f(5) = 5

f(4)      f(3)  2
 3           f(2) f(1)
f(3) f(2)      1    1
 2    1      f(1) f(0)          f(1) f(0)
f(2) f(1)     1   0              1    0
 1    1
f(1) f(0)
 1    0


f(5): once
f(4): once
f(3): 2 times
f(2): 3 times
f(1): 5 times

This traditional recursive fibonacci algorithm does so repeated work that it runs in THETA (fib(n)) time, THETA (((1+sqrt(5))/2)^n) time.

Recursion sucks if it starts doing a lot of repeated work.  There's no need to compute fib(3) three times.  Once is enough.

So, if you can replace recursion with iteration and store stuff in a table rather than use recursion, this is dynamic programming.

"Programming" is an old mathematical term for storing information in a table.

char *a = "HELLO";
a[0] = 'J';
printf ("%s\n","HELLO");