fenwick_tree.java: Add Fenwick Tree Data

This adds Fenwick Data Structure which can update
an element of a list and query the sum of any range
of it in only O(log(N)) time complexity.

Closes #218

README.md

@@ -36,6 +36,7 @@ This repository contains examples of various algorithms written on different pro
 | [Linear Linked List](https://en.wikipedia.org/wiki/Linked_list)                                 | [:octocat:](linked_list/C)            | [:octocat:](linked_list/Cpp)          |                                       | [:octocat:](linked_list/Python)       |
 | [AVL Tree](https://en.wikipedia.org/wiki/AVL_tree)                                              | [:octocat:](avl_tree/C)               |                                       | [:octocat:](avl_tree/Java)            | [:octocat:](avl_tree/Python)          |
 | [Binary Search Tree](https://en.wikipedia.org/wiki/Binary_search_tree)                          |                                       | [:octocat:](binary_search_tree/Cpp)                                       |                                       |                                       |
+| [Fenwick Tree](https://en.wikipedia.org/wiki/Fenwick_tree)                                      |                                       |                                       | [:octocat:](fenwick_tree/java)        |                                       |
 
 
 ## Sample Run

fenwick_tree/java/fenwick_tree.java

@@ -0,0 +1,100 @@
+public class fenwick_tree {
+    private int[] data;
+
+    public fenwick_tree(int size) {
+        data = new int[size + 1];
+    }
+
+    /**
+     * Returns the sum from 0 to right (inclusive)
+     * @param right the inclusive right index
+     * @return sum([0; right])
+     */
+    public int sum(int right) {
+        int sum = 0;
+        int index = right + 1;// Convert to 1-based index
+        for (; index > 0; index -= LSB(index)) {
+            sum += data[index];
+        }
+        return sum;
+    }
+
+    /**
+     * Returns the sum from left (inclusive) to right (inclusive)
+     * @param left the inclusive left index
+     * @param right the inclusive right index
+     * @return sum([left; right])
+     */
+    public int sum(int left, int right) {
+        return sum(right) - sum(left - 1);
+    }
+
+    /**
+     * Add the difference to the data index
+     * @param index the index to update
+     * @param diff the amount to add to that index
+     */
+    public void add(int index, int diff) {
+        index++; // Convert to 1-based index
+        for (; index < data.length; index += LSB(index)) {
+            data[index] += diff;
+        }
+    }
+
+    /**
+     * Returns the tree's capacity
+     * @return tree sizes
+     */
+    public int getSize() {
+        return data.length - 1;// The 0 index isn't used
+    }
+
+    private static int LSB(int x) {
+        // Last Significant Bit
+        return x & -x;
+    }
+
+
+    /**
+     * Example usage
+     * run with "java -ea fenwick_tree" to enable assertions
+     */
+    public static void main(String[] args) {
+        fenwick_tree tree = new fenwick_tree(8);
+
+        // Set initial value (by default it's 0)
+        for (int i = 0; i < 8; i++) {
+            tree.add(i, i);
+        }
+        // Now it's 0, 1, 2, 3, 4, 5, 6, 7
+
+        // [0, 1, 2, 3, 4, 5, 6, 7]
+        //  ^--------------------^
+        // 0 + 1 + 2 ... + 7 = 28
+        assert tree.sum(0, 7) == 28;
+
+        // [0, 1, 2, 3, 4, 5, 6, 7]
+        //              ^-----^
+        // 4 + 5 + 6 = 15
+        assert tree.sum(4, 6) == 15;
+
+        // [0, 1, 2, 3, 4, 5, 6, 7]
+        //  ^--------^
+        // 0 + 1 + 2 + 3 = 6
+        assert tree.sum(3) == 6;
+
+        // Update the numbers again
+        for (int i = 0; i < 8; i++) {
+            tree.add(i, 1 - i);
+            // Initial value i
+            // Added: 1 - i
+            // Res: i + 1 - i = 1
+        }
+
+        // [1, 1, 1, 1, 1, 1, 1, 1]
+        //  ^--------------------^
+        // 1 * 8 = 8
+        assert tree.sum(0, 7) == 8;
+        System.out.println("Tests passed");
+    }
+}