 # Most frequent substring problem.

#1

Given a string, we want to know the maximum no. of occurrences of any substring that satisfies following two conditions:

1. The substring’s lengths is within in inclusive range of `minLength` to `maxLength`.
2. The total no. of unique characters in the string doesn’t exceed `maxUnique`.

For example, given a string s=abcde, minLength=2, maxLength=5, maxUnique=3, the substrings matching the criteria are (ab, bc, cd, de, abc, bcd, cde). Any shorter string fails he `minLength>=2` any longer will fail `maxUnique <= 3`. Each of the substring occurs only one time.

INPUT :
First line contains a string, second line contains minLength, third line contains maxLength, and the last line contains maxUnique.

Constraints :

• 2<=n<=105
• 2<=minLength<= maxLength <=26
• maxLength<n
• 2<=maxUnique<=26

SAMPLE INPUT :

``````ababab
2
3
4
``````

SAMPLE OUTPUT :

``````3
``````

**EXPLANATIONS : **

We want to find the no. of occurrences of the most frequently occurring substring of s= “ababab” that has the length in the inclusive range from minLength = 2 and maxLength=3 and contains maximum of maxUnique = 4 unique characters. The substring ab occurs three times aba, bab and ba occurs twice. Because we want maximum of this frequencies we return 3 as our answer.

#2

(Part 1)

Obviously we shouldn’t care for maxLength,since we wanna maximize ocuurrence(as lets say if a substring of length x,occurs y times,then there must be a substring of length (x-1) that occurs>=y times)

So we just have to find max no.of occurrences of a substring of length minLength

(Part 2)

unique thing can easily be done using frequency arrays

(Part 3)

One simple way is to use rolling hashing see this: https://threads-iiith.quora.com/String-Hashing-for-competitive-programming

for counting max occurence of a substring of given length

(Part 1)

Proof: Lets say a substring s of length x occurs b times,then there will be a substring s’ of length < x occuring >=b times(1 such substring would be a substring of s)

like ababa

ab occurs 2 times,so obviously a occurs>=2,b>=2

So better to find minimum Length String,as it will have less unique characters and also occurs greater number of times

(Part 2)

how to check if a substring s[i:j] is valid (no.of unique characters<=maxUnique)

lets construct a prefix sum freq array

where:

freq*[‘a’]=freq[i-1][‘a’]+(s*==‘a’)

freq*[‘b’]=freq[i-1][‘b’]+(s*==‘b’)

So for calculating no.of unique characters in s[i:j]

`uniqueCount=0 for(c='a';c <= 'z';c++) if((freq[j][c]-freq[i-1][c])>0) uniqueCount++`

(Part 3)

we can now iterate for all substring of length minLength

so :

``````for(i=0;i< s.length()-minLength;i++)
{
//so i to i+minLength-1 is substring starting at i
//first we'll check if its valid(unique characters ...),i have explained it in part 2
//if its unique,find hash value of substring s[i:i+minLength-1],which can be found quickly
//if u use rolling hashing(read the link i provided)
int hashValue=hash(i,i+minLength-1)
map[hashValue]++;
}
Now iterate through the map to find highest frequency hash value``````

#3

@vivek_1998299

Can you please provide more detailed explanation, I am finding it hard to understand.

#4

OOh sorry,for the late reply!!

These bugs…

#5

@vivek_1998299

I have got the idea from the explanation and the link, can you explain me about implementing hashing. I have encountered this kind of problem for the first time that’s why I am facing difficulty.

#6

Can anyone help me with this problem.

#7

If u had sincerely read the link ,u wouldn’t have asked this…:(.

Plz read from link,and do a bit of searching too!!,i don’t support spoon feeding…

#8

@vivek_1998299 In the worst case, Time complexity of your approach is O(N^2). Is there any O(N log N) algorithm for the same thing?

#9

@vivek_1998299 In the worst case, Time complexity of your approach is O(N^2). Is there any O(N log N) algorithm for the same thing?