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There are a bitwise function that calculates the sucessor of any node of this (labelled) complete binary tree of depth k?

The labels are bit strings. For each level l, with 0>l≥k, there are 2^l labels of l bits. In the illustration k=3. The order of the labels is lexicographical (same as preorder in binary-tree terminology).

It is not possible to use a bynary-tree data structure, the function must use only the label (!). The successor function use also the parameter k, so it is s(x,k). Some examples of results of the function:

• 
  00 == s(0,3)


• 
  001 == s(000,3)


• 
  1 == s(011,3)


• 
  10 == s(1,3)


• null == s(111,3)

It is an inference based on the syntax rules of the labels, not on a data structure.

The aim is bitwise function for a binary representation.

PS: the solution can be a link to a library... Any language. Can use internal binary buffer or usual integer (e.g. 64 bits) to labels; can use Javascript, C, or any other language...

---

No problem to map to other label representation if there are a simple bijective relation. For example we can represent labels by a pair of integers (size,value)

(size,value) BitString representation
(1,0) 0
(2,0) 00
(3,0) 000
(4,0) 0000
(4,1) 0001
(3,1) 001
(4,2) 0010
(4,3) 0011
(2,1) 01
... ...

---

For ASCII strings, of course, there are a "visual solution". Expressing with Javascript:

function s(x,k) 
 let l = x.length
 if (l<k) 
 return x+'0';
 l--;
 if (x[l]=='0')
 return x.slice(0,l)+'1'
 else 
 return (x=='1'.padEnd(k,'1'))? null: x.slice(1)
 

binary-tree

share|improve this question

edited Mar 26 at 0:46

Peter Krauss

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges

add a comment | 

0

There are a bitwise function that calculates the sucessor of any node of this (labelled) complete binary tree of depth k?

The labels are bit strings. For each level l, with 0>l≥k, there are 2^l labels of l bits. In the illustration k=3. The order of the labels is lexicographical (same as preorder in binary-tree terminology).

It is not possible to use a bynary-tree data structure, the function must use only the label (!). The successor function use also the parameter k, so it is s(x,k). Some examples of results of the function:

• 
  00 == s(0,3)


• 
  001 == s(000,3)


• 
  1 == s(011,3)


• 
  10 == s(1,3)


• null == s(111,3)

It is an inference based on the syntax rules of the labels, not on a data structure.

The aim is bitwise function for a binary representation.

PS: the solution can be a link to a library... Any language. Can use internal binary buffer or usual integer (e.g. 64 bits) to labels; can use Javascript, C, or any other language...

---

No problem to map to other label representation if there are a simple bijective relation. For example we can represent labels by a pair of integers (size,value)

(size,value) BitString representation
(1,0) 0
(2,0) 00
(3,0) 000
(4,0) 0000
(4,1) 0001
(3,1) 001
(4,2) 0010
(4,3) 0011
(2,1) 01
... ...

---

For ASCII strings, of course, there are a "visual solution". Expressing with Javascript:

function s(x,k) 
 let l = x.length
 if (l<k) 
 return x+'0';
 l--;
 if (x[l]=='0')
 return x.slice(0,l)+'1'
 else 
 return (x=='1'.padEnd(k,'1'))? null: x.slice(1)
 

binary-tree

share|improve this question

edited Mar 26 at 0:46

Peter Krauss

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges

add a comment | 

There are a bitwise function that calculates the sucessor of any node of this (labelled) complete binary tree of depth k?

The labels are bit strings. For each level l, with 0>l≥k, there are 2^l labels of l bits. In the illustration k=3. The order of the labels is lexicographical (same as preorder in binary-tree terminology).

It is not possible to use a bynary-tree data structure, the function must use only the label (!). The successor function use also the parameter k, so it is s(x,k). Some examples of results of the function:

• 
  00 == s(0,3)


• 
  001 == s(000,3)


• 
  1 == s(011,3)


• 
  10 == s(1,3)


• null == s(111,3)

It is an inference based on the syntax rules of the labels, not on a data structure.

The aim is bitwise function for a binary representation.

PS: the solution can be a link to a library... Any language. Can use internal binary buffer or usual integer (e.g. 64 bits) to labels; can use Javascript, C, or any other language...

---

No problem to map to other label representation if there are a simple bijective relation. For example we can represent labels by a pair of integers (size,value)

(size,value) BitString representation
(1,0) 0
(2,0) 00
(3,0) 000
(4,0) 0000
(4,1) 0001
(3,1) 001
(4,2) 0010
(4,3) 0011
(2,1) 01
... ...

---

For ASCII strings, of course, there are a "visual solution". Expressing with Javascript:

function s(x,k) 
 let l = x.length
 if (l<k) 
 return x+'0';
 l--;
 if (x[l]=='0')
 return x.slice(0,l)+'1'
 else 
 return (x=='1'.padEnd(k,'1'))? null: x.slice(1)
 

binary-tree

share|improve this question

edited Mar 26 at 0:46

Peter Krauss

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges

(size,value) BitString representation
(1,0) 0
(2,0) 00
(3,0) 000
(4,0) 0000
(4,1) 0001
(3,1) 001
(4,2) 0010
(4,3) 0011
(2,1) 01
... ...

function s(x,k) 
 let l = x.length
 if (l<k) 
 return x+'0';
 l--;
 if (x[l]=='0')
 return x.slice(0,l)+'1'
 else 
 return (x=='1'.padEnd(k,'1'))? null: x.slice(1)
 

share|improve this question

edited Mar 26 at 0:46

Peter Krauss

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges

share|improve this question

edited Mar 26 at 0:46

Peter Krauss

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges

asked Mar 25 at 22:19

Peter KraussPeter Krauss

5,8311111 gold badges8888 silver badges191191 bronze badges