"Hiho" Hiho 31st week two maximum match, some of the basic conclusions will be updated here

Test instructions

Maximum matching of binary graphs

Ideas:

The maximum matching algorithm of binary graph is the Hungarian algorithm, which is similar to the finding of the augmented path in the network flow.

Personal preference Dfs Version = =

At that time also look at Kuangbin big template just gradually groping

Supplemental Definitions and theorems:

Maximum matches: the number of matching edges that match the maximum
minimum Point coverage : Select a minimum point so that at least one end of any edge is selected
maximum independent number : Select the most points so that any selected two points are not connected
Minimum path coverage : For a DAG (directed acyclic graph), select the fewest paths so that each vertex belongs to and belongs to only one path. The path length can be 0 (that is, a single point).

Theorem 1: Maximum number of matches = minimum point coverage (this is the Konig theorem)
Theorem 2: Maximum number of matches = maximum Independent number
Theorem 3: Minimum path coverage = number of vertices-maximum number of matches

Note that the maximum matching number of the graph is divided by 2, because it is a graph without direction!

Attached code:

#include <iostream>#include<stdio.h>#include<algorithm>#include<string.h>#include<string>#include<math.h>#include<stack>#include<queue>#include<vector>#include<map>#include<Set>#pragmaWarning (disable:4996)#defineZero (a) memset (a, 0, sizeof (a))#defineNeg (a) memset (a,-1, sizeof (a))#defineAll (a) A.begin (), A.end ()#definePB push_back#defineREPF (i,a,b) for (i = a;i <= b; i++)#defineLson l,m,rt<<1#defineRson m+1,r,rt<<1|1#defineRoot 1,n,1#defineLD RT << 1#defineRd RT << 1 | 1#definell Long Long#defineMAXN 1005#defineMoD 10007using namespacestd;intLINKER[MAXN];BOOLUsed[maxn];vector<int>MP[MAXN];intUN;BOOLDfsintu) {     for(inti =0; I<mp[u].size (); i++){        if(!Used[mp[u][i]]) {Used[mp[u][i]]=true; if(Linker[mp[u][i]] = =-1||DFS (Linker[mp[u][i])) {Linker[mp[u][i]]=u; return true; }        }    }    return false;}intHungary () {intu; intres =0; MEMSET (linker,-1,sizeof(linker));  for(U =1; U <= UN; u++) {memset (used,false,sizeof(used)); if(Dfs (U)) res++; }    returnRes;}intMain () {intK;  while(~SCANF ("%d%d", &un, &k)) {         for(inti =1; I <= UN; ++i)        {mp[i].clear (); }        intu, v;  while(k--) {scanf ("%d%d", &u, &v);            Mp[u].push_back (v);        Mp[v].push_back (U); } printf ("%d\n%d\n", Hungary ()/2, Un-hungary ()/2); }    return 0;}

"Hiho" Hiho 31st week two maximum match, some of the basic conclusions will be updated here