Question

I just came through this question , and I could not think any better approach for other than bruteforce Given a 2D array of chars and a raw list of valid words.
1) Find all the valid words from the array. From each element in the array, you can traverse up, down, right or left.
Eg,

g o d b o d y
t a m o p r n 
u i r u s m p

valid words from the above 2D array -> god, goat, godbody, amour,….

Answer 1

Make sure you have an alphabetically sorted list of valid words. You could build this in n lg n time.

Now you have this sorted list, you could verify if a sequence of characters is a start of a correct word in lg n time.

Use a set of valid words to validate if a sequence of letters is a valid word (in constant time).

Now call getWords(input, startX, startY, new ArrayList(), “”) for every startposition and merge the resulting lists:

public List<String> getWords(char[][] input, int x, int y, List<String> result, String current){
    if(isValidWord(current))
         result.add(current);

    if(isValidStartOfWord(current)){
         // call getWords recursively for all valid directions, concatenating the char to current
    }

    return result;
 }

This way you will find your answer in O(x^2 * y^2 * lg w) time, with x and y dimensions of char array and w the size of the valid word list. That is not better than worst case (given the lg w validation), but that does not seem possible to me. The expected runtime is better this way.

If the list of valid words is small, you could also build a set for all valid starts of a correct word. In that case, you could verify in constant time if you are on your way to a correct word, and worst case is reduced to O(x^2 * y^2).

Good luck.