From dcc79d0dae00bd3d4f8ce3850955a471cd504659 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sun, 3 Mar 2019 22:57:11 -0300
Subject: [PATCH] Add hopcroft karp algorithm
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/hopcroft_karp.cpp | 83 ++++++++++++++++++++++++++++++
1 file changed, 83 insertions(+)
create mode 100644 algorithms/graph/hopcroft_karp.cpp
diff --git a/algorithms/graph/hopcroft_karp.cpp b/algorithms/graph/hopcroft_karp.cpp
new file mode 100644
index 0000000..0969bde
--- /dev/null
+++ b/algorithms/graph/hopcroft_karp.cpp
@@ -0,0 +1,83 @@
+/**
+ * Hopcroft-Karp
+ *
+ * Complexity (Time): O(E * sqrt(V))
+ * Complexity (Space): O(V + E)
+ */
+
+int dist[MAX];
+int matchL[MAX], matchR[MAX];
+
+vector<int> graph[MAX];
+
+// Builds an alternating level graph rooted at unmatched vertices in L
+// using BFS, and returns whether there is an augmenting path in the graph
+// or not
+bool bfs(int n) {
+ queue<int> Q;
+
+ // Add unmatched vertices in L to the queue
+ for (int l = 1; l <= n; ++l)
+ if (matchL[l] == 0) {
+ dist[l] = 0;
+ Q.push(l);
+ } else
+ dist[l] = inf;
+
+ dist[0] = inf;
+ while (!Q.empty()) {
+ int l = Q.front(); Q.pop();
+
+ if (dist[l] < dist[0]) {
+ for (auto r : graph[l])
+ if (dist[matchR[r]] == inf) {
+ dist[matchR[r]] = dist[l] + 1;
+ Q.push(matchR[r]);
+ }
+ }
+ }
+
+ return (dist[0] != inf);
+}
+
+
+// Augments path starting in l if there is one, returns
+// whether a path was augmented or not
+bool dfs(int l) {
+ if (l == 0)
+ return true;
+
+ for (auto r : graph[l]) {
+
+ // The augmenting path has increasing dist, set by the BFS
+ if (dist[matchR[r]] == dist[l] + 1)
+ if (dfs(matchR[r])) {
+ matchR[r] = l;
+ matchL[l] = r;
+ return true;
+ }
+ }
+
+ dist[l] = inf;
+ return false;
+}
+
+
+// Returns number of matched vertices on the left (matched edges)
+int hopcroft_karp(int n) {
+ mset(matchL, 0);
+ mset(matchR, 0);
+
+ int ans = 0;
+
+ // While there is an augmenting path
+ while (bfs(n)) {
+
+ // Augment the path when is possible
+ for (int l = 1; l <= n; ++l)
+ if (matchL[l] == 0 && dfs(l))
+ ans++;
+ }
+
+ return ans;
+}
--
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