Suppose we have a string s, we have to find the number of distinct palindromes we can generate using all characters. If the answer is very large then mod the result by 10^9 + 7.
So, if the input is like s = "xyzzy", then the output will be 2, as we can make "zyxyz" and "yzxzy"
To solve this, we will follow these steps −
m = 10^9+7
char_freq := a map holding each character of s and their frequencies
odd := 0
for each character k and frequency v in char_freq, do
if v mod 2 is 1, then
odd := odd + 1
if odd > 1, then
return 0
half_length := quotient of (size of s) / 2
res := factorial of half_length
dividor := 1
for each character k and frequency v in char_freq, do
dividor := dividor * factorial of (quotient of v/2)
return (quotient of res/dividor) mod m
Let us see the following implementation to get better understanding −
Example
from math import factorial
class Solution:
def solve(self, s):
m = (10**9+7)
char_freq = {}
for c in s:
char_freq[c] = char_freq.get(c, 0) + 1
odd = 0
for k,v in char_freq.items():
if v % 2 == 1:
odd +=1
if odd > 1:
return 0
half_length = len(s)//2
res = factorial(half_length)
dividor = 1
for k,v in char_freq.items():
dividor *= factorial(v//2)
return (res//dividor) % m
ob = Solution()
print(ob.solve("xyzzy"))Input
"xyzzy"
Output
2