From bcb0c48f8d9e7a7c6e666d46fab90a78cf90d3a0 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Mon, 11 Mar 2019 16:31:14 -0300
Subject: [PATCH] Improve Articulations/Bridges comments
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/articulations_bridges.cpp | 36 +++++++++++++++++-----
1 file changed, 28 insertions(+), 8 deletions(-)
diff --git a/algorithms/graph/articulations_bridges.cpp b/algorithms/graph/articulations_bridges.cpp
index e3a6c69..4943220 100644
--- a/algorithms/graph/articulations_bridges.cpp
+++ b/algorithms/graph/articulations_bridges.cpp
@@ -6,9 +6,15 @@
*/
vector<int> graph[MAX];
+int visited[MAX], parent[MAX];
-int cont[MAX], parent[MAX];
-int low[MAX], L[MAX];
+// The level of a node x (L[x]) is the "height" of x relative to the root
+// of the DFS
+int L[MAX];
+
+// The low-link value of a node x (low[x]) is defined as the smallest level
+// of another node reachable from x when doing a DFS
+int low[MAX];
// Answer vector with bridges (edges)
vector<ii> bridges;
@@ -22,24 +28,35 @@ vector<int> articulations;
*/
void dfs(int x) {
int child = 0;
- cont[x] = 1;
+ visited[x] = 1;
for (auto i : graph[x]) {
- if (!cont[i]) {
+ if (!visited[i]) {
child++;
parent[i] = x;
+ // Initially low[i] is equal to low[x]
low[i] = L[i] = L[x] + 1;
dfs(i);
+
+ // After the DFS, low[i] might have changed, in that case, low[x]
+ // should be updated if a lower value has been found
low[x] = min(low[x], low[i]);
- if ((parent[x] == -1 && child > 1) || (parent[x] != -1 &&
- low[i] >= L[x]))
+ // If x is the root and has more than one child, or if it's not the
+ // root and the child i of x has no back edges, then x is an
+ // articulation vertex
+ if ((parent[x] == -1 && child > 1) ||
+ (parent[x] != -1 && low[i] >= L[x]))
articulations.pb(x);
+ // If node i can't reach a node above x (has no back edges), then it
+ // the egde (x,i) is a bridge
if (low[i] > L[x])
bridges.pb(ii(x, i));
+ // If i has been visited but it's not x's parent, then i is "above"
+ // (has smaller level then x), meaning that the edge (x,i) is a "back edge"
} else if (parent[x] != i)
low[x] = min(low[x], L[i]);
}
@@ -49,9 +66,12 @@ void dfs(int x) {
* Applies tarjan algorithm and format articulations vector.
* @param x root vertex
*/
-void tarjan(int x) {
+void tarjan(int n) {
mset(parent, -1);
- dfs(x);
+
+ for (int i = 0; i < n; ++i)
+ if (!visited[i])
+ dfs(i);
// Remove duplicates for articulations
sort(all(articulations));
--
GitLab