Comparision of Program for Fibonacci numbers. Implement using Dynamic Programming and Conventional Implementation.

fib.erl

%
% timer:tc(fun() -> fib:fib(41) end).
% {1398640,165580141}
%
% timer:tc(fun() -> fib:fib_dp1(41) end).
% {84,165580141}
%
% timer:tc(fun() -> fib:fib_dp2(41) end).
% {5,165580141}
%  
-module(fib).

-export([fib/1, fib_dp1/1, fib_dp2/1]).

fib(X) when X < 2 -> X;
fib(X) -> fib(X - 1) + fib(X - 2).

fib_dp1(N, X, Memo) when N =< X ->
    Memo1 = Memo#{N := maps:get(N - 1, Memo) + maps:get(N - 2, Memo)},
    fib_dp(N + 1, X, Memo1);
fib_dp1(_, _, Memo) ->
    Memo.

fib_dp1(X) ->
    FoldFun = fun(N, Acc) -> maps:put(N, 0, Acc) end,
    Memo0 = lists:foldr(FoldFun, #{}, lists:seq(0, X)),
    Memo1 = fib_dp1(2, X, Memo0#{0 := 0, 1 := 1}),
    maps:get(X, Memo1).

fib_dp2(N) ->
    fib_dp(N, 0, 1).

fib_dp2(0, Acc1, _) -> Acc1;
fib_dp2(C, Acc1, Acc2) ->
    fib_dp2(C-1, Acc1+Acc2, Acc1).