How optimal do your groupings need to be? And what do you consider to be optimal?

For example, in the following set of numbers, those algorithms that start a new group when adding the next value causes the current grouping to break the limit would group the first two values, 122.45 & 122.55 in a group by themselves as adding the third value, 122.67 causes the first value to be outside the lower boundary. The next five values can then form a second group.

However, isolating that first value into it's own group, allows the next 4 values to become a group, leaving the last two as a third group.

Not well demonstrated, trying to come up with a good demonstration is labourious, but it is possible to see that sometimes it will be better to drop the first value from a grouping rather than the last added in order to incorporate as many values as possible into a group.

Hence the questions at the top. Possibilities for optimal might be

• Smallest number of groups
• Biggest group sizes.
• Even group sizes.
• Quickest to calculate (that doesn't place each value in a separate group :)
• Other?

values    2      3       4       5       6       7
        122.35  122.517 122.455 122.488 122.483 122.533  low limit
122.45
        122.5
122.55          122.567
                        122.605
122.67                          122.638
                                        122.633
122.75                                          122.683

122.77

122.79

122.80
        122.65  122.817 122.755 122.788 122.783 122.833   high limit
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