Question

I created a word solver for all directions. It finds words horizontally, vertically and reverse. However, I am having problems making it go all directions. So to take “hello” in:

H  E  i  l
x  L  p  q
c  L  O  m

Anyone can point me on how to do that? Here is my algorithm to that searches for the words (in C++):

/*
 * For loops that search each row, each column in all 8 possible directions.
 */
void Scramble::solve() {

cout << "Output:" << endl;

for (int row = 0; row < getRows(); row++) {
    for (int col = 0; col < getCols(); col++)
        for (int rowDir = -1; rowDir <= 1; rowDir++)
            for (int colDir = -1; colDir <=1; colDir++)
                if (rowDir != 0 || colDir != 0)
                    findWords(row, col, rowDir, colDir);
}
}

/*
 * Finds the matches in a given direction. Also calls verifyWord() to verify that the
 * current sequence of letters could possibly form a word. If not, search stops.
 */
void Scramble::findWords(int startingRow, int startingCol, int rowDir, int colDir) {

int searchResult;
string sequence = "";
sequence = sequence + wordsArr[startingRow][startingCol];

for (int i = startingRow + rowDir, j = startingCol + colDir; i >= 0 && j >= 0
&& i < getRows() && j < getCols(); i = i + rowDir, j = j + colDir) {

    sequence = sequence + wordsArr[i][j];

    if (sequence.length() >= 3) {

        searchResult = verifyWord(words, sequence);

        if ((unsigned int)searchResult == words.size())
            break;

        if (words[searchResult].rfind(sequence) > words[searchResult].length())
            break;

        if (words[searchResult] == (sequence))
            cout << sequence << endl;
    }
}
}

/*
 * Performs the verifyWord search method.
 * Searches the word to make sure that so far, there is possibly that the current sequence
 * of letter could form a word. That is to avoid continuing to search for a word
 * when the first sequence of characters do not construct a valid word in the dictionary.
 *
 * For example, if we have 'xzt', when this search is done it prevents the search
 * to continue since no word in the dictionary starts with 'xzt'
 */
int Scramble::verifyWord(vector<string> words, string str) {

int low = 0;
int mid = 0;
int high = words.size();

while (low < high) {

    mid = (low + high) / 2;

    if (str > words[mid]) {
        low = mid + 1;
    }

    else if (str < words[mid]) {
        high = mid - 1;
    }

    else
        return mid;
}
}

Answer 1

1) Currently, your solve() function looks for a word in a straight line starting at each point: is this what you intend? I only ask because ‘hello’ doesn’t appear as a straight line in your sample matrix:

H  E  i  l
x  L  p  q
c  L  O  m

If you do want straight-line words only, then fine (this is how I’ve always understood these puzzles to work anyway), but if in fact you want to find words in a snake-wise fashion, then a recursive search like Zilchonum and BlueRaja are suggesting would be a good bet. Just be careful you don’t end up looping back on letters you’ve already used.

2) In either case, your verifyWord() function also has some problems: at the very least it needs to return some value in the case where you exit the while (low < high) loop.

Even so, it still won’t quite do what you want it to: for example, say your dictionary
contains {"ant", "bat" "hello", "yak", "zoo"}, and you call verifyWord() with str="hel", you’d like to return a value of 2, but at the moment it does this:

step  low   mid  high
 0     0     0     5   // initialise
 1     0     2     5   // set mid = (0+5)/2 = 2... words[2] == "hello" 
 2     0     2     1   // "hel" < "hello" so set high = mid - 1
 3     0     0     1   // set mid = (0+1)/2 = 0... words[0] == "ant"
 4     1     0     1   // "hel" > "ant" so set low = mid + 1     
 5  // now (low<high) is false, so we exit the loop with mid==0

Rather than comparing “hel” with “hello”, perhaps you’d be better off truncating the words in the dictionary to the same length as str: ie comparing str to word[mid].substr(0,str.length())?