to create list of , elementswe do the following and pass it to the lookup parameter of the dyna_fib functionmap_set [none]*( this list will store the value of the computation of the various calls to the dyna_fib(functionif < lookup[ any call to the dyna_fib(with being less than or equal to will return when dyna_fib( is evaluatedwe store the value at index of map_setwrite the condition for lookup[ ]as the followingif lookup[nis nonelookup[ndyna_fib( - lookupdyna_fib( - lookupwe pass lookup so that it can be referenced when evaluating the subproblems the calls to dyna_fib( - lookupand dyna_fib( - lookupare stored in lookup[nwhen th we run our updated implementation of the function to find the term of the fibonacci serieswe realize that there is considerable improvement this implementation runs much faster than our initial implementation supply the value to both implementations and witness the difference in the execution speed the algorithm sacrificed space complexity for time because of the use of memory in storing the result to the function calls the tabulation technique there is second technique in dynamic programmingwhich involves the use of table of results or matrix in some cases to store results of computations for later use this approach solves the bigger problem by first working out route to the final solution in the case of the fib(functionwe will develop table with the values of fib( and fib( predetermined based on these two valueswe will work our way up to fib( )def fib( )results [ for in range( )results append(results[ - results[ - ]return results[-