Leetcode #2450: Number of Distinct Binary Strings After Applying Operations
In this guide, we solve Leetcode #2450 Number of Distinct Binary Strings After Applying Operations 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 a binary string s and a positive integer k. You can apply the following operation on the string any number of times: Choose any substring of size k from s and flip all its characters, that is, turn all 1's into 0's, and all 0's into 1's.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Math, String
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
Example
Input: s = "1001", k = 3
Output: 4
Explanation: We can obtain the following strings:
- Applying no operation on the string gives s = "1001".
- Applying one operation on the substring starting at index 0 gives s = "0111".
- Applying one operation on the substring starting at index 1 gives s = "1110".
- Applying one operation on both the substrings starting at indices 0 and 1 gives s = "0000".
It can be shown that we cannot obtain any other string, so the answer is 4.
Python Solution
class Solution:
def countDistinctStrings(self, s: str, k: int) -> int:
return pow(2, len(s) - k + 1) % (10**9 + 7)
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.