249 lines
7.2 KiB
C#
249 lines
7.2 KiB
C#
//
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// Copyright 2012 Hakan Kjellerstrand
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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using System;
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using System.Collections;
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using System.Collections.Generic;
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using System.Linq;
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using Google.OrTools.ConstraintSolver;
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public class SecretSanta2
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{
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/**
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*
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* Secret Santa problem II in Google CP Solver.
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*
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* From Maple Primes: 'Secret Santa Graph Theory'
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* http://www.mapleprimes.com/blog/jpmay/secretsantagraphtheory
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* """
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* Every year my extended family does a 'secret santa' gift exchange.
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* Each person draws another person at random and then gets a gift for
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* them. At first, none of my siblings were married, and so the draw was
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* completely random. Then, as people got married, we added the restriction
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* that spouses should not draw each others names. This restriction meant
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* that we moved from using slips of paper on a hat to using a simple
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* computer program to choose names. Then people began to complain when
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* they would get the same person two years in a row, so the program was
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* modified to keep some history and avoid giving anyone a name in their
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* recent history. This year, not everyone was participating, and so after
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* removing names, and limiting the number of exclusions to four per person,
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* I had data something like this:
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*
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* Name: Spouse, Recent Picks
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*
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* Noah: Ava. Ella, Evan, Ryan, John
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* Ava: Noah, Evan, Mia, John, Ryan
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* Ryan: Mia, Ella, Ava, Lily, Evan
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* Mia: Ryan, Ava, Ella, Lily, Evan
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* Ella: John, Lily, Evan, Mia, Ava
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* John: Ella, Noah, Lily, Ryan, Ava
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* Lily: Evan, John, Mia, Ava, Ella
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* Evan: Lily, Mia, John, Ryan, Noah
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* """
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*
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* Note: I interpret this as the following three constraints:
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* 1) One cannot be a Secret Santa of one's spouse
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* 2) One cannot be a Secret Santa for somebody two years in a row
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* 3) Optimization: maximize the time since the last time
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*
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* This model also handle single persons, something the original
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* problem don't mention.
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*
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*
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* Also see http://www.hakank.org/or-tools/secret_santa2.py
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*
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*/
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private static void Solve(int single=0)
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{
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Solver solver = new Solver("SecretSanta2");
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Console.WriteLine("\nSingle: {0}", single);
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//
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// The matrix version of earlier rounds.
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// M means that no earlier Santa has been assigned.
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// Note: Ryan and Mia has the same recipient for years 3 and 4,
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// and Ella and John has for year 4.
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// This seems to be caused by modification of
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// original data.
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//
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int n_no_single = 8;
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int M = n_no_single + 1;
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int[][] rounds_no_single = {
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// N A R M El J L Ev
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new int[] {0, M, 3, M, 1, 4, M, 2}, // Noah
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new int[] {M, 0, 4, 2, M, 3, M, 1}, // Ava
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new int[] {M, 2, 0, M, 1, M, 3, 4}, // Ryan
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new int[] {M, 1, M, 0, 2, M, 3, 4}, // Mia
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new int[] {M, 4, M, 3, 0, M, 1, 2}, // Ella
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new int[] {1, 4, 3, M, M, 0, 2, M}, // John
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new int[] {M, 3, M, 2, 4, 1, 0, M}, // Lily
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new int[] {4, M, 3, 1, M, 2, M, 0} // Evan
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};
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//
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// Rounds with a single person (fake data)
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//
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int n_with_single = 9;
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M = n_with_single + 1;
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int[][] rounds_single = {
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// N A R M El J L Ev S
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new int[] {0, M, 3, M, 1, 4, M, 2, 2}, // Noah
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new int[] {M, 0, 4, 2, M, 3, M, 1, 1}, // Ava
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new int[] {M, 2, 0, M, 1, M, 3, 4, 4}, // Ryan
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new int[] {M, 1, M, 0, 2, M, 3, 4, 3}, // Mia
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new int[] {M, 4, M, 3, 0, M, 1, 2, M}, // Ella
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new int[] {1, 4, 3, M, M, 0, 2, M, M}, // John
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new int[] {M, 3, M, 2, 4, 1, 0, M, M}, // Lily
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new int[] {4, M, 3, 1, M, 2, M, 0, M}, // Evan
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new int[] {1, 2, 3, 4, M, 2, M, M, 0} // Single
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};
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int Noah = 0;
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int Ava = 1;
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int Ryan = 2;
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int Mia = 3;
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int Ella = 4;
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int John = 5;
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int Lily = 6;
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int Evan = 7;
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int n = n_no_single;
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int[][] rounds = rounds_no_single;
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if (single == 1) {
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n = n_with_single;
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rounds = rounds_single;
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}
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M = n + 1;
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IEnumerable<int> RANGE = Enumerable.Range(0, n);
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String[] persons = {"Noah", "Ava", "Ryan", "Mia", "Ella",
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"John", "Lily", "Evan", "Single"};
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int[] spouses = {
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Ava, // Noah
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Noah, // Ava
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Mia, // Rya
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Ryan, // Mia
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John, // Ella
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Ella, // John
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Evan, // Lily
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Lily, // Evan
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-1 // Single has no spouse
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};
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//
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// Decision variables
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//
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IntVar[] santas = solver.MakeIntVarArray(n, 0, n-1, "santas");
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IntVar[] santa_distance = solver.MakeIntVarArray(n, 0, M, "santa_distance");
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// total of "distance", to maximize
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IntVar z = santa_distance.Sum().VarWithName("z");
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//
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// Constraints
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//
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solver.Add(santas.AllDifferent());
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// Can't be one own"s Secret Santa
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// (i.e. ensure that there are no fix-point in the array.)
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foreach(int i in RANGE) {
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solver.Add(santas[i] != i);
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}
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// no Santa for a spouses
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foreach(int i in RANGE) {
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if (spouses[i] > -1) {
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solver.Add(santas[i] != spouses[i]);
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}
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}
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// optimize "distance" to earlier rounds:
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foreach(int i in RANGE) {
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solver.Add(santa_distance[i] == rounds[i].Element(santas[i]));
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}
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// cannot be a Secret Santa for the same person
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// two years in a row.
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foreach(int i in RANGE) {
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foreach(int j in RANGE) {
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if (rounds[i][j] == 1) {
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solver.Add(santas[i] != j);
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}
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}
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}
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//
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// Objective (minimize the distances)
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//
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OptimizeVar obj = z.Maximize(1);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(santas,
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Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
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Solver.ASSIGN_CENTER_VALUE);
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solver.NewSearch(db, obj);
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while (solver.NextSolution()) {
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Console.WriteLine("\ntotal distances: {0}", z.Value());
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Console.Write("santas: ");
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for(int i = 0; i < n; i++) {
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Console.Write(santas[i].Value() + " ");
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}
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Console.WriteLine();
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foreach(int i in RANGE) {
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Console.WriteLine("{0}\tis a Santa to {1} (distance {2})",
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persons[i],
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persons[santas[i].Value()],
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santa_distance[i].Value());
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}
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}
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Console.WriteLine("\nSolutions: {0}", solver.Solutions());
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Console.WriteLine("WallTime: {0}ms", solver.WallTime());
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Console.WriteLine("Failures: {0}", solver.Failures());
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Console.WriteLine("Branches: {0} ", solver.Branches());
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solver.EndSearch();
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}
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public static void Main(String[] args)
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{
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int single = 0;
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Solve(single);
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single = 1;
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Solve(single);
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}
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}
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