ajout de MaxBipartiteMatching_sqrt.cc

code/MaxBipartiteMatching_sqrt.cc

@@ -0,0 +1,59 @@
+// O(sqrt(n)*E)
+// Use : set G (adjacency list), set uN, then m = MaxMatch() and the result is in Mx and My
+
+const int MAXN = 1000; const int INF = 0x3f3f3f3f; vector<int>G [MAXN];
+int uN;
+int Mx[MAXN],My[MAXN]; int dx[MAXN],dy[MAXN]; int dis;
+bool used[MAXN];
+bool SearchP() {
+  queue<int>Q;
+  dis = INF;
+  memset(dx,-1,sizeof(dx)); memset(dy,-1,sizeof(dy));
+  for(int i = 0 ; i < uN; i++)
+		if(Mx[i] == -1) {
+		  Q.push(i);
+		  dx[i] = 0;
+    }
+  while(!Q.empty()) {
+    int u = Q.front();
+    Q.pop();
+    if(dx[u] > dis) break;
+    int sz = G[u].size();
+    for(int i = 0;i < sz;i++) {
+      int v = G[u][i];
+      if(dy[v] == -1) {
+      	dy[v] = dx[u] + 1;
+      	if(My[v] == -1) dis = dy[v];
+        else {
+    	    dx[My[v]] = dy[v] + 1;
+    	    Q.push( My[v ]);
+        }
+      }
+    }
+  }
+  return dis != INF;
+}
+bool DFS(int u) {
+  int sz = G[u].size();
+  for(int i = 0;i < sz;i++) {
+    int v = G[u][i];
+    if(!used[v] && dy[v] == dx[u] + 1) {
+      used[v] = true;
+      if(My[v] != -1 && dy[v] == dis) continue;
+      if(My[v] == -1 || DFS(My[v])) {
+        My[v] = u; Mx[u] = v; return true;
+      }
+    }
+  }
+  return false;
+}
+int MaxMatch() {
+  int res = 0;
+  memset(Mx,-1,sizeof(Mx)); memset(My,-1,sizeof(My));
+  while(SearchP()) {
+	  memset(used,false,sizeof(used));
+    for(int i = 0;i < uN;i++)
+		   if(Mx[i] == -1 && DFS(i)) res++;
+	}
+  return res;
+}

main.tex

@@ -57,6 +57,7 @@ Temps de cuisson : $O(n)$
 
 \subsection{Max bipartite matching}
 {\scriptsize\lstinputlisting{code/MaxBipartiteMatching.cc}}
+{\scriptsize\lstinputlisting{code/MaxBipartiteMatching_sqrt.cc}}
 
 \subsection{Global min cut}
 {\scriptsize\lstinputlisting{code/MinCut.cc}}