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2311. Longest Binary Subsequence Less Than or Equal to K

Difficulty Topics

Description

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

Solution

longest-binary-subsequence-less-than-or-equal-to-k.py
class Solution:
    def longestSubsequence(self, s: str, k: int) -> int:
        n = len(s)
        res = s.count("0")
        val = 0
        base = 1

        for x in s[::-1]:
            if val + base > k: break

            if x == "1":
                res += 1
                val += base

            base *= 2

        return res