从上到下到自下而上的算法（DP）

Question

I have created this algorithm to compute the longest palindrome subsequence (word that is the same when mirrors, ie "aba", "racecar"), and have done so using a recursive top-down approach. I know that it's possible to turn these into iterative algorithms working from the bottom-up, but I am having trouble seeing how this could be accoplished

My code

def palindrome(string, r = {})
    return 1 if string.length == 1
    return 2 if string[0] == string[1] and string.length == 2
    return r[string] if r.include?(string)
    n = string.length
    if string[0] == string[n-1]     
        r[string] = palindrome(string[1..n-2],r) + 2
    else
        r[string] = [palindrome(string[0..n-2],r), palindrome(string[1..n-1],r)].max
    end
end

Answer 1

1. When you use negative numbers when fetching an item from an array, the array counts the elements from the end , so you don't have to keep the n variable

    if string[0] == string[-1] # <= same as string[n-1] r[string] = palindrome(string[1..-2],r) + 2 # <= same as string[1..n-2] 

2. I don't know how performant this is, but here is a top-down suggestion:

    def palindrome(string) chars = string.chars chars.length.downto(1).find do |length| chars.each_cons(length).any? { |cons| cons == cons.reverse } end end