Leetcode #2961: Double Modular Exponentiation

In this guide, we solve Leetcode #2961 Double Modular Exponentiation in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Leetcode

Problem Statement

You are given a 0-indexed 2D array variables where variables[i] = [ai, bi, ci, mi], and an integer target. An index i is good if the following formula holds: 0 <= i < variables.length ((aibi % 10)ci) % mi == target Return an array consisting of good indices in any order.

Quick Facts

Difficulty: Medium
Premium: No
Tags: Array, Math, Simulation

Intuition

There is a mathematical invariant or formula that directly leads to the result.

Using math avoids unnecessary loops and reduces complexity.

Approach

Derive the formula or update rule, then compute the answer directly.

Handle edge cases like overflow or zero carefully.

Steps:

Identify the math relationship.
Compute the result with a loop or formula.
Handle edge cases.

Example

Input: variables = [[2,3,3,10],[3,3,3,1],[6,1,1,4]], target = 2
Output: [0,2]
Explanation: For each index i in the variables array:
1) For the index 0, variables[0] = [2,3,3,10], (23 % 10)3 % 10 = 2.
2) For the index 1, variables[1] = [3,3,3,1], (33 % 10)3 % 1 = 0.
3) For the index 2, variables[2] = [6,1,1,4], (61 % 10)1 % 4 = 2.
Therefore we return [0,2] as the answer.

Python Solution

class Solution:
    def getGoodIndices(self, variables: List[List[int]], target: int) -> List[int]:
        return [
            i
            for i, (a, b, c, m) in enumerate(variables)
            if pow(pow(a, b, 10), c, m) == target
        ]

Complexity

The time complexity is $O(n \times \log M)$ , where $n$ is the length of the array $variables$ ; and $M$ is the maximum value in $b_i$ and $c_i$ , in this problem $M \le 10^3$ . The space complexity is $O(1)$ .

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.

Example

Input: variables = [[2,3,3,10],[3,3,3,1],[6,1,1,4]], target = 2
Output: [0,2]
Explanation: For each index i in the variables array:
1) For the index 0, variables[0] = [2,3,3,10], (23 % 10)3 % 10 = 2.
2) For the index 1, variables[1] = [3,3,3,1], (33 % 10)3 % 1 = 0.
3) For the index 2, variables[2] = [6,1,1,4], (61 % 10)1 % 4 = 2.
Therefore we return [0,2] as the answer.

Leetcode #2961: Double Modular Exponentiation

Problem Statement

Quick Facts

Intuition

Approach

Example

Python Solution

Complexity

Edge Cases and Pitfalls

Summary

Ace your next coding interview

Leetcode #2961: Double Modular Exponentiation

Problem Statement

Quick Facts

Intuition

Approach

Example

Python Solution

Complexity

Edge Cases and Pitfalls

Summary

Ace your next coding interview