Question

Formatted question description: https://leetcode.ca/all/372.html

 372	Super Pow

 Your task is to calculate: a^b mod 1337
 where a is a positive integer and b is an extremely large positive integer given in the form of an array.

 Example 1:

 Input: a = 2, b = [3]
 Output: 8

 Example 2:

 Input: a = 2, b = [1,0]
 Output: 1024

Algorithm

Related maths

        a^b % 1337 = (a%1337)^b % 1337

        xy % 1337 = ((x%1337) * (y%1337)) % 1337

Reduced by half, the difference is that the remainder of 1337 is added. Since the given exponent b is a representation of a one-dimensional array, it must be very inconvenient to deal with it if we halve it.

So we use bitwise processing, such as 2^23 = (2^2)^10 * 2^3, so we can start from the highest bit of b, calculate a result and store it in res, and then go to the next bit , The tenth power of res is multiplied by the power of a and the remainder is 1337.

Code

Java

public class Super_Pow {

    class Solution {

        // 2^23 = (2^2)^10 * 2^3
        public int superPow(int a, int[] b) {

            int res = 1;
            for (int i = 0; i < b.length; ++i) {
                res = pow(res, 10) * pow(a, b[i]) % 1337;
            }
            return res;
        }

        int pow(int x, int n) {
            if (n == 0) return 1;
            if (n == 1) return x % 1337;
            return pow(x % 1337, n / 2) * pow(x % 1337, n - n / 2) % 1337;
        }
    }
}

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