Longest Ideal Subsequence - Solution & Explanation

This approach utilizes dynamic programming where we maintain an array "dp" of size 26 (number of alphabets) representing the longest ideal subsequence ending with each character from 'a' to 'z'. The value of dp[char] will be updated by considering the valid preceding characters which are within the range of 'k'. For each character in the string, we update our dp array by iterating over possible characters that are within distance 'k' in the alphabet. The maximum value in the dp array by the end of the iteration gives us the length of the longest ideal subsequence.

The Python code initializes a dp array with 26 elements set to 0. It iterates through each character in the string, calculates its respective index in the dp array, and then checks all indices in the dp that are within a distance 'k'. It updates the dp value at the current character index to be the maximum of the current or the sum of max_len and 1. Finally, it returns the maximum value in the dp array.

This approach leverages a HashMap to dynamically track the maximum subsequence length for characters encountered in the string, rather than maintaining a fixed size dp array. The HashMap keys represent characters and the values represent the maximum subsequence length possible for the corresponding character. For each character in the string, it checks and updates the longest subsequence length using nearby characters within distance 'k'.

This JavaScript code initializes an array dp of length 26 to keep track of the maximum length of the subsequence that ends with each character. It iterates over each character of the string, calculates its index in dp, and checks all indices that are within k-distance. The dp array is updated with the maximum value found plus one for the current character. The solution is returned as the maximum value in dp array.