1# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com 2# 3# Licensed under the Apache License, Version 2.0 (the "License"); 4# you may not use this file except in compliance with the License. 5# You may obtain a copy of the License at 6# 7# http://www.apache.org/licenses/LICENSE-2.0 8# 9# Unless required by applicable law or agreed to in writing, software 10# distributed under the License is distributed on an "AS IS" BASIS, 11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12# See the License for the specific language governing permissions and 13# limitations under the License. 14""" 15 16 Ski assignment in Google CP Solver. 17 18 From Jeffrey Lee Hellrung, Jr.: 19 PIC 60, Fall 2008 Final Review, December 12, 2008 20 http://www.math.ucla.edu/~jhellrun/course_files/Fall%25202008/PIC%252060%2520-%2520Data%2520Structures%2520and%2520Algorithms/final_review.pdf 21 ''' 22 5. Ski Optimization! Your job at Snapple is pleasant but in the winter 23 you've decided to become a ski bum. You've hooked up with the Mount 24 Baldy Ski Resort. They'll let you ski all winter for free in exchange 25 for helping their ski rental shop with an algorithm to assign skis to 26 skiers. Ideally, each skier should obtain a pair of skis whose height 27 matches his or her own height exactly. Unfortunately, this is generally 28 not possible. We define the disparity between a skier and his or her 29 skis to be the absolute value of the difference between the height of 30 the skier and the pair of skis. Our objective is to find an assignment 31 of skis to skiers that minimizes the sum of the disparities. 32 ... 33 Illustrate your algorithm by explicitly filling out the A[i, j] table 34 for the following sample data: 35 * Ski heights: 1, 2, 5, 7, 13, 21. 36 * Skier heights: 3, 4, 7, 11, 18. 37 ''' 38 39 Compare with the following models: 40 * Comet : http://www.hakank.org/comet/ski_assignment.co 41 * MiniZinc: http://hakank.org/minizinc/ski_assignment.mzn 42 * ECLiPSe : http://www.hakank.org/eclipse/ski_assignment.ecl 43 * SICStus: http://hakank.org/sicstus/ski_assignment.pl 44 * Gecode: http://hakank.org/gecode/ski_assignment.cpp 45 46 This model was created by Hakan Kjellerstrand (hakank@gmail.com) 47 Also see my other Google CP Solver models: 48 http://www.hakank.org/google_or_tools/ 49""" 50import sys 51 52from ortools.constraint_solver import pywrapcp 53 54 55def main(): 56 57 # Create the solver. 58 solver = pywrapcp.Solver('Ski assignment') 59 60 # 61 # data 62 # 63 num_skis = 6 64 num_skiers = 5 65 ski_heights = [1, 2, 5, 7, 13, 21] 66 skier_heights = [3, 4, 7, 11, 18] 67 68 # 69 # variables 70 # 71 72 # which ski to choose for each skier 73 x = [solver.IntVar(0, num_skis - 1, 'x[%i]' % i) for i in range(num_skiers)] 74 z = solver.IntVar(0, sum(ski_heights), 'z') 75 76 # 77 # constraints 78 # 79 solver.Add(solver.AllDifferent(x)) 80 81 z_tmp = [ 82 abs(solver.Element(ski_heights, x[i]) - skier_heights[i]) 83 for i in range(num_skiers) 84 ] 85 solver.Add(z == sum(z_tmp)) 86 87 # objective 88 objective = solver.Minimize(z, 1) 89 90 # 91 # search and result 92 # 93 db = solver.Phase(x, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT) 94 95 solver.NewSearch(db, [objective]) 96 97 num_solutions = 0 98 while solver.NextSolution(): 99 num_solutions += 1 100 print('total differences:', z.Value()) 101 for i in range(num_skiers): 102 x_val = x[i].Value() 103 ski_height = ski_heights[x[i].Value()] 104 diff = ski_height - skier_heights[i] 105 print('Skier %i: Ski %i with length %2i (diff: %2i)' %\ 106 (i, x_val, ski_height, diff)) 107 print() 108 109 solver.EndSearch() 110 111 print() 112 print('num_solutions:', num_solutions) 113 print('failures:', solver.Failures()) 114 print('branches:', solver.Branches()) 115 print('WallTime:', solver.WallTime()) 116 117 118if __name__ == '__main__': 119 main() 120