Algorithm to find the minimum length of substring having all characters of other string

Question

I have a two strings:
string1 - hello how are you,
String2 - olo (including space character)

Output: lo ho ( hello

Answer 1

There is this algorithm which does this in O(N).

Idea: Have 2 arrays, viz. isRequired[256] and isFound[256] which tells the frequency of each character in S and while parsing the string S, the frequency of each character that has found yet. Also, keep a counter which tells when a valid window is found. Once a valid window is found, we can shift the window (towards right) maintaining the given invariant of the question.

Program in C++:

void findMinWindow(const char *text, const char *pattern, int &start, int &end){
        //Calcuate lengths of text and pattern
        int textLen = strlen(text);
        int patternLen = strlen(pattern);

        // Declare 2 arrays which keep tab of required & found frequency of each char in pattern
        int isRequired[256] ; //Assuming the character set is in ASCII
        int isFound[256];
        int count = 0; //For ascertaining whether a valid window is found

        // Keep a tab of minimum window 
        int minimumWindow = INT_MAX;

        //Prepare the isRequired[] array by parsing the pattern
        for(int i=0;i isRequired[s[i]]){
                   //Either of the above 2 conditions means we should increment i; however we 
                   // must decrease isFound for this char as well.
                   //Hence do a check again
                   if(isFound[s[i]] > isRequired[s[i]]){
                      isFound[s[i]]--;
                   }
                   i++;
              }

               // Note that after the while loop, the invariant is still maintained
               // Lets check if we did better
               int winLength = j-i+1;
               if(winLength < minimumWindow){
                  //update the references we got
                  begin = i;
                  end = j;
                  //Update new minimum window lenght
                  minimumWindow = winLength;
               }
          } //End of if(count == patternLen)
     } //End of for loop 
}