I have a problem that I need to find the right algorithm for and I am not sure which avenues are going to be easiest.
I have a 'row' of fixed height and we can assume infinite length.
fig.1
-------------------> X we can assume is infinite
^
| Y is fixed.
v
-------------
Then I have a series of objects that need to fill vertically the 'row' and that have a fixed horizontal position.
fig2.
---------------
|--1--|
|---3---|
|----2----|
---------------
fig3.
----------------------
|--1--| |----3----|
|---2---|
----------------------
So as we see. In fig 2 the maximum allowed height for the objects in our 'row' are 1/3 as all objects overlap, the vertical order is not important. In fig 3 they are 1/2, as only 1 and 2 and 2 and 3 overlap, vertical order therefore puts 1 and 3 in the same vertical position and 2 in a vertical position of its own.
Is there one or a set of algoritms that I should be looking into to help solve this problem? The ones I have read about tend to assume fixed sizes of objects and space, and that order of the packing is not important.
This is for a calendar control built in software, so will need to accomodate best guess and some limitations that I don't mind working out. I appereciate that this is an NP problem and if a lot of overlaps occur into the 'future' there might be NO viable solution.
Any help would be very warmly recieved!