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ski_assignment

First, you must install ortools package in this colab.

%pip install ortools

Ski assignment in Google CP Solver.

From Jeffrey Lee Hellrung, Jr.: PIC 60, Fall 2008 Final Review, December 12, 2008 http://www.math.ucla.edu/~jhellrun/course_files/Fall%25202008/PIC%252060%2520-%2520Data%2520Structures%2520and%2520Algorithms/final_review.pdf ''' 5. Ski Optimization! Your job at Snapple is pleasant but in the winter you've decided to become a ski bum. You've hooked up with the Mount Baldy Ski Resort. They'll let you ski all winter for free in exchange for helping their ski rental shop with an algorithm to assign skis to skiers. Ideally, each skier should obtain a pair of skis whose height matches his or her own height exactly. Unfortunately, this is generally not possible. We define the disparity between a skier and his or her skis to be the absolute value of the difference between the height of the skier and the pair of skis. Our objective is to find an assignment of skis to skiers that minimizes the sum of the disparities. ... Illustrate your algorithm by explicitly filling out the A[i, j] table for the following sample data: * Ski heights: 1, 2, 5, 7, 13, 21. * Skier heights: 3, 4, 7, 11, 18. '''

Compare with the following models:

• Comet : http://www.hakank.org/comet/ski_assignment.co
• MiniZinc: http://hakank.org/minizinc/ski_assignment.mzn
• ECLiPSe : http://www.hakank.org/eclipse/ski_assignment.ecl
• SICStus: http://hakank.org/sicstus/ski_assignment.pl
• Gecode: http://hakank.org/gecode/ski_assignment.cpp

This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

import sys

from ortools.constraint_solver import pywrapcp


def main():

  # Create the solver.
  solver = pywrapcp.Solver('Ski assignment')

  #
  # data
  #
  num_skis = 6
  num_skiers = 5
  ski_heights = [1, 2, 5, 7, 13, 21]
  skier_heights = [3, 4, 7, 11, 18]

  #
  # variables
  #

  # which ski to choose for each skier
  x = [solver.IntVar(0, num_skis - 1, 'x[%i]' % i) for i in range(num_skiers)]
  z = solver.IntVar(0, sum(ski_heights), 'z')

  #
  # constraints
  #
  solver.Add(solver.AllDifferent(x))

  z_tmp = [
      abs(solver.Element(ski_heights, x[i]) - skier_heights[i])
      for i in range(num_skiers)
  ]
  solver.Add(z == sum(z_tmp))

  # objective
  objective = solver.Minimize(z, 1)

  #
  # search and result
  #
  db = solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT)

  solver.NewSearch(db, [objective])

  num_solutions = 0
  while solver.NextSolution():
    num_solutions += 1
    print('total differences:', z.Value())
    for i in range(num_skiers):
      x_val = x[i].Value()
      ski_height = ski_heights[x[i].Value()]
      diff = ski_height - skier_heights[i]
      print('Skier %i: Ski %i with length %2i (diff: %2i)' %\
            (i, x_val, ski_height, diff))
    print()

  solver.EndSearch()

  print()
  print('num_solutions:', num_solutions)
  print('failures:', solver.Failures())
  print('branches:', solver.Branches())
  print('WallTime:', solver.WallTime())


main()