Problem 3084. Scrabble Scores - 11

This problem builds on the previous problem, wherein you were provided a letter of an existing word on the board and from which you played a word to find the highest scoring word. See the previous problem for more details.

Now, you will be provided a multiplier character array that represents the fifteen possible squares that can be played on, ranging from seven above the existing letter (in which case the existing letter is the last letter in an eight-letter word) to seven below the existing letter (in which case the existing letter is the first letter in an eight-letter word) with the existing letter fixed in the 8th position. The multipliers are the same as in previous problems:

 * D: double word
 * T: triple word
 * Q: quadruple word
 * d: double letter
 * t: triple letter
 * q: quadruple letter

The center multiplier square will be left blank, since it's already covered by a tile. Write a routine to determine the highest scoring word(s) based on the multiplier squares.

Once again, you will be provided a cell array of strings containing all possible words based on the existing letter and the letters on your tray. In addition to providing the highest score, also provide the word(s) that achieve that score in a cell array. See the test suite for examples. Due to high-scoring tiles, the highest score may not be achieved by the longest word(s).

Related problems:

Previous problem: 10 - Word score optimization (known letter). Next problem: 12 - Word score optimization (first word).