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Program to count number of homogenous substrings in Python
Suppose we have a string s, we have to find the number of homogenous substrings of s. The answer may be very large, so return answer modulo 10^9+7. A string is said to be homogenous when all the characters of the string are the same.
So, if the input is like s = "xyyzzzxx", then the output will be 13 because the homogenous substrings are listed like
1."x" appears thrice.
"xx" appears once.
3. "y" appears twice.
"yy" appears once.
5. "z" appears thrice.
"zz" appears twice.
"zzz" appears once.
so , (3 + 1 + 2 + 1 + 3 + 2 + 1) = 13.
To solve this, we will follow these steps −
s := s concatenate "@"
h:= a new map
prev:= s[0]
c:= 1
for each i in s from index 1 to end, do
if prev is not same as i, then
if prev*c is present in h, then
h[prev*c] := h[prev*c] + 1
otherwise,
h[prev*c]:= 1
c:= 1
if prev is same as i, then
c := c + 1
prev := i
fin:= 0
for each i in h, do
t:= size of i
k:= 0
while t is not same as 0, do
k := k + t
t := t - 1
fin := fin + k*h[i]
return fin mod 10^9+7
Example
Let us see the following implementation to get better understanding −
def solve(s):
s+="@"
h={}
prev=s[0]
c=1
for i in s[1:]:
if prev!=i:
if prev*c in h:
h[prev*c]+=1
else:
h[prev*c]=1
c=1
if prev == i:
c += 1
prev = i
fin=0
for i in h:
t=len(i)
k=0
while t!=0:
k+=t
t-=1
fin+=k*h[i]
return fin % 1000000007
s = "xyyzzzxx"
print(solve(s))Input
"xyyzzzxx"
Output
13
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