Longest Ideal Subsequence Python Solution

LeetCode 2370, Medium. Topics: Hash Table, String, Dynamic Programming. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 27 parametrized pytest cases, and a playground notebook:

lcpy gen -n 2370   # by problem number
lcpy gen -s longest_ideal_subsequence   # by problem name

Problem

You are given a string s consisting of lowercase letters and an integer k. We call a string t ideal if the following conditions are satisfied:

t is a subsequence of the string s.
The absolute difference in the alphabet order of every two adjacent letters in t is less than or equal to k.

Return the length of the longest ideal string. 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. Note that the alphabet order is not cyclic. For example, the absolute difference in the alphabet order of 'a' and 'z' is 25, not 1.

Examples

Input: s = "acfgbd", k = 2
Output: 4

Explanation: The longest ideal string is "acbd". The length of this string is 4, so 4 is returned. Note that "acfgbd" is not ideal because 'c' and 'f' have a difference of 3 in alphabet order.

Input: s = "abcd", k = 3
Output: 4

Explanation: The longest ideal string is "abcd". The length of this string is 4, so 4 is returned.

Constraints

1 <= s.length <= 10^5
0 <= k <= 25
s consists of lowercase English letters.

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(26 * n)
    # Space: O(26)
    def longest_ideal_string(self, s: str, k: int) -> int:
        best = [0] * 26
        for ch in s:
            c = ord(ch) - ord("a")
            window = best[max(0, c - k) : min(26, c + k + 1)]
            best[c] = max(best[c], 1 + max(window))
        return max(best)

Complexity

Time	Space
O(26 * n)	O(26)

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Longest Ideal Subsequence Python Solution

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