the exponent.
* @return the value {@code a}<sup>{@code b}</sup>.
*/
public static long pow(int a, int b) {
if (b == 0) {
return 1;
} else {
return a * pow(a, b - 1);
}
}
}
