Add Edmonds-Karp

Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>

algorithms/graph/edmonds_karp.cpp

+/**
+ * Edmonds-Karp 
+ * 
+ * Complexity (time): O(V*E^2)
+ * Complexity (space): O(V^2)
+ */
+
+int N;
+int par[MAX];
+int graph[MAX][MAX], rg[MAX][MAX];
+
+bool cont[MAX];
+
+// Finds if there's a path between s and t using non-full
+// residual edges
+bool path(int s, int t) {
+  queue<int> Q;
+  Q.push(s);
+  cont[s] = true;
+
+  while (!Q.empty()) {
+    int u = Q.front(); Q.pop();
+
+    if (u == t)
+      return true;
+
+    for (int i = 0; i < N; ++i)
+      if (!cont[i] && rg[u][i]) {
+        cont[i] = true;
+        par[i] = u;
+        Q.push(i);
+      }
+  }
+
+  return false;
+}
+
+
+// Returns maximum flow between s (source) and t (sink)
+int edmonds_karp(int s, int t) {
+  int ans = 0;
+  par[s] = -1;
+
+  mset(cont, 0);
+  memcpy(rg, graph, sizeof(graph));
+
+  // Repeat while there's a valid path between s and t
+  while (path(s, t)) {
+    int flow = inf;
+
+    // Get the minimum capacity among all edges of the chosen path
+    for (int i = t; par[i] != -1; i = par[i])
+      flow = min(f, rg[par[i]][i]);
+
+    // Update residual graph
+    for (int i = t; par[i] != -1; i = par[i]) {
+      rg[par[i]][i] -= flow;
+      rg[i][par[i]] += flow;
+    }
+
+    ans += flow;
+    mset(cont, 0);
+  }
+
+  return ans;
+}

algorithms/graph/ford_fulkerson.cpp

@@ -2,7 +2,7 @@
  * Ford-Fulkerson
  * 
  * Complexity (time): O(Ef)
- * Complexity (space): O(V + E)
+ * Complexity (space): O(V^2)
  */
 
 int N;

testing.py

@@ -32,6 +32,7 @@ def gen_code_latex(arr, depth):
     for i in arr:
         print('\\' + depth + '{' + i + '}')
 
+
 def gen_latex(tree):
     stack = [ (tree, 0) ]
     depth = ['chapter', 'section', 'subsection']