 # Length of the smallest sub-string consisting of maximum distinct characters

Given a string of length N, find the length of the smallest sub-string consisting of maximum distinct characters. Note : Our output can have same character. Examples:

```Input : "AABBBCBB"
Output : 5

Input : "AABBBCBBAC"
Output : 3
Explanation : Sub-string -> "BAC"

Input : "GEEKSGEEKSFOR"
Output : 8
Explanation : Sub-string -> "GEEKSFOR"```

Method 1 (Brute Force)

We can consider all sub-strings one by one and check for each sub-string both conditions together
1. sub-string%u2019s distinct characters is equal to maximum distinct characters
2. sub-sting%u2019s length should be minimum .
Time Complexity : O(n^3)

Implementation:
/* C++ program to find the length of the smallest
substring consisting of maximum distinct characters */
#include <bits/stdc++.h>
using namespace std;
#define NO_OF_CHARS 256
// Find maximum distinct characters in any string
int max_distinct_char(string str, int n){
// Initialize all character's count with 0
int count[NO_OF_CHARS] = {0};
// Increase the count in array if a character
// is found
for (int i = 0; i < n; i++)
count[str[i]]++;
int max_distinct = 0;
for (int i = 0; i < NO_OF_CHARS; i++)
if (count[i] != 0)
max_distinct++;
return max_distinct;
}
int smallesteSubstr_maxDistictChar(string str){
int n = str.size(); // size of given string
// Find maximum distinct characters in any string
int max_distinct = max_distinct_char(str, n);
int minl = n; // result
// Brute force approach to find all substrings
for (int i=0 ;i<n ;i++){
for (int j=0; j<n; j++){
string subs = str.substr(i,j);
int subs_lenght = subs.size();
int sub_distinct_char = max_distinct_char(subs, subs_lenght);
// We have to check here both conditions together
// 1. substring's distinct characters is equal
// to maximum distinct characters
// 2. substing's length should be minimum
if (subs_lenght < minl && max_distinct == sub_distinct_char){
minl = subs_lenght;
}
}
}
return minl;
}
/* Driver program to test above function */
int main()
{
// Input String
string str = "AABBBCBB";
int len = smallesteSubstr_maxDistictChar(str);
cout << " The length of the smallest substring"
" consisting of maximum distinct "
"characters : " << len;
return 0;
}
Output:
``` The length of the smallest substring consisting
of maximum distinct characters : 5
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