1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
//
// Copyright 2012 Hakan Kjellerstrand
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using Google.OrTools.ConstraintSolver;
public class SkiAssignment
{
/**
*
* 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.
* """
*
* Also see http://www.hakank.org/or-tools/ski_assignment.py
*
*/
private static void Solve()
{
Solver solver = new Solver("SkiAssignment");
//
// Data
//
int num_skis = 6;
int num_skiers = 5;
int[] ski_heights = { 1, 2, 5, 7, 13, 21 };
int[] skier_heights = { 3, 4, 7, 11, 18 };
//
// Decision variables
//
IntVar[] x = solver.MakeIntVarArray(num_skiers, 0, num_skis - 1, "x");
//
// Constraints
//
solver.Add(x.AllDifferent());
IntVar[] z_tmp = new IntVar[num_skiers];
for (int i = 0; i < num_skiers; i++)
{
z_tmp[i] = (ski_heights.Element(x[i]) - skier_heights[i]).Abs().Var();
}
// IntVar z = solver.MakeIntVar(0, ski_heights.Sum(), "z");
// solver.Add(z_tmp.Sum() == z);
// The direct cast from IntExpr to IntVar is potentially faster than
// the above code.
IntVar z = z_tmp.Sum().VarWithName("z");
//
// Objective
//
OptimizeVar obj = z.Minimize(1);
//
// Search
//
DecisionBuilder db = solver.MakePhase(x, Solver.CHOOSE_FIRST_UNBOUND, Solver.INT_VALUE_DEFAULT);
solver.NewSearch(db, obj);
while (solver.NextSolution())
{
Console.Write("z: {0} x: ", z.Value());
for (int i = 0; i < num_skiers; i++)
{
Console.Write(x[i].Value() + " ");
}
Console.WriteLine();
}
Console.WriteLine("\nSolutions: {0}", solver.Solutions());
Console.WriteLine("WallTime: {0}ms", solver.WallTime());
Console.WriteLine("Failures: {0}", solver.Failures());
Console.WriteLine("Branches: {0} ", solver.Branches());
solver.EndSearch();
}
public static void Main(String[] args)
{
Solve();
}
}