Add lowpoint (articulations_bridges)

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

graph/articulations_bridges.cpp

+/**
+ * Articulations and Bridges
+ *
+ * Complexity (Time): O(n + m)
+ * Complexity (Space): O(n + m)
+ */
+
+vector<int> graph[MAX];
+
+int cont[MAX], parent[MAX];
+int low[MAX], L[MAX];
+
+// Find all articulations and bridges in the graph
+void dfs(int x) {
+  int child = 0;
+  cont[x] = 1;
+
+  for (auto i : graph[x]) {
+    if (!cont[i]) {
+      child++;
+      parent[i] = x;
+
+      low[i] = L[i] = L[x] + 1;
+      dfs(i);
+      low[x] = min(low[x], low[i]);
+
+      if ((parent[x] == -1 && child > 1) || (parent[x] != -1 && low[i] >= L[x]))
+        // CAUTION: may be executed more than once for the same vertex
+        // ==== x is an articulation point ====
+
+      if (low[i] > L[x])
+        // ==== (x,i) is a bridge ====
+
+    } else if (parent[x] != i) {
+      low[x] = min(low[x], L[i]);
+    }
+  }
+}

graph/bfs.cpp

 /**
  * Breadth First Search - BFS
  *
- * Complexity (Time): O(|V| + |E|)
- * Complexity (Space): O(|V| + |E|)
+ * Complexity (Time): O(n + m)
+ * Complexity (Space): O(n + m)
  */
 
 bool cont[MAX];

graph/dfs.cpp

 /**
  * Depth First Search - DFS
  *
- * Complexity (Time): O(|V| + |E|)
- * Complexity (Space): O(|V| + |E|)
+ * Complexity (Time): O(n + m)
+ * Complexity (Space): O(n + m)
  */
 
 bool cont[MAX];

graph/dijkstra.cpp

 /**
  * Dijkstra
  *
- * Complexity (Time): O(|E| + |V| log |V|)
- * Complexity (Space): O(|E| + |V|)
+ * Complexity (Time): O(m + n log n)
+ * Complexity (Space): O(n + m)
  */
 
 int dist[MAX];

graph/lca.cpp

@@ -5,7 +5,6 @@
  *   preprocess -> O(n log n)
  *   query      -> O(log n)
  * Complexity (Space): O(n + m + n log n)
- * 
  *
  * OBS: *  = return sum path to LCA
  *      ** = return max value on path to LCA