From 9facd3655e2b86799699a6fdbd566cb4b2a7fb1c Mon Sep 17 00:00:00 2001
From: Paul Jungeblut <paul.jungeblut@gmail.com>
Date: Fri, 22 Dec 2017 12:49:35 +0100
Subject: Adding new code for sparse table implementation and LCA.

---
 graph/LCA.cpp   | 21 ---------------------
 graph/graph.tex |  2 +-
 graph/lca.cpp   | 28 ++++++++++++++++++++++++++++
 3 files changed, 29 insertions(+), 22 deletions(-)
 delete mode 100644 graph/LCA.cpp
 create mode 100644 graph/lca.cpp

(limited to 'graph')

diff --git a/graph/LCA.cpp b/graph/LCA.cpp
deleted file mode 100644
index c79cc5c..0000000
--- a/graph/LCA.cpp
+++ /dev/null
@@ -1,21 +0,0 @@
-vector<int> visited(2*MAX_N), first(MAX_N, 2*MAX_N), depth(2*MAX_N);
-vector<vector<int>> graph(MAX_N);
-
-// Funktioniert nur mit von der Wurzel weggerichteten Kanten.
-// Falls ungerichtete Kanten, visited-check einführen.
-void initLCA(int gi, int d, int &c) { // Laufzeit: O(n)
-	visited[c] = gi, depth[c] = d, first[gi] = min(c, first[gi]), c++;
-	for(int gn : graph[gi]) {
-		initLCA(gn, d+1, c);
-		visited[c] = gi, depth[c] = d, c++;
-}}
-
-int getLCA(int a, int b) { // Laufzeit: O(1)
-	return visited[queryRMQ(
-			min(first[a], first[b]), max(first[a], first[b]))];
-}
-
-// Benutzung:
-int c = 0;
-initLCA(0, 0, c);
-initRMQ(); // Ersetze das data im RMQ-Code von oben durch depth.
diff --git a/graph/graph.tex b/graph/graph.tex
index 7b901f9..37356f6 100644
--- a/graph/graph.tex
+++ b/graph/graph.tex
@@ -58,7 +58,7 @@ VISIT(v):
 \lstinputlisting{graph/euler.cpp}
 
 \subsection{Lowest Common Ancestor}
-\lstinputlisting{graph/LCA.cpp}
+\lstinputlisting{graph/lca.cpp}
 
 \subsection{Max-Flow}
 
diff --git a/graph/lca.cpp b/graph/lca.cpp
new file mode 100644
index 0000000..d6548e9
--- /dev/null
+++ b/graph/lca.cpp
@@ -0,0 +1,28 @@
+struct LCA {
+  vector<int> depth, visited, first;
+  int idx;
+  SparseTable st;
+
+  void init(vector<vector<int>> &g, int root) { // Laufzeit: O(|V|)
+    depth.assign(2 * g.size(), 0);
+    visited.assign(2 * g.size(), -1);
+    first.assign(g.size(), 2 * g.size());
+    idx = 0;
+    visit(g, root, 0);
+    st.init(&depth);
+  }
+
+  void visit(vector<vector<int>> &g, int v, int d) {
+    visited[idx] = v, depth[idx] = d, first[v] = min(idx, first[v]), idx++;
+
+    for (int w : g[v]) {
+      if (first[w] == 2 * (int)g.size()) {
+        visit(g, w, d + 1);
+        visited[idx] = v, depth[idx] = d, idx++;
+  }}}
+
+  int getLCA(int a, int b) { // Laufzeit: O(1)
+    if (first[a] > first[b]) swap(a, b);
+    return visited[st.queryIdempotent(first[a], first[b])];
+  }
+};
-- 
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