Update hopcroft_karp.cpp

This commit is contained in:
Krishna Pal Deora
2020-09-25 20:37:01 +05:30
committed by GitHub
parent db3f902a97
commit a859bbdff1

View File

@@ -6,7 +6,6 @@
* and produces as output a maximum cardinality matching, it runs in O(E√V) time in worst case.
*
* ###Bipartite graph :
* A bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint
* and independent sets U and V such that every edge connects a vertex in U to one in V.
* Vertex sets U and V are usually called the parts of the graph.
@@ -53,8 +52,8 @@
#include <queue>
#include <list>
#include <climits>
#define NIL 0
#define INF INT_MAX
const int NIL = 0;
const int INF = INT_MAX;
// A class to represent Bipartite graph for
// Hopcroft Karp implementation
@@ -74,6 +73,7 @@ class BGraph
public:
BGraph(int m, int n); // Constructor
~BGraph(); // destructor
void addEdge(int u, int v); // To add edge
// Returns true if there is an augmenting path
@@ -102,10 +102,12 @@ int BGraph::hopcroftKarpAlgorithm()
dist = new int[m + 1];
// Initialize NIL as pair of all vertices
for (int u = 0; u <= m; u++)
for (int u = 0; u <= m; u++){
pair_u[u] = NIL;
for (int v = 0; v <= n; v++)
}
for (int v = 0; v <= n; v++){
pair_v[v] = NIL;
}
// Initialize result
int result = 0;
@@ -115,13 +117,15 @@ int BGraph::hopcroftKarpAlgorithm()
while (bfs())
{
// Find a free vertex to check for a matching
for (int u = 1; u <= m; u++)
for (int u = 1; u <= m; u++){
// If current vertex is free and there is
// an augmenting path from current vertex
// then increment the result
if (pair_u[u] == NIL && dfs(u))
if (pair_u[u] == NIL && dfs(u)){
result++;
}
}
}
return result;
}
@@ -135,16 +139,16 @@ bool BGraph::bfs()
for (int u = 1; u <= m; u++)
{
// If this is a free vertex, add it to queue
if (pair_u[u] == NIL)
{
if (pair_u[u] == NIL){
// u is not matched so distance is 0
dist[u] = 0;
q.push(u);
}
// Else set distance as infinite so that this vertex is considered next time for availibility
else
else{
dist[u] = INF;
}
}
// Initialize distance to NIL as infinite
@@ -222,6 +226,15 @@ BGraph::BGraph(int m, int n)
adj = new std::list<int>[m + 1];
}
// destructor
BGraph::~BGraph()
{
delete[] pair_u;
delete[] pair_v;
delete[] dist;
delete[] adj;
}
// function to add edge from u to v
void BGraph::addEdge(int u, int v)
{
@@ -243,24 +256,23 @@ void BGraph::addEdge(int u, int v)
Output:
// size of maximum matching
Maximum matching is 4
*/
int main()
{
int v1, v2, e;
int v1 = 0, v2 = 0, e = 0;
std::cin >> v1 >> v2 >> e; // vertices of left side, right side and edges
BGraph g(v1, v2); //
int u, v;
int u = 0, v = 0;
for (int i = 0; i < e; ++i)
{
std::cin >> u >> v;
g.addEdge(u, v);
}
int res = g.hopcroftKarpAlgorithm();
std::cout << "Maximum matching is " << res <<"\n";
return 0;
}
}