2466. Count Ways To Build Good Strings

Problem Link

Description

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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

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Python3

class Solution:
    def countGoodStrings(self, low: int, high: int, zero: int, one: int) -> int:
        MOD = 10 ** 9 + 7
        dp = [0] * (high + 1)
        dp[0] = 1
        res = 0
 
        for i in range(high + 1):
            if i + zero <= high:
                dp[i + zero] = (dp[i + zero] + dp[i]) % MOD
            
            if i + one <= high:
                dp[i + one] = (dp[i + one] + dp[i]) % MOD
            
            if low <= i <= high:
                res += dp[i]
                res %= MOD
 
        return res