2466. Count Ways To Build Good Strings

Description

Given the integers zero, one, low, and high, we can construct a string by starting with an empty string, and then at each step perform either of the following:

• Append the character '0' zero times.
• Append the character '1' one times.

This can be performed any number of times.

A good string is a string constructed by the above process having a length between low and high (inclusive).

Return the number of different good strings that can be constructed satisfying these properties. Since the answer can be large, return it modulo 109 + 7.

 

Example 1:

Input: low = 3, high = 3, zero = 1, one = 1
Output: 8
Explanation: 
One possible valid good string is "011". 
It can be constructed as follows: "" -> "0" -> "01" -> "011". 
All binary strings from "000" to "111" are good strings in this example.

Example 2:

Input: low = 2, high = 3, zero = 1, one = 2
Output: 5
Explanation: The good strings are "00", "11", "000", "110", and "011".

 

Constraints:

• 1 <= low <= high <= 105
• 1 <= zero, one <= low

Solution

count-ways-to-build-good-strings.py

class Solution:
    def countGoodStrings(self, low: int, high: int, zero: int, one: int) -> int:
        M = 10 ** 9 + 7

        @cache
        def go(k):
            if k > high: return 0

            res = 0

            if low <= k <= high:
                res += 1

            return (res + go(k + zero) + go(k + one)) % M

        return go(0)