From 4f887bee84a39deb2c474b503a94ebaf60ca0a20 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Tue, 12 Mar 2019 16:45:40 -0300
Subject: [PATCH] Add URI1128 and fix tarjan
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/articulations_bridges.cpp | 3 +
algorithms/graph/tarjan.cpp | 56 +++++++----
contests/Cadernaveis/MANUT.cpp | 3 +-
contests/Cadernaveis/TUBOS.cpp | 81 ++++++++++++++++
contests/Cadernaveis/URI1128.cpp | 103 +++++++++++++++++++++
5 files changed, 228 insertions(+), 18 deletions(-)
create mode 100644 contests/Cadernaveis/TUBOS.cpp
create mode 100644 contests/Cadernaveis/URI1128.cpp
diff --git a/algorithms/graph/articulations_bridges.cpp b/algorithms/graph/articulations_bridges.cpp
index 4943220..5cab796 100644
--- a/algorithms/graph/articulations_bridges.cpp
+++ b/algorithms/graph/articulations_bridges.cpp
@@ -67,8 +67,11 @@ void dfs(int x) {
* @param x root vertex
*/
void tarjan(int n) {
+ mset(L, 0);
+ mset(visited, 0);
mset(parent, -1);
+ // Apply tarjan in every component
for (int i = 0; i < n; ++i)
if (!visited[i])
dfs(i);
diff --git a/algorithms/graph/tarjan.cpp b/algorithms/graph/tarjan.cpp
index dac3ee0..8c6799c 100644
--- a/algorithms/graph/tarjan.cpp
+++ b/algorithms/graph/tarjan.cpp
@@ -1,57 +1,79 @@
/**
- * Tarjan - Strongly Connected Components
+ * Tarjan - Strongly Connected Components (SCC)
*
* Complexity (Time): O(V + E)
* Complexity (Space): O(V + E)
*/
+stack<int> S;
vector<int> graph[MAX];
-vector<int> scc[MAX];
-stack<int> S;
int ncomp, ind;
-int cont[MAX], parent[MAX];
-int low[MAX], L[MAX];
+int visited[MAX];
+
+// The id of a node x (id[x]) is the order in which x was visited in the DFS
+int id[MAX];
+
+// The low-link value of a node x (low[x]) is defined as the smallest id
+// of another node reachable from x when doing a DFS
+int low[MAX];
+
+// scc[i] contains the i-th SCC stored as a vector with the ids of the
+// vertices in it
+vector<int> scc[MAX];
/**
* Fills SCC with strongly connected components of graph.
* @param x any vertex
*/
void dfs(int x) {
- L[x] = ind;
- low[x] = ind++;
- cont[x] = 1;
+ id[x] = low[x] = ind++;
+ visited[x] = 1;
+
S.push(x);
for (auto i : graph[x])
- if (L[i] == -1) {
+ if (id[i] == -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]);
- } else if (cont[i])
- low[x] = min(low[x], L[i]);
- if (low[x] == L[x]) {
+ // If i has been visited, then i is "above" (has smaller id then x),
+ // meaning that the edge (x,i) is a "back edge"
+ } else if (visited[i])
+ low[x] = min(low[x], id[i]);
+
+ // A SCC was found
+ if (low[x] == id[x]) {
int w;
- ncomp++;
+ // Every node on top of x in the stack belongs to the SCC found
do {
w = S.top(); S.pop();
- cont[w] = 0;
+ visited[w] = 0;
scc[ncomp].pb(w);
} while (w != x);
+
+ ncomp++;
}
}
/**
- * Return number of SCCs.
+ * Returns number of SCCs.
* @param n number of vertices
*/
int tarjan(int n) {
- mset(L, -1);
+ mset(id, -1);
ncomp = ind = 0;
for (int i = 0; i < n; ++i)
- if (L[i] == -1)
+ scc[i].clear();
+
+ // Apply tarjan in every component
+ for (int i = 0; i < n; ++i)
+ if (id[i] == -1)
dfs(i);
return ncomp;
diff --git a/contests/Cadernaveis/MANUT.cpp b/contests/Cadernaveis/MANUT.cpp
index 286be05..ceec4bf 100644
--- a/contests/Cadernaveis/MANUT.cpp
+++ b/contests/Cadernaveis/MANUT.cpp
@@ -52,10 +52,11 @@ void dfs(int x) {
}
void tarjan(int n) {
+ mset(L, 0);
mset(visited, 0);
mset(parent, -1);
- mset(L, 0);
articulations.clear();
+
dfs(n);
sort(all(articulations));
diff --git a/contests/Cadernaveis/TUBOS.cpp b/contests/Cadernaveis/TUBOS.cpp
new file mode 100644
index 0000000..2a94641
--- /dev/null
+++ b/contests/Cadernaveis/TUBOS.cpp
@@ -0,0 +1,81 @@
+#include <bits/stdc++.h>
+
+#define MAX 1010
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+typedef long long ll;
+typedef pair<int,int> ii;
+
+vector<int> graph[MAX];
+int visited[MAX], parent[MAX];
+
+int L[MAX];
+int low[MAX];
+vector<ii> bridges;
+
+void dfs(int x) {
+ int child = 0;
+ visited[x] = 1;
+
+ for (auto i : graph[x]) {
+ if (!visited[i]) {
+ child++;
+ parent[i] = x;
+
+ low[i] = L[i] = L[x] + 1;
+ dfs(i);
+
+ low[x] = min(low[x], low[i]);
+
+ if (low[i] > L[x])
+ bridges.pb(ii(x, i));
+
+ } else if (parent[x] != i)
+ low[x] = min(low[x], L[i]);
+ }
+}
+
+void tarjan(int n) {
+ mset(visited, 0);
+ mset(parent, -1);
+ mset(L, 0);
+ bridges.clear();
+ dfs(n);
+}
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ int n, m;
+ while (cin >> n >> m && (n || m)) {
+ for (int i = 0; i < n; ++i)
+ graph[i].clear();
+
+ for (int i = 0; i < m; ++i) {
+ int x, y; cin >> x >> y;
+ x--, y--;
+ graph[x].pb(y);
+ graph[y].pb(x);
+ }
+
+ tarjan(0);
+ cout << (bridges.size() ? "N" : "S") << ende;
+ }
+
+ return 0;
+}
diff --git a/contests/Cadernaveis/URI1128.cpp b/contests/Cadernaveis/URI1128.cpp
new file mode 100644
index 0000000..4e48af8
--- /dev/null
+++ b/contests/Cadernaveis/URI1128.cpp
@@ -0,0 +1,103 @@
+#include <bits/stdc++.h>
+
+#define MAX 2010
+#define EPS 1e-6
+#define MOD 1000000007
+#define inf 0x3f3f3f3f
+#define llinf 0x3f3f3f3f3f3f3f3f
+
+#define fi first
+#define se second
+#define pb push_back
+#define ende '\n'
+
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+#define mset(x, y) memset(&x, (y), sizeof(x))
+
+using namespace std;
+
+typedef long long ll;
+typedef pair<int,int> ii;
+
+stack<int> S;
+vector<int> graph[MAX];
+
+int ncomp, ind;
+int visited[MAX];
+
+int id[MAX];
+
+int low[MAX];
+
+vector<int> scc[MAX];
+
+void dfs(int x) {
+ id[x] = low[x] = ind++;
+ visited[x] = 1;
+
+ S.push(x);
+
+ for (auto i : graph[x])
+ if (id[i] == -1) {
+ dfs(i);
+
+ low[x] = min(low[x], low[i]);
+
+ } else if (visited[i])
+ low[x] = min(low[x], id[i]);
+
+ if (low[x] == id[x]) {
+ int w;
+
+ do {
+ w = S.top(); S.pop();
+ visited[w] = 0;
+ scc[ncomp].pb(w);
+ } while (w != x);
+
+ ncomp++;
+ }
+}
+
+int tarjan(int n) {
+ mset(id, -1);
+ ncomp = ind = 0;
+
+ for (int i = 0; i < n; ++i)
+ scc[i].clear();
+
+ for (int i = 0; i < n; ++i)
+ if (id[i] == -1)
+ dfs(i);
+
+ return ncomp;
+}
+
+
+int main() {
+ ios::sync_with_stdio(0);
+ cin.tie(0);
+
+ int n, m;
+ while (cin >> n >> m && (n || m)) {
+ for (int i = 0; i < n; ++i)
+ graph[i].clear();
+
+ for (int i = 0; i < m; ++i) {
+ int v, w, p; cin >> v >> w >> p;
+ v--, w--;
+ if (p == 1)
+ graph[v].pb(w);
+ else {
+ graph[v].pb(w);
+ graph[w].pb(v);
+ }
+ }
+
+ int ans = tarjan(n);
+ cout << (ans == 1) << ende;
+ }
+
+ return 0;
+}
--
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