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Program to find n length string made of letters from m sized alphabet with no palindrome in Python
Suppose we have m number of letters and another value n. We have to count number of strings of length n created with letters by taking from these m letters, and string has no palindromic substring of length greater than 1. If answer is too large then mod the result by 10^9+7.
So, if the input is like n = 2 m = 3, then the output will be 6 because m = 3, so if the alphabets are {x,y,z}, we can generate strings like: [xx,xy,xz,yx,yy,yz,zx,zy,zz] but [xx,yy,zz] are not valid so there are 6 strings.
To solve this, we will follow these steps −
- p := 10^9+7
- if n is same as 1, then
- return m mod p
- if n is same as 2, then
- return m *(m - 1) mod p
- if m <= 2, then
- return 0
- return m*(m-1) * ((m-2)^(n-2) mod p) mod p
Example
Let us see the following implementation to get better understanding −
def solve(n, m):
p = 10**9+7
if n == 1:
return m % p
if n == 2:
return m * (m - 1) % p
if m <= 2:
return 0
return m * (m - 1) * pow(m - 2, n - 2, p) % p
n = 2
m = 3
print(solve(n, m))Input
3, [1,2,3,4,1]
Output
6
Updated on: 25-Oct-2021
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