0091__decode_ways.py

"""
LeetCode: https://leetcode.com/problems/decode-ways/

[[Blind75]]

A message containing letters from A-Z can be encoded into numbers using the following mapping:

'A' -> "1"
'B' -> "2"
...
'Z' -> "26"
To decode an encoded message, all the digits must be grouped then mapped back into letters using the reverse of the
mapping above (there may be multiple ways). For example, "11106" can be mapped into:

* "AAJF" with the grouping (1 1 10 6)
* "KJF" with the grouping (11 10 6)

Note that the grouping (1 11 06) is invalid because "06" cannot be mapped into 'F' since "6" is different from "06".

Given a string s containing only digits, return the number of ways to decode it.

The test cases are generated so that the answer fits in a 32-bit integer.

## Example 1

Input: s = "12"
Output: 2
Explanation: "12" could be decoded as "AB" (1 2) or "L" (12).

## Example 2

Input: s = "226"
Output: 3
Explanation: "226" could be decoded as "BZ" (2 26), "VF" (22 6), or "BBF" (2 2 6).

## Example 3

Input: s = "06"
Output: 0
Explanation: "06" cannot be mapped to "F" because of the leading zero ("6" is different from "06").

## Constraints

* 1 <= s.length <= 100
* s contains only digits and may contain leading zero(s).
"""
from typing import Dict
from unittest import TestCase


class Solution(TestCase):
    def test_it(self):
        options = [
            ("example 1", 2, "12"),
            ("example 2", 3, "226"),
            ("example 3 (leading zero)", 0, "06"),
            ("a lot of 1s", 10946, "1" * 20),
            ("a lot of 1s v2", 5702887, "1" * 33),
            ("999", 1, "999"),
        ]

        for name, expected, string in options:
            with self.subTest(name):
                self.assertEqual(expected, self.numDecodings(string))

    def numDecodings(self, s: str) -> int:
        if s[0] == "0":
            return 0

        cache: Dict[int, int] = {}

        def dfs(start_with: int) -> int:
            if start_with in cache:
                return cache[start_with]

            if start_with == len(s):
                return 1

            if s[start_with] == "0":
                return 0

            res = dfs(start_with + 1)

            if start_with + 1 < len(s) and int(s[start_with:start_with + 2]) <= 26:
                res += dfs(start_with + 2)

            cache[start_with] = res

            return res

        return dfs(0)