If X = {0, 2, 5, 10, 12},
a minimal coverage will be: [0,5], [10,12]?
in this example a possible minimal coverage will be
[-0.5 , 0.5] , [1.7 , 2.7] , [4.3 , 5.3] , [9.9 , 10.9] , [11 , 12]
X
נתונה ממויינת מראש ?
if the answer to the question is no, what is the maximal digits after the dot that we must take in account?
edit: by minimal, do you mean that the number of groups will be minimal? e.g. for the given example in the beginning of the post, the answer is 5?
Can the unit-intervals exceed the largest point in X, i.e. if Xn = 9.5, can [9.5 - 10.5] be included in the solution?
Can the unit-intervals overlap each other? i.e. if 0.5, 1 and 1.6 are my points, can [0.5-1.5], [0.6-1.6] be a legal solution?
Minimal - in terms of area covered, or in terms of units used? i.e. if 1 and 2.1 are my points, [1..2] and [1.1 .. 2.1] cover both points with minimal area covered (since they overlap), and [0..1], [1.1..2.1] also cover both points but more than the minimal possible area.
The way I see it, the last unit-interval can exceed the largest-value point, as long as the number of intervals is minimal (and correct me if I'm wrong). Same thing about overlaping intervals.
Look at the example in the 2nd reply above, which explains this well.
2) Yes
3) minimal in number of intervals used(units)
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