# Does SWI-Prolog have N+K-trees? **URL:** \ **Category:** Data Structure\ **Created:** [September 24, 2019, 2:14pm UTC](https://swi-prolog.discourse.group/t/does-swi-prolog-have-n-k-trees/1310 "2019-09-24T14:14:34Z")\ **Posts on this page:** 1\ **Showing post:** 5
**Author:** ![jan](https://yyz2.discourse-cdn.com/free1/user_avatar/swi-prolog.discourse.group/jan/32/4_2.png) [@jan](https://swi-prolog.discourse.group/u/jan)\ **Post date:** [September 25, 2019, 3:41pm UTC](https://swi-prolog.discourse.group/t/does-swi-prolog-have-n-k-trees/1310/5 "2019-09-25T15:41:19Z")
It is always a bit of work to get the math correct. After a little playing, I get at: ```prolog :- debug(dyn). dyn_new(Max, Dyn) :- Subs is msb(Max)+1, functor(Dyn, dyn, Subs). dyn_access(I, Dyn, Value) :- must_be(positive_integer, I), I1 is msb(I), I11 is I1+1, I2 is I-(2**I1-1), debug(dyn, 'Located at index ~D in ~D', [I2, I11]), arg(I11, Dyn, A2), ( var(A2) -> Len is 2**I1, debug(dyn, 'Created sub array of length ~D for ~D', [Len, I11]), functor(A2, s, Len) ; true ), arg(I2, A2, Value). ``` Then we can run some tests and (by induction) conclude we are fine 🙂 ```prolog % Located at index 1 in 1 % Created sub array of length 1 for 1 X = dyn(s(1), _10312, _10314, _10316, _10318, _10320). 116 ?- dyn_new(32, X), dyn_access(2, X, 1). % Located at index 1 in 2 % Created sub array of length 2 for 2 X = dyn(_10296, s(1, _10444), _10300, _10302, _10304, _10306). 117 ?- dyn_new(32, X), dyn_access(3, X, 1). % Located at index 2 in 2 % Created sub array of length 2 for 2 X = dyn(_10296, s(_10442, 1), _10300, _10302, _10304, _10306). 118 ?- dyn_new(32, X), dyn_access(4, X, 1). % Located at index 1 in 3 % Created sub array of length 4 for 3 X = dyn(_10300, _10302, s(1, _10448, _10450, _10452), _10306, _10308, _10310). ``` --- _[View the full topic](https://swi-prolog.discourse.group/t/does-swi-prolog-have-n-k-trees/1310)._