Merge pull request xtaci#39 from Gabriel123Duarte/master

Add Fenwick Tree algorithm - Gabriel123Duarte

Author: xtaci

include/.goutputstream-UUQE8X

@@ -0,0 +1,61 @@
+/*******************************************************************************
+ * Fenwick Tree
+ *
+ * Data structure providing prefix sums and modify the table in O(log n) - n is the size o the table.
+ *
+ * In this algorithm we use two functions:
+ * - RSQ - This function calculates the range sum query in O(log n)
+ * - Update - This function adjusts the values in the given range in O(log n)
+ *
+ * https://en.wikipedia.org/wiki/Fenwick_tree
+ * 
+ * @author Gabriel Duarte (gabriellagoa10@yahoo.com.br)
+ * @github Gabriel123Duarte
+ *
+ ******************************************************************************/
+
+#ifndef __FENWICK_H__
+#define __FENWICK_H__
+
+#include <vector>
+
+#define LSONE(x) (x & (-x))
+
+class Fenwick
+{
+private:
+// Vector representing the table
+std::vector<int> fen;
+public:
+Fenwick() {}
+
+// We don't use the index 0, because it is the base case
+Fenwick(int n)
+{
+fen.assign(n + 1, 0);
+}
+
+// Calculate the 
+int rsq(int a)
+{
+int ans = 0;
+for(; a; a -= LSONE(a))
+ans += fen[a];
+return ans;
+}
+
+// RSQ a..b
+inline int rsq(int a, int b)
+{
+return rsq(b) - (a == 1 ? 0 : rsq(a - 1));
+}
+
+// Update the value of the k-th element by x
+void update(int k, int x)
+{
+for(; k < (int)fen.size(); k += LSONE(k))
+fen[k] += x;
+}
+};
+
+#endif

include/fenwick_tree.h

@@ -0,0 +1,61 @@
+/*******************************************************************************
+ * Fenwick Tree
+ *
+ * Data structure providing prefix sums and modify the table in O(log n) - n is the size o the table.
+ *
+ * In this algorithm we use two functions:
+ * - RSQ - This function calculates the range sum query in O(log n)
+ * - Update - This function adjusts the values in the given range in O(log n)
+ *
+ * https://en.wikipedia.org/wiki/Fenwick_tree
+ * 
+ * @author Gabriel Duarte (gabriellagoa10@yahoo.com.br)
+ * @github Gabriel123Duarte
+ *
+ ******************************************************************************/
+
+#ifndef __FENWICK_H__
+#define __FENWICK_H__
+
+#include <vector>
+
+#define LSONE(x) (x & (-x))
+
+class Fenwick
+{
+private:
+// Vector representing the table
+std::vector<int> fen;
+public:
+Fenwick() {}
+
+// We don't use the index 0, because it is the base case
+Fenwick(int n)
+{
+fen.assign(n + 1, 0);
+}
+
+// Calculate the 
+int rsq(int a)
+{
+int ans = 0;
+for(; a; a -= LSONE(a))
+ans += fen[a];
+return ans;
+}
+
+// RSQ a..b
+inline int rsq(int a, int b)
+{
+return rsq(b) - (a == 1 ? 0 : rsq(a - 1));
+}
+
+// Update the value of the k-th element by x
+void update(int k, int x)
+{
+for(; k < (int)fen.size(); k += LSONE(k))
+fen[k] += x;
+}
+};
+
+#endif

src/fenwick_tree_demo.cpp

@@ -0,0 +1,16 @@
+#include <cstdio>
+#include "fenwick_tree.h"
+
+int main()
+{
+Fenwick ft(5);
+
+ft.update(2, 1);
+ft.update(4, 10);
+
+printf("%d\n", ft.rsq(1));
+
+ft.update(1, 5);
+printf("%d\n", ft.rsq(1));
+return 0;
+}