[r-t] Algorithm for determining the order of Calling Position Headings

[Graham John]

As a weekend challenge, can anyone suggest an efficient algorithm for
determining the optimal sequence of calling position headings when
formatting a composition?

 

The requirements are:-

1. Minimise the number of lines required to display the composition

2. Within the above, calling positions with fewer leads between them should
be closer together

3. Minimise the need for courseheads in parentheses

3. Home, where present, should be the last column (this is probably a
personal preference, although it can conflict with 1 and may not be
appropriate for snap start and finish compositions - happy to debate this
point!)

 

The data to be processed by the algorithm can be considered as a table such
as that shown below. Do not assume though that the number of leads between
calling positions is fixed, as this needs to work for Spliced with mixed
lead orders as well as single methods.

 


Leads

Calling Position


1

H


1

H


3

M


5

M


1

W


3

M


4

H


2

W


1

W


1

W


3

I


1

H


5

H

 

This example is taken from the beginning of a split tenors composition of
the Nottingham 8 

<http://www.changeringing.co.uk/ssmajor.htm#5024-8m3>

 

I have worked out an algorithm that should work, but I am sure that there
must be a more elegant and efficient solution possible. Answers in program
code or pseudo-code welcome.

 

Graham

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