Minimum of sum of absolute values

Question

Problem statement:

There are 3 arrays A,B,C all filled with positive integers, and all the three arrays are of the same size.

Find min(|a-b|+|b-c|+|c-a|) whe

Answer 1

I would write a really simple program like this:

#!/usr/bin/python
import sys, os, random
A = random.sample(range(100), 10)
B = random.sample(range(100), 10)
C = random.sample(range(100), 10)
minsum = sys.maxint
for a in A:
 for b in B:
  for c in C:
   print 'checking with a=%d b=%d c=%d' % (a, b, c)
   abcsum = abs(a - b) + abs(b - c) + abs(c - a)
   if abcsum < minsum:
    print 'found new low sum %d with a=%d b=%d c=%d' % (abcsum, a, b, c)
    minsum = abcsum

And test it over and over until I saw some pattern emerge. The pattern I found here is what would be expected: the numbers that are closest together in each set, regardless of whether the numbers are "high" or "low", are those that produce the smallest minimum sum. So it becomes a nearest-number problem. For whatever that's worth, probably not much.