Sedgewick gives a dynamic programming example of efficiently
calculating the nth Fibonacci number as follows:
/*
* we will use this array to store computations and avoid repeating
* work that has already been completed.
*
*/
int known_fib[MAX_FIB];
/*
* assume that known_fib is initialized to all UNKNOWN or with valid
* Fibonnacci numbers
*
*/
int fib(int i) {
int t;
if (known_fib[i] != UNKNOWN) return(know_fib[i]);
if (i == 0) t = 0;
if (i == 1) t = 1;
if (i > 1) t = fib(i  1) + fib(i  1);
known_fib[i] = t;
return(t);
}
