Detect loops in computer player in a cardgame

Question

A while ago I created a small cardgame web app for fun. The player plays against the computer and mostly it works fine. Sometimes though the computer player gets into a loop, the point of the game is to lose all your cards and if you don't have a card to play you take the pile. Sometimes the computer plays x,y,z, takes the pile, plays x,yz, takes the pile etc.

I keep track of the moves I've made, so at any point I have an array that looks something like : [C2,D5,H2,S4,C5,H2,S4,C5,H2,S4,C5]

In this case I can see that I've gotten into a loop of playing H2,S4,C5, then taking the pile and then repeating.

So, the generalized problem is, what's the best way to detect repeating patterns in a list? I could probably whip something up using a simple for loop, trying to find the card I'm about to play and if I find that in position x then I could check whether the pattern from x to n repeats at position x-(n-x) to x, but this seems like the kind of problem that could have a nice algorithm for it. How would you code this given the following function signature:

function findLoops(previousMoves, nextMove, maxPatternLength) {
    //Return [loopLength, loopCount] or null if there are no loops
}

p.s. this is not a homework assignment, the game exists and is at http://www.idiot-cardgame.com if anyone is interested :)

Answer 1

First the general question: Your suggested method

trying to find the card I'm about to play and if I find that in position x then I could check whether the pattern from x to n repeats at position x-(n-x) to x,

looks really good. I would suggest basically the same. It is O(n) and needs a fixed amount of storage, and is simple: what else would you wish for?

Second: You can check for repetition in games generally if you keep a hash table of all previous game states (complete state, nothing left out). Everytime you reach a new state look up if it is in the hashtable, if its in it: you game state is looping.

In Javascript you have builtin hastables so this is very easy to do with something similar like this:

 new_state = next_move(old_state);
 new_encoded_state = encode(new_state);  // make it into a string
 if (allstates[new_encoded_state]) {
       // we are looping!
 } else {
       allstates[new_encoded_state] = 1;
       // no looping
 }

The variable allstates is not an Array but of type Object. You can have array like access with strings and this uses the Object as hastable.