Programmers' Challenge

By Mike Scanlin, MacTutor Regular Contributing Author

Programming Challenge of the Month - How many ways can you spell "cat"?

Given an order N (from 2 to 10) of a graph matrix and a character value for each node in the graph, calculate the number of unique paths that correctly spell out a given word (starting from any node). For instance, if N is 3 and the nodes are C, T, C, A, R, A, T, A and C, your input graph looks like figure 1.

Given an input word, say "CAT", you start at each of the 9 nodes and see how many unique paths there are that spell out "CAT". In this example, there are two solutions: (1,1), (2,1), (3,1) and (3,3), (3,2), (3,1). If the input word is "CAR", then there are four solutions: (1,1), (2,1), (2,2) and (1,3), (2,3), (2,2) and (3,3), (2,3), (2,2) and (3,3), (3,2), (2,2). For the input word "CATARACT" there are eight solutions.

Each path may cross any node any number of times but you cannot go diagonally from node to node, nor can you use the same node twice in a row (in the event of two letters next to each other in the input word that are the same). Don't worry about case sensitivity (assume everything is upper or lower case). The input word length is from 1 to 255 (a PString).

The goal is to find the number of unique paths (returned as a long). Here's the prototype:

long CountPaths(order, nodeValuesPtr, inputWordPtr)
short order;
char  *nodeValuesPtr;
StringPtr inputWordPtr;

Example:

Input:

order = 3

*nodeValuesPtr = "CTCARATAC"

*inputWordPtr = "\pCAT"

Output:

function result = 2

The winning solution will be the one that is (1) most correct, (2) fastest, (3) smallest (code size), and (4) elegant (in approximately that order of importance).

All solutions should be marked "Attn: Challenge Solution" and sent either via AppleLink or mail to Xplain Corporation (see page 2 for contact information).

And if you have any great ideas for future programming challenges send them in, too.

The Rules

Here’s how it works: Each month there will be a different programming challenge presented here. First, you must write some code that solves the challenge. Second, you must optimize your code (a lot). Then, submit your solution to MacTutor. A winner will be chosen based on code correctness, speed, size and elegance (in that order of importance) as well as the postmark of the answer. In the event of multiple equally desirable solutions, one winner will be chosen at random (with honorable mention, but no prize, given to the runners up). The prize for the best solution each month is $50 and a limited edition “I won the MacTutor Programming Challenge” T-shirt (not to be found in stores).1