This is one of those NP problems which are usually tractable, this is an interesting article from American Scientist.

One greedy algorithm assuming you have a standard length of skirting board and varying wall lengths. The steps are

  1. Find the "odd" lengths, that is the remaining length on each wall after using the standard lengths.
  2. Sort the remainders by length, longest first.
  3. Select the longest and assign it to the shortest length of skirting board it will fit in, if it can't be fitted to an existing board then use a new one..
  4. Repeat previous step until there are no remaining lengths

An example 

skirting length: 5
wall lengths: 24 16 21 4 3 12
remainders: 4 1 1 4 3 2
sorted rem: 4 4 3 2 1 1

Skirting 1: 4 ( available 1 )
sorted rem: 4 3 2 1 1

Skirting 1: 4 ( available 1 )
Skirting 2: 4 ( available 1 )
sorted rem: 3 2 1 1

Skirting 1: 4 ( available 1 )
Skirting 2: 4 ( available 1 )
Skirting 3: 3 ( available 2 )
sorted rem: 2 1 1

Skirting 1: 4 ( available 1 )
Skirting 2: 4 ( available 1 )
Skirting 3: 3 2 ( available 0 )
sorted rem: 1 1

Skirting 1: 4 1 ( available 0 )
Skirting 2: 4 ( available 1 )
Skirting 3: 3 2 ( available 0 )
sorted rem: 1

Skirting 1: 4 1 ( available 0 )
Skirting 2: 4 1 ( available 0 )
Skirting 3: 3 2 ( available 0 )

[download]

In reply to Re: "The Skirting Board Problem" by hipowls
in thread "The Skirting Board Problem" by loris

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