Leetcode #2533: Number of Good Binary Strings
In this guide, we solve Leetcode #2533 Number of Good Binary Strings in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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].
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
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".
It can be proven that there are only 5 good strings satisfying all conditions.
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
The time complexity is , and the space complexity is , where . The space complexity is , where .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.