From 9f85ba26ad6f24c07c460d705cd28e7ff771b11a Mon Sep 17 00:00:00 2001
From: kittobi92 <Tobias.Heuer@gmx.net>
Date: Wed, 2 Dec 2015 21:00:28 +0100
Subject: Add Fenwick-Tree to section datastructures

---
 datastructures/datastructures.tex |  4 ++++
 datastructures/fenwickTree.cpp    | 21 +++++++++++++++++++++
 2 files changed, 25 insertions(+)
 create mode 100644 datastructures/fenwickTree.cpp

(limited to 'datastructures')

diff --git a/datastructures/datastructures.tex b/datastructures/datastructures.tex
index 7edb390..7b5b076 100644
--- a/datastructures/datastructures.tex
+++ b/datastructures/datastructures.tex
@@ -8,6 +8,10 @@
 \lstinline{update()} kann so umgeschrieben werden, dass ganze Intervalle geändert werden.
 Dazu muss ein Offset in den inneren Knoten des Baums gespeichert werden.
 
+\subsection{Fenwick Tree}
+\lstinputlisting{datastructures/fenwickTree.cpp}
+
+
 \subsection{Range Minimum Query}
 \lstinputlisting{datastructures/RMQ.cpp}
 
diff --git a/datastructures/fenwickTree.cpp b/datastructures/fenwickTree.cpp
new file mode 100644
index 0000000..02be7d4
--- /dev/null
+++ b/datastructures/fenwickTree.cpp
@@ -0,0 +1,21 @@
+vector<int> FT; //Fenwick-Tree
+
+//Build an Fenwick-Tree over an array a. Time Complexity: O(n*log(n))
+buildFenwickTree(vector<int>& a) {
+  n = a.size();
+  FT.assign(n+1,0);
+  for(int i = 0; i < n; i++)  updateFT(i,a[i]);
+}
+
+//Prefix-Sum of intervall [0..i]. Time Complexity: O(log(n))
+int prefix_sum(int i) {
+  int sum = 0; i++;
+  while(i > 0) { sum += FT[i]; i -= (i & (-i)); }	
+  return sum;
+}
+
+//Adds val to index i. Time Complexity O(log(n))
+void updateFT(int i, int val) {
+	i++; while(i <= n) { FT[i] += val; i += (i & (-i)); }
+}
+	
-- 
cgit v1.2.3


From 591ebd0e965a7849d53e5a2543c814db6468321b Mon Sep 17 00:00:00 2001
From: JBatzill <batzilljohannes@gmail.com>
Date: Wed, 2 Dec 2015 22:37:54 +0100
Subject: added runtime of rmq

---
 datastructures/RMQ.cpp | 2 ++
 1 file changed, 2 insertions(+)

(limited to 'datastructures')

diff --git a/datastructures/RMQ.cpp b/datastructures/RMQ.cpp
index 9047b33..3c3f44c 100644
--- a/datastructures/RMQ.cpp
+++ b/datastructures/RMQ.cpp
@@ -1,6 +1,7 @@
 vector<int> data(RMQ_SIZE);
 vector<vector<int>> rmq(floor(log2(RMQ_SIZE)) + 1, vector<int>(RMQ_SIZE));
 
+//Runtime: O(n*log(n))
 void initRMQ() {
 	for(int i = 0, s = 1, ss = 1; s <= RMQ_SIZE; ss=s, s*=2, i++) {
 		for(int l = 0; l + s <= RMQ_SIZE; l++) {
@@ -13,6 +14,7 @@ void initRMQ() {
 	}
 }
 //returns index of minimum! [l, r)
+//Runtime: O(1)
 int queryRMQ(int l, int r) {
 	if(l >= r) return l;
 	int s = floor(log2(r-l)); r = r - (1 << s);
-- 
cgit v1.2.3