LeetCode 2450 LintCode 3841 Number of Distinct Binary Strings After Applying Operations

Table of contents

Description

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.

Return the number of distinct strings you can obtain. Since the answer may be too large, return it modulo 10^9 + 7.

Note that:

• A binary string is a string that consists only of the characters 0 and 1.
• A substring is a contiguous part of a string.

Example 1:

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.

Example 2:

Input: s = "10110", k = 5
Output: 2
Explanation: We can obtain the following strings:
- Applying no operation on the string gives s = "10110".
- Applying one operation on the whole string gives s = "01001".
It can be shown that we cannot obtain any other string, so the answer is 2.

Constraints:

• 1 <= k <= s.length <= 10^5
• s[i] is either 0 or 1.

Idea

let n = s.length

There are n-k+1 substrings of length k, and each substring can be flipped, so there are $2^{n-k+1}$ ways to flip.

Complexity: Time $O(n)$, Space $O(1)$.

Python

class Solution:
    """81 ms, 5.32 mb"""

    def count_distinct_strings(self, s: str, k: int) -> int:
        return pow(2, len(s) - k + 1) % (10 ** 9 + 7)

Java

class Solution {
    public static final int MOD = (int) 1e9 + 7;

    public int countDistinctStrings(String s, int k) {
        int ans = 1;
        for (int i = 0; i < s.length() - k + 1; i++) ans = (ans * 2) % MOD;
        return ans;
    }
}

C++

class Solution {
public:
    const int mod = 1e9 + 7;

    int countDistinctStrings(string s, int k) {
        int ans = 1;
        for (int i = 0; i < s.size() - k + 1; ++i) ans = (ans * 2) % mod;
        return ans;
    }
};