Problem Description
You are given a string s consisting of lowercase letters and an integer k. We call a string t ideal if it is a subsequence of the string s and 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.
Key Insights
- An ideal string must be a subsequence of the original string
s. - The difference in the alphabet order of adjacent characters must be no greater than
k. - We can utilize dynamic programming to keep track of the longest ideal subsequence for each character in the alphabet.
Space and Time Complexity
Time Complexity: O(n + 26) where n is the length of the string s (26 is for the fixed number of lowercase letters).
Space Complexity: O(1) since we are using a fixed-size array of 26 for counting.
Solution
We can solve this problem using a dynamic programming approach. We maintain an array dp of size 26, where dp[i] will store the length of the longest ideal subsequence ending with the character corresponding to i (0 for 'a', 1 for 'b', ..., 25 for 'z').
For each character in the string s, we check its position in the alphabet and update our dp array based on the allowed range of characters determined by k. Specifically, for each character s[j], we can look at characters from s[j]-k to s[j]+k and calculate the maximum ideal subsequence length that can end with s[j].