Recursive Backtracking Solution - How To Cache Answers Into Appropriate Array

I can often write a recursive backtracking solution, but don't know how to cache the answers into an appropriate array.

For example:

Java Code:

public static int max(int[] costs, int index, int total, int shares) {
if(index >= costs.length) {
return total;
}
int buy = max(costs, index + 1, total - costs[index], shares + 1); // buy one stock
int sell = max(costs, index + 1, total + shares * costs[index], 0); // sell all stocks
return Math.max(total, Math.max(buy, sell)); // compares between buy, sell, and doing nothing
} mh_sh_highlight_all('java');

This is a dynamic programming exercise, but I have no idea what dimensions the dp array should be (I was thinking maybe dp[index][total][shares], but that seemed like overkill). Is this just because my understanding of recursion isn't solid enough or am I missing something else?