2311. Longest Binary Subsequence Less Than or Equal to K

Problem

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 <= 10^9

Solution (Java)

class Solution {
    public int longestSubsequence(String s, int k) {
        int res = 0;
        int cost = 1;
        int n = s.length();
        for (int i = n - 1; i >= 0; i--) {
            if (s.charAt(i) == '0' || cost <= k) {
                k -= cost * (s.charAt(i) - '0');
                ++res;
            }
            if (cost <= k) {
                cost *= 2;
            }
        }
        return res;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).