don.lotto@[EMAIL PROTECTED]
wrote:
> A0 33 954. found body at intersection. min dist /upper bound/
> detective must walk to grid search area.. PUZZLES..
>
> [crime victim could have staggerred n blocks = x+y. ]
>
> area of square-diamond = 2n^2.
> detective walks 2 new sides of perimeter squares [spiral] and double 3
> axes.
Attempted translation into English: What is the minimum length
of a path that visits all points (x,y) where x and y are integers
and |x|+|y| <= n?
Requests for clarification: Must the path begin at (0,0)? Can
it cross points (p,q) where neither p nor q is an integer?
Sample paths for n = 1:
* (0,0) to (0,1) to (0,0) to (1,0) to (0,0) to (0,-1) to (0,0) to
(-1,0) [length 7]
* (0,1) to (0,0) to (1,0) to (0,0) to (0,-1) to (0,0) to (-1,0)
[length 6]
* (0,0) to (0,1) to (1,0) to (0,-1) to (-1,0) [length 1 + 4*sqrt(2)]
* (0,1) to (1,0) to (0,0) to (-1,0) to (0,-1) [length 2 + 2*sqrt(2)]
> what about spherical globe? igloo? ice-house.
All points (x,y,z) where x and y and z are integers, |x|+|y|+|z| <= n,
and (for an igloo) x >= 0.
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