Number of Good Binary Strings — LeetCode 2533 Python Solution

The problem

You are given four integers minLength, maxLength, oneGroup and zeroGroup. A binary string is good if it satisfies the following conditions: The length of the string is in the range [minLength, maxLength].

Example

Input

minLength = 2, maxLength = 3, oneGroup = 1, zeroGroup = 2

Output

5

Explanation

There are 5 good binary strings in this example: "00", "11", "001", "100", and "111".

Python solution

class Solution:
    def goodBinaryStrings(
        self, minLength: int, maxLength: int, oneGroup: int, zeroGroup: int
    ) -> int:
        mod = 10**9 + 7
        f = [1] + [0] * maxLength
        for i in range(1, len(f)):
            if i - oneGroup >= 0:
                f[i] += f[i - oneGroup]
            if i - zeroGroup >= 0:
                f[i] += f[i - zeroGroup]
            f[i] %= mod
        return sum(f[minLength:]) % mod

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2533. Number of Good Binary Strings is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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