The fastest solution you're going to get will probably involve storing your dictionary in a trie. Then, create a queue of triplets (x, y, s), where each element in the queue corresponds to a prefix s of a word which can be spelled in the grid, ending at location (x, y). Initialize the queue with N x N elements (where N is the size of your grid), one element for each square in the grid. Then, the algorithm proceeds as follows:
While the queue is not empty: Dequeue a triple (x, y, s) For each square (x', y') with letter c adjacent to (x, y): If s+c is a word, output s+c If s+c is a prefix of a word, insert (x', y', s+c) into the queue If you store your dictionary in a trie, testing if s+c is a word or a prefix of a word can be done in constant time (provided you also keep some extra metadata in each queue datum, such as a pointer to the current node in the trie), so the running time of this algorithm is O(number of words that can be spelled).
implementation in Python that I just coded up:
Similar Problem:
Grid[n][n] contains letters from 'A' to 'Z' randomly. You have to print all possible words from grid.
You are allowed to move Left, Right, Up and Down ( no diagonal move).
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