O Algoritmo Húngaro é um algoritmo de otimização combinatória para resolver problemas de atribuição de tarefas em tempo polinomial e conduziu a abordagem primal-dual posterior. Em 1955, WW Kuhn construiu esta solução usando um teorema do matemático húngaro D. Kőnig, por isso é chamado de método húngaro. [2]
Matriz de Adjacência-C
#include<stdio.h>
#include<string.h>
int n1, n2, m, ans;
int result[101];//记录V2中的点匹配的点的编号
bool state[101];//记录V2中的每个点是否被搜索过
bool data[101][101];//邻接矩阵true代表有边相连
void init()
{
int t1, t2;
memset(data, 0, sizeof(data));
memset(result, 0, sizeof(result));
ans = 0;
scanf("%d%d%d", &n1, &n2, &m);
for(int i = 1; i <= m; i++)
{
scanf("%d%d", &t1, &t2);
data[t1][t2] = true;
}
return;
}
bool find(inta)
{
for(int i = 1; i <= n2; i++)
{
if(data[a][i] == 1 && !state[i]) //如果节点i与a相邻并且未被查找过
{
state[i] = true; //标记i为已查找过
if(result[i] == 0 //如果i未在前一个匹配M中
|| find(result[i])) //i在匹配M中，但是从与i相邻的节点出发可以有增广路
{
result[i] = a; //记录查找成功记录
return true;//返回查找成功
}
}
}
return false;
}
int main()
{
init();
for(int i = 1; i <= n1; i++)
{
memset(state, 0, sizeof(state)); //清空上次搜索时的标记
if(find(i))
{
ans++; //从节点i尝试扩展
}
}
printf("%d\n", ans);
return 0;
}matriz de adjacência-pascal
Programhungary;
Const
max=100;
Var
data:array[1..max,1..max]ofboolean;{邻接矩阵}
result:array[1..max]ofinteger;{记录当前连接方式}
state:array[1..max]ofboolean;{记录是否遍历过，防止死循环}
m,n1,n2,i,t1,t2,ans:integer;
Function dfs(p:integer):boolean;
var
i:integer;
begin
for i:=1 to n2 do
if data[p,i]and not(state[i]) then{有边存在且没有被搜索过}
begin
state[i]:=true;
if (result[i]=0)or dfs(result[i]) then{没有被连过或寻找到增广路}
begin
result[i]:=p;
exit(true);
end;
end;
exit(false);
end;
begin
readln(n1,n2,m);
fillchar(data,sizeof(data),0);
fori:=1 to mdo
begin
readln(t1,t2）；
data[t1,t2]:=true;
end;
fillchar(result,sizeof(result),0);
ans:=0;
fori:=1 to n1 do
begin
fillchar(state,sizeof(state),0);
if dfs(i) then inc(ans);
end;
writeln(ans);
end.Adjacência list-pascal (usando lista encadeada dinâmica)
programhungarian_algorithm;//匈牙利算法
type
node=^link;//链表定义
link=record
g:longint;//指向节点
next:node;
end;
var
n1,n2,m,a,v1,v2,ans:longint;
flag:array[1..1000000]ofboolean;//记录在main递归过程中是否已访问过，防止死循环
nd:array[1..1000000]ofnode;//邻接表
resultt:array[1..1000000]oflongint;//记录v2中节点的最终匹配于v1中的几号节点
functionmain(wei:longint):boolean;
varp:node;
begin
p:=nd[wei];
whilep<>nildo
begin
ifflag[p^.g]{没有被搜索过}
thenbegin
flag[p^.g]:=false;
if(resultt[p^.g]=0)or(main(resultt[p^.g])){没有被连过或原来指向的节点寻找到新的增广路}
thenbegin
resultt[p^.g]:=wei;
exit(true);
end;
end;
p:=p^.next;
end;
exit(false)
end;
procedureaddd(v1,v2:longint);//建立邻接表过程
varp:node;
begin
new(p);
p^.g:=v2;
p^.next:=nd[v1];
nd[v1]:=p;
end;
begin
readln(n1,n2,m);
fora:=1tomdo
begin
readln(v1,v2);
addd(v1,v2);
end;
ans:=0;
fillchar(resultt,sizeof(resultt),0);
fora:=1ton1do
begin
fillchar(flag,sizeof(flag),true);
ifmain(a)
theninc(ans);
end;
writeln(ans);
fora:=1ton2do
ifresultt[a]<>0
thenwriteln(resultt[a],'---',a);
end.Lista de adjacências-C++
#include<iostream>
#include<cstring>
using namespace std;
//定义链表
struct link{
int data;//存放数据
link*next;//指向下一个节点
link(int=0);
};
link::link(int n){
data=n;
next=NULL;
}
int n1,n2,m,ans=0;
int result[101];//记录n1中的点匹配的点的编号
bool state[101];//记录n1中的每个点是否被搜索过
link*head[101];//记录n2中的点的邻接节点
link*last[101];//邻接表的终止位置记录
//判断能否找到从节点n开始的增广路
bool find(const int n){
link*t=head[n];
while(t!=NULL){//n仍有未查找的邻接节点时
if(!(state[t->data])){//如果邻接点t->data未被查找过
state[t->data]=true;//标记t->data为已经被找过
if((result[t->data]==0)||//如果t->data不属于前一个匹配M
(find(result[t->data]))){//如果t->data匹配到的节点可以寻找到增广路
result[t->data]=n;//那么可以更新匹配M'，其中n1中的点t->data匹配n
return true;//返回匹配成功的标志
}
}
t=t->next;//继续查找下一个n的邻接节点
}
return false;
}
int main(){
int t1=0,t2=0;
cin>>n1>>n2>>m;
for(int i=0;i<m;i++){
cin>>t1>>t2;
if(last[t1]==NULL)
last[t1]=head[t1]=new link(t2);
else
last[t1]=last[t1]->next=new link(t2）；
}
for(int i=1;i<=n1;i++){
memset(state,0,sizeof(state));
if(find(i))ans++;
}
cout<<ans<<endl;
return 0;
}Matriz de Adjacência - C++
#include<iostream>
#include<cstring>
using namespace std;
int map[105][105];
int visit[105],flag[105];
int n,m;
bool dfs(int a)
{
for(int i=1; i<=n; i++)
{
if(map[a][i]&&!visit[i])
{
visit[i]=1;
if(flag[i]==0||dfs(flag[i]))
{
flag[i]=a;
return true;
}
}
}
return false;
}
int main()
{
int n1,n2;
while(cin>>n1 >>n2 >>m)
{
n=n1;
memset(map,0,sizeof(map));
for(int i=1; i<=m; i++)
{
int x,y;
cin>>x>>y;
map[x][y]=1;
}
memset(flag,0,sizeof(flag));
int result=0;
for(int i=1; i<=n1; i++)
{
memset(visit,0,sizeof(visit));
if(dfs(i))result++;
}
cout<<result<<endl;
}
return 0;
}conceito
referências:
(2) Introdução ao Algoritmo Húngaro_Hungary Blog-CSDN Blog_Hungarian Algorithm
Fun to Write Algorithm Series - Blog do Algorithm_Dark_Scope Húngaro-Blog da CSDN