Help required for Hilbert Space Filing Curve problem

Question

Can someone suggest the algorithm for the following problem:
Given an N � N array A, generate the index of each location A[i][j] according to Hilbert Space Filling curve. The Hilbert curve generates the indices recursively as follows - for a 2 � 2 square the numbering is
2 3
1 4
For a 2^i � 2^i array, the array is first partitioned into 4 subsquares of 2^(i-1) � 2^(i-1). Then the indices of each sub-square is generated recursively such that the lower-left array has the lowest indices followed by upper-left array and then the upper-right and the lower-right array. Moreover, consecutive indices should be in neighbouring squares. For a 4 � 4 array, the indices are
6 7 10 11
5 8 9 12
4 3 14 13
1 2 15 16
Thanks

Answer 1

HeadSwipe wrote:
Can someone suggest the algorithm for the following problem:
Given an N � N array A, generate the index of each location A[i][j] according to Hilbert Space Filling curve. The Hilbert curve generates the indices recursively as follows - for a 2 � 2 square the numbering is
2 3
1 4
I'd recommend one that features recursion.
For a 2^i � 2^i array, the array is first partitioned into 4 subsquares of 2^(i-1) � 2^(i-1). Then the indices of each sub-square is generated recursively such that the lower-left array has the lowest indices followed by upper-left array and then the upper-right and the lower-right array. Moreover, consecutive indices should be in neighbouring squares. This IS the algorithm. You've been given it. You either don't understand it or can't code it.
I'd start wih a Matrix class that would make it easy to do the partitioning into submatricies. Then I'd write a method that would take a Matrix as an argument and call it recursively until I reached my 2x2 Matrix stopping condition.
For a 4 � 4 array, the indices are
6 7 10 11
5 8 9 12
4 3 14 13
1 2 15 16
ThanksSounds like you've been given the algorithm, now all you have to do is implement. That's where you come in.
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