Algorithm review for time complexity

Question

1. I would like to know whether this works in worst case as Θ(n+m)?

n is size of i_StringForSearch, m is size of i_SubStringToFind.

2.Is there any program which is recommended to check time complexity of a given code, I prefer a free tool which is well recognized.

Thank you

public static boolean isSubstring(String i_StringForSearch, String i_SubStringToFind)
    {
        int strForSearchIndex = 0;
        int subStrToFindIndex = 0;
        boolean endOfStringToSearch = false;
        boolean foundSubString = false;
        boolean isThereASequenceOfMatching = false;


        while(!endOfStringToSearch && !foundSubString)
        {
            if(strForSearchIndex == i_StringForSearch.length())
            {
                endOfStringToSearch = true;
            }

            else if(i_StringForSearch.charAt(strForSearchIndex) == i_SubStringToFind.charAt(subStrToFindIndex))
            {
                isThereASequenceOfMatching = true;
                if(subStrToFindIndex == i_SubStringToFind.length() -1 )
                {
                    foundSubString = true;
                }
                subStrToFindIndex++;
                strForSearchIndex++;
            }

            else if(i_StringForSearch.charAt(strForSearchIndex) != i_SubStringToFind.charAt(subStrToFindIndex))
            {
                if(isThereASequenceOfMatching)
                {
                    subStrToFindIndex = 0;
                    isThereASequenceOfMatching = false;
                }
                strForSearchIndex++;
            }
        }

       return foundSubString;
    }

Answer 1

1. Answering your question: yes, the algorithm is O(n+m). Each iteration increases strForSearchIndex, so there are at most n iterations. [this is assuming i_StringForSearch.length() is done in O(1), which is usually true].

2. The algorithm is wrong with the counter example of isSubstring("aaab","aab") == false.

3. You might want to have a look on Knuth Morris Pratt algorithm and/or Rabin-Karp algorithm and/or Aho-Corasick Algorithm