Memoization

Memoization is an optimization technique where we the store results of previous expensive operations and use them without repeating the operation. It helps us speed up the solution significantly. When we have problems where we can have repetitive sub problems, we can easily apply this technique to store those results and use them later on without repeating the steps. Since PHP has a great support for associative arrays and dynamic array properties, we can cache the results without any problems. One thing we have to remember is that though we are saving time by caching the results, we will require more memory to store these results in the cache. So, we have to make the trade-off between space and memory. Now, let's revisit Chapter 5, Applying Recursive Algorithms - Recursion, for our recursive example of generating Fibonacci numbers. We will just modify that function...