Merge pull request #152 from TheAlgorithms/count-sorted-vowel-strings-dd-memoization

DIRECTORY.md

@@ -74,6 +74,7 @@
 
 ## Dynamic Programming
   * [Coin Change](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/coin_change.rb)
+  * [Count Sorted Vowel Strings](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/count_sorted_vowel_strings.rb)
   * [Fibonacci](https://github.com/TheAlgorithms/Ruby/blob/master/dynamic_programming/fibonacci.rb)
 
 ## Maths

dynamic_programming/count_sorted_vowel_strings.rb

@@ -0,0 +1,91 @@
+# Challenge name: Count Sorted Vowel Strings
+#
+# Given an integer n, return the number of strings of length n that consist only
+# of vowels (a, e, i, o, u) and are lexicographically sorted.
+#
+# A string s is lexicographically sorted if for all valid i, s[i] is the same as
+# or comes before s[i+1] in the alphabet.
+#
+#
+# Example 1:
+#
+# Input: n = 1
+# Output: 5
+# Explanation: The 5 sorted strings that consist of vowels only are ["a","e","i","o","u"].
+#
+# Example 2:
+#
+# Input: n = 2
+# Output: 15
+# Explanation: The 15 sorted strings that consist of vowels only are
+# ["aa","ae","ai","ao","au","ee","ei","eo","eu","ii","io","iu","oo","ou","uu"].
+# Note that "ea" is not a valid string since 'e' comes after 'a' in the alphabet.
+#
+# Example 3:
+#
+# Input: n = 33
+# Output: 66045
+
+#
+# Approach: Using Recursion + Memoization, Top Down Dynamic Programming
+#
+
+# 
+# Algorithm: Dynamic Programming state transition.
+# 
+# F(0) = 1
+# F(n)a = F(n-1)a + F(n-1)e + F(n-1)i + F(n-1)o +F(n-1)u
+# F(n)e = F(n-1)e + F(n-1)i + F(n-1)o + F(n-1)u
+# F(n)i = F(n-1)i + F(n-1)o +F(n-1)u
+# F(n)o = F(n-1)o + F(n-1)u
+# F(n)u = F(n-1)u
+# 
+
+# @param {Integer} n
+# @return {Integer}
+
+def count_vowel_strings(n, letter = 'a')
+  return 1 if n < 1
+
+  @h ||= {}
+  key = [n, letter]
+  return @h[key] if @h[key]
+
+  result = case letter
+           when 'a'
+             count_vowel_strings(n - 1, letter = 'a') +
+             count_vowel_strings(n - 1, letter = 'e') +
+             count_vowel_strings(n - 1, letter = 'i') +
+             count_vowel_strings(n - 1, letter = 'o') +
+             count_vowel_strings(n - 1, letter = 'u')
+           when 'e'
+             count_vowel_strings(n - 1, letter = 'e') +
+             count_vowel_strings(n - 1, letter = 'i') +
+             count_vowel_strings(n - 1, letter = 'o') +
+             count_vowel_strings(n - 1, letter = 'u')
+           when 'i'
+             count_vowel_strings(n - 1, letter = 'i') +
+             count_vowel_strings(n - 1, letter = 'o') +
+             count_vowel_strings(n - 1, letter = 'u')
+           when 'o'
+             count_vowel_strings(n - 1, letter = 'o') +
+             count_vowel_strings(n - 1, letter = 'u')
+           when 'u'
+             count_vowel_strings(n - 1, letter = 'u')
+           end
+
+  @h[key] = result
+  @h[key]
+end
+
+n = 33
+puts count_vowel_strings(n)
+# Output: 66045
+
+n = 2
+puts count_vowel_strings(n)
+# Output: 15
+
+n = 1
+puts count_vowel_strings(n)
+# Output: 5