2311. Longest Binary Subsequence Less Than or Equal to K

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

 

Solutions

Solution: Greedy

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {string} s
 * @param {number} k
 * @return {number}
 */
const longestSubsequence = function (s, k) {
  const n = s.length;
  let power = 1;
  let current = 0;
  let result = 0;

  for (let index = n - 1; index >= 0; index--) {
    if (s[index] === '0') {
      result += 1;
    } else if (current + power <= k) {
      current += power;
      result += 1;
    }

    power *= 2;
  }

  return result;
};