Stable Matching (Gale Sharpley Algorithm)
稳定婚配问题：n个男生n个女生，其中每个人都有自己心仪的列表。问如何达成稳定的匹配(比如, b想B求婚，但是B已有的对象的优先级高于b,此时b的魅力不足以拆散B所处的那一对，即达到稳定状态。)
（Gale_Shapley algorithm）总体策略：男士负责求婚，女士负责接受或者拒绝。
题目原型： HDUOJ 1914 The Stable Marriage Problem
以下为数据生成函数，生成boys_rankings.txt 和 girls_rankings.txt
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <sstream>
#include <algorithm>
#include <vector>
#include <ctime>
#include <fstream>
using namespace std;
vector<string> gen_boys(int number)
{
vector<string> result;
for(int i = 0; i < number; i++){
string boy = "B";
string s;
stringstream ss;
ss << i;
ss >> s;
boy.append(s);
result.push_back(boy);
}
return result;
}
vector<string> gen_girls(int number)
{
vector<string> result;
for(int i = 0; i < number; i++){
string boy = "G";
string s;
stringstream ss;
ss << i;
ss >> s;
boy.append(s);
result.push_back(boy);
}
return result;
}
vector<string> gen_ranking(vector<string> candidate)
{
random_shuffle(candidate.begin(), candidate.end());
return candidate;
}
void write_rankings(vector<string> people, vector<vector<string> > rankings, string out_file)
{
ofstream ofs(out_file.c_str());
if(ofs.fail()){
cerr << "Error: " << out_file << endl;
return;
}
for(int i = 0; i < people.size(); i++){
ofs << people[i] << ":";
for(int j = 0; j < rankings[i].size(); j++){
ofs << " " << rankings.at(i).at(j);
}
ofs << endl;
}
ofs.close();
}
int main(int argc, char ** argv)
{
srand(time(NULL));
int n = 200;
vector<string> boys = gen_boys(n);
vector<string> girls = gen_girls(n);
vector<vector<string> > boys_rankings;
vector<vector<string> > girls_rankings;
for(int i = 0; i < n; i++){
boys_rankings.push_back(gen_ranking(girls));
girls_rankings.push_back(gen_ranking(boys));
}
write_rankings(boys, boys_rankings, "boys_rankings.txt");
write_rankings(girls, girls_rankings, "girls_rankings.txt");
return 1;
}
以下为Gale_Sharpley算法实现：
/******************************************************
* Projects : Implementation of Gale_Shapley algorithm
* Author : johnsondu
* Time : 2014-10-20 21:18
*******************************************************/
#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <fstream>
#include <map>
#include <vector>
#include <cstring>
#include <string>
using namespace std;
// The max size of the number of the boy.
const int MAXN = 1000;
// STL map, map boy's name to integer ID
map<string, int> boy;
// STL map, map girl's name to integer ID
map<string, int> girl;
// STL map, map corresponding boy's integer id to original string name
map<int, string> boyName;
// STL map, map corresponding girl's integer id to original string name
map<int, string> girlName;
// boy's preference ranking list
int boysRankings[MAXN][MAXN];
// girl's preference ranking list
int girlsRankings[MAXN][MAXN];
// the partner that boy matched. if no, marked as -1
int boysPartner[MAXN];
// the partner that girl matched. if no, marked as -1
int girlsPartner[MAXN];
/*******************************************************
* function description:
* let every boy and girl have it's own integer identity.
* key variable: <string, int>(map string name to integer
* id), <int, string>(map integer id to original string
* name)
********************************************************/
void SerialNumber(int &n)
{
ifstream in1("boys_rankings.txt");
ifstream in2("girls_rankings.txt");
string str;
int idb = 0; // boy's id
int idg = 0; // girl's id
while(getline(in1, str)){
string name = "";
int i = 0;
// get boys's name
while(str[i] != ':') name += str[i ++];
// map string to int.
boy[name] = idb ;
boyName[idb] = name;
idb ++;
// get the number of boys.
n ++;
}
while(getline(in2, str)){
string name = "";
int i = 0;
// get boys's name
while(str[i] != ':') name += str[i ++];
// map string to int.
girl[name] = idg;
girlName[idg] = name;
idg ++;
}
return;
}
/*********************************************
* function description:
* Rereading two files, and get corresponding
* preference list of boys and girls. Save it
* in two dimension array: girlsRankings and
* boysRankings.
*******************************************/
void GetRankings(const int n)
{
ifstream in1("boys_rankings.txt");
ifstream in2("girls_rankings.txt");
string str;
// boy's id.
int id = 0;
while(getline(in1, str)){
string gname;
int i = 0;
int cnt = 0;
while(str[i] != ' ') i ++;
if(str[i] == ' ') i ++;
for(; i < str.size();)
{
gname = "";
while(str[i] != ' ' && i < str.size()) {
gname += str[i];
i ++;
}
boysRankings[id][cnt ++] = girl[gname];
if(str[i] == ' ') i ++;
}
id ++;
}
// girls id;
id = 0;
while(getline(in2, str)){
string bname;
// string size index.
int i = 0;
// the rankings in the girl's list.
int cnt = 0;
// prefix guarantee
while(str[i] != ' ') i ++;
if(str[i] == ' ') i ++;
for(; i < str.size();)
{
bname = "";
while(str[i] != ' ' && i < str.size()) {
bname += str[i];
i ++;
}
girlsRankings[id][cnt ++] = boy[bname];
if(str[i] == ' ') i ++;
}
id ++;
}
return ;
}
/*************************************
* function description:
* set status for boys and girls,
* marked -1, no partner.
**************************************/
void InitStatus(const int n)
{
for(int i = 0; i < n; i ++)
{
boysPartner[i] = -1;
girlsPartner[i] = -1;
}
}
/****************************************
* function description:
* when one boy propose to one girl, and
* that girl already have a partner, this
* function is used for get ratings of
* two boys in that girl's preference list.
*****************************************/
int GetId(int boyId, int gId, const int n)
{
for(int i = 0; i < n; i ++)
{
if(girlsRankings[gId][i] == boyId) return i;
}
return -1;
}
/****************************************
* function description:
* once a man have dumped by a girl, set
* his status to no partner, and set his
* preference list of that girl as -1,
* stand for have been proposed before.
*****************************************/
void SetStatus(int boyId, int girlId, const int n)
{
boysPartner[boyId] = -1;
for(int i = 0; i < n; i ++)
if(boysRankings[boyId][i] == girlId){
boysRankings[boyId][i] = -1;
return;
}
}
/****************************************
* function description:
* Implementation of Gale_Shapley algorithm
*****************************************/
void StableMatch(const int n)
{
InitStatus(n);
while(true)
{
bool flag = false;
bool endOfFor = false;
// guarantee all the boys have a partner.
for(int i = 0; i < n; i ++){
if(boysPartner[i] == -1 || girlsPartner[i] == -1)
{
flag = true;
break;
}
}
if(!flag) break;
// for boy who have no partner.
for(int i = 0; i < n; i ++)
{
if(boysPartner[i] == -1){
for(int j = 0; j < n; j ++){
// Since in the list of preference, j had rejected before.
if(boysRankings[i][j] == -1) continue;
// if j have no partner, then accept.
if(girlsPartner[boysRankings[i][j]] == -1){
boysPartner[i] = boysRankings[i][j];
girlsPartner[boysRankings[i][j]] = i;
endOfFor = true;
break;
}
else{ // judge whether match is stable or not
int useId = GetId(girlsPartner[boysRankings[i][j]], boysRankings[i][j], n);
int curId = GetId(i, boysRankings[i][j], n);
// if not stable
if(curId < useId){
// girl's partner's list, set -1 to mean the girl have rejected.
SetStatus(girlsPartner[boysRankings[i][j]], boysRankings[i][j], n);
boysPartner[i] = boysRankings[i][j];
girlsPartner[boysRankings[i][j]] = i;
endOfFor = true;
break;
}
}
}
}
// find a partner, break out of the loop.
if(endOfFor) break;
}
}
}
/****************************************
* function description:
* print out result.
*****************************************/
void Print(const int n)
{
freopen("result.txt", "w", stdout);
cout << "The Matching Results are follows:" << endl;
for(int i = 0; i < n; i ++){
cout << boyName[i]
<< "--" << girlName[boysPartner[i]] << " " << endl;
}
}
/****************************************
* function description:
* Main function
*****************************************/
int main()
{
int n = 0;
// let every boy and girl have it's own identity.
// and get integer ranking array list.
SerialNumber(n);
// get rankings.S
GetRankings(n);
// Stable match
StableMatch(n);
// Print solution
Print(n);
return 0;
}