The Super Pow coding problem is a mathematical challenge where you need to calculate a^b mod 1337. The twist is that a is an integer, but b is given as a very large array of digits (e.g., b = [1, 2, 3] means b = 123). Because b can be extremely large, you cannot calculate the power directly. You must use properties of modular arithmetic and recursion to break the problem into smaller, manageable pieces.
This question is asked by companies like Google and Apple to test a candidate's grasp of modular arithmetic and the Divide and Conquer strategy. It requires more than just coding skills; it requires an understanding of mathematical properties like (x * y) % n = ((x % n) * (y % n)) % n. It also checks if you can implement power functions efficiently (logarithmic time) and handle recursion over an array of digits.
The primary algorithmic pattern is Divide and Conquer, specifically combined with Modular Exponentiation. The logic follows the rule: a^[1, 2, 3] = (a^[1, 2])^10 * a^3. This recursive formula allows you to process the array b one digit at a time from right to left (or left to right). At each step, you need a helper function to calculate x^y mod 1337 where y is a small number (0-10), which can be done efficiently using binary exponentiation.
Calculate 2^[1, 2] mod 1337.
This is 2^12 mod 1337.
Using the recursion: 2^12 = (2^1)^10 * 2^2.
2^1 = 22^10 = 10242^2 = 4(1024 * 4) % 1337 = 4096 % 1337.
4096 = 3 * 1337 + 85.
So the result is 85.
By breaking 12 into (1)*10 + 2, we simplified the exponentiation into smaller powers.A common mistake is not applying the modulo at every multiplication step, which leads to integer overflow even before the final result is reached. Another error is implementing the power function with O(n) complexity instead of O(log n), which might be too slow if the exponent digits are large. Some also struggle with the recursive structure, specifically how to correctly reduce the array b in each step.
When studying for the Super Pow interview question, review the properties of exponents and modular arithmetic. Practice implementing the "Power" function using binary exponentiation (square and multiply). This is a foundational skill for many cryptography and math-related coding problems. Understanding the Divide and Conquer interview pattern will help you structure the recursion for the array of digits correctly.
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