linear_partition.coffee

# Linear partition
# Partitions a sequence of non-negative integers into k ranges
# Based on Óscar López implementation in Python (http://stackoverflow.com/a/7942946)
# Also see http://www8.cs.umu.se/kurser/TDBAfl/VT06/algorithms/BOOK/BOOK2/NODE45.HTM
# Dependencies: UnderscoreJS (http://www.underscorejs.org)
# Example: linear_partition([9,2,6,3,8,5,8,1,7,3,4], 3) => [[9,2,6,3],[8,5,8],[1,7,3,4]]
 
linear_partition = (seq, k) =>
  n = seq.length
  
  return [] if k <= 0
  return seq.map((x) -> [x]) if k > n
 
  table = (0 for x in [0...k] for y in [0...n])
  solution = (0 for x in [0...k-1] for y in [0...n-1])
  table[i][0] = seq[i] + (if i then table[i-1][0] else 0) for i in [0...n]
  table[0][j] = seq[0] for j in [0...k]
  for i in [1...n]
    for j in [1...k]
      m = _.min(([_.max([table[x][j-1], table[i][0]-table[x][0]]), x] for x in [0...i]), (o) -> o[0])
      table[i][j] = m[0]
      solution[i-1][j-1] = m[1]
 
  n = n-1
  k = k-2
  ans = []
  while k >= 0
    ans = [seq[i] for i in [(solution[n-1][k]+1)...n+1]].concat ans
    n = solution[n-1][k]
    k = k-1
 
  [seq[i] for i in [0...n+1]].concat ans