From e8e9f941ac106b29ba4b84fa47a45f9ccaf17fbc Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Thu, 8 Feb 2018 14:46:07 -0200
Subject: [PATCH] Add lowpoint (articulations_bridges)
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
graph/articulations_bridges.cpp | 38 +++++++++++++++++++++++++++++++++
graph/bfs.cpp | 4 ++--
graph/dfs.cpp | 4 ++--
graph/dijkstra.cpp | 4 ++--
graph/lca.cpp | 1 -
5 files changed, 44 insertions(+), 7 deletions(-)
create mode 100644 graph/articulations_bridges.cpp
diff --git a/graph/articulations_bridges.cpp b/graph/articulations_bridges.cpp
new file mode 100644
index 0000000..a88d707
--- /dev/null
+++ b/graph/articulations_bridges.cpp
@@ -0,0 +1,38 @@
+/**
+ * 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]);
+ }
+ }
+}
diff --git a/graph/bfs.cpp b/graph/bfs.cpp
index 5a7179a..e57da24 100644
--- a/graph/bfs.cpp
+++ b/graph/bfs.cpp
@@ -1,8 +1,8 @@
/**
* 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];
diff --git a/graph/dfs.cpp b/graph/dfs.cpp
index 8748a19..46373f8 100644
--- a/graph/dfs.cpp
+++ b/graph/dfs.cpp
@@ -1,8 +1,8 @@
/**
* 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];
diff --git a/graph/dijkstra.cpp b/graph/dijkstra.cpp
index 86a350c..fcaee37 100644
--- a/graph/dijkstra.cpp
+++ b/graph/dijkstra.cpp
@@ -1,8 +1,8 @@
/**
* 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];
diff --git a/graph/lca.cpp b/graph/lca.cpp
index 79f835d..e66190c 100644
--- a/graph/lca.cpp
+++ b/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
--
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