Double Modular Exponentiation

Problem Description

You are given a 0-indexed 2D array variables where variables[i] = [a_i, b_i, c_i, m_i], and an integer target. An index i is good if the following formula holds:

((a_i^b_i % 10)^c_i) % m_i == target.

Return an array consisting of good indices in any order.

Key Insights

• The problem involves modular exponentiation, which can be computed efficiently using properties of modular arithmetic.
• The modulo operation with 10 simplifies the computation of a_i^b_i % 10, which only requires the last digit of the result.
• The exponentiation by c_i can also be simplified using properties of modularity.
• The constraints allow for straightforward iteration through the variables array since variables.length can be at most 100.

Space and Time Complexity

Time Complexity: O(n), where n is the number of variables.
Space Complexity: O(k), where k is the number of good indices to be returned.

Solution

The approach involves iterating through each entry in the variables array, calculating the values using modular exponentiation, and checking if the computed result matches the target. The final step is to collect all the indices that satisfy the condition.

Code Solutions