2466.Count Ways To Build Good Strings

tags: Medium,DP

2466. Count Ways To Build Good Strings

題目描述

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.

範例

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

解答

Reference

Python

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

Yen-Chi ChenSat, May 13, 2023

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