2311 Longest Binary Subsequence Less Than or Equal to K

You are given a binary string s and a positive integer k.

Return the length of the longest subsequence of s that makes up a binary number less than or equal to k.

Note:

• The subsequence can contain leading zeroes.
• The empty string is considered to be equal to 0.
• A subsequence is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.

Example 1:

Input: s = "1001010", k = 5
Output: 5
Explanation: The longest subsequence of s that makes up a binary number less than
or equal to 5 is "00010", as this number is equal to 2 in decimal.
Note that "00100" and "00101" are also possible, which are equal to 4 and 5
in decimal, respectively.
The length of this subsequence is 5, so 5 is returned.

Example 2:

Input: s = "00101001", k = 1
Output: 6
Explanation: "000001" is the longest subsequence of s that makes up a binary number
less than or equal to 1, as this number is equal to 1 in decimal.
The length of this subsequence is 6, so 6 is returned.

Constraints:

• 1 <= s.length <= 1000
• s[i] is either '0' or '1'.
• 1 <= k <= 109

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

class Solution:
    def longestSubsequence(self, s: str, k: int) -> int:
        n = len(s)
        count = 0
        current = 0
        for i in range(n-1, -1, -1):
            if s[i] == '0':
                count += 1
            elif current + 2 ** (n-1-i) <= k:
                count += 1
                current += 2 ** (n-1-i)
        return count