Count Good Numbers — LeetCode 1922 Python Solution

The problem

A digit string is good if the digits (0-indexed) at even indices are even and the digits at odd indices are prime (2, 3, 5, or 7). For example, "2582" is good because the digits (2 and 8) at even positions are even and the digits (5 and 2) at odd positions are prime.

Example

Input

n = 1

Output

5

Explanation

The good numbers of length 1 are "0", "2", "4", "6", "8".

Python solution

class Solution:
    def countGoodNumbers(self, n: int) -> int:
        mod = 10**9 + 7
        return pow(5, (n + 1) >> 1, mod) * pow(4, n >> 1, mod) % mod

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1922. Count Good Numbers is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

Related problems