Program to count number of strings we can make using grammar rules in Python

Python Server Side Programming Programming

Suppose we have a number n, we have to find the number of strings of length n can be generated using the following rules −

Each character is a lower case vowel [a, e, i, o, u]
"a" may only be followed by one "e"
"e" may only be followed by any of "a" and "i"
"i" may not be followed by another "i"
"o" may only be followed by any of "i" and "u"
"u" may only be followed by one "a"

If the result is very large, mod the result by 10^9 + 7.

So, if the input is like n = 2, then the output will be 10, as we can generate the following two letter strings: ["ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou", "ua"]

To solve this, we will follow these steps −

m = 10^9 + 7
if n is same as 0, then
- return 0
define five variables a, e, i, o, u, all are 1 initially
- for _ in range 0 to n-1, do
  - a := e+i+u
  - e := a+i
  - i := e+o
  - o := i
  - u := i+o
return (a + e + i + o + u) mod m

Let us see the following implementation to get better understanding −

Example

Live Demo

class Solution:
   def solve(self, n):
      m = (10 ** 9 + 7)
      if n == 0:
         return 0
      a = e = i = o = u = 1
      for _ in range(n-1):
         a, e, i, o, u = e+i+u, a+i, e+o, i, i+o
      return (a + e + i + o + u) % m

ob = Solution()
print(ob.solve(3))

Input

Output

Arnab Chakraborty

Updated on: 2020-10-08T14:22:32+05:30

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