fix: Remove FenwickTree (#856)

* Remove FenwickTree

FenwickTree is the same Data Structure as Binary Indexed Tree located in file "range_queries/bit.cpp" so it could be removed.

* Fix cpplint errors

* docs: Update documentation

* docs: Update FenwickTree documentation

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

range_queries/fenwick_tree.cpp

@@ -0,0 +1,82 @@
+/**
+ * @file
+ * @brief Fenwick tree
+ *
+ * A Fenwick tree or binary indexed tree is a data structure
+ * that can efficiently update elements and calculate
+ * prefix sums in a table of numbers.
+ */
+#include <cassert>
+#include <iostream>
+#include <vector>
+
+/**
+ * n --> No. of elements present in input array.
+ * bit[0..n] --> Array that represents Binary Indexed Tree.
+ */
+class FenwickTree {
+    int n;
+    std::vector<int> bit;
+
+    /** Returns the highest power of two which is not more than x */
+    inline int offset(int x) { return (x & (-x)); }
+
+ public:
+    /** Constructor
+     * \param[in] arr --> Input array for which prefix sum is evaluated.
+     */
+    explicit FenwickTree(const std::vector<int>& arr) {
+        n = arr.size();
+        bit.assign(n + 1, 0);
+        for (int i = 0; i < n; ++i) {
+            update(i, arr[i]);
+        }
+    }
+
+    /** Constructor
+     * \param[in] x --> Size of array that represents Binary Indexed Tree.
+     */
+    explicit FenwickTree(int x) {
+        n = x;
+        bit.assign(n + 1, 0);
+    }
+
+    /** Add val at id */
+    void update(int id, int val) {
+        id++;
+        while (id <= n) {
+            bit[id] += val;
+            id += offset(id);
+        }
+    }
+
+    /** Get prefix sum upto id */
+    int sum(int id) {
+        id++;
+        int res = 0;
+        while (id > 0) {
+            res += bit[id];
+            id -= offset(id);
+        }
+        return res;
+    }
+
+    /** Returns the prefix sum in range from l to r */
+    int sum_range(int l, int r) { return sum(r) - sum(l - 1); }
+};
+
+/** Main function */
+int main() {
+    int n = 5;
+    std::vector<int> arr = {1, 2, 3, 4, 5};
+    FenwickTree fenwick_tree(arr);
+
+    assert(fenwick_tree.sum_range(0, 0) == 1);
+    assert(fenwick_tree.sum_range(0, 1) == 3);
+    assert(fenwick_tree.sum_range(0, 2) == 6);
+    fenwick_tree.update(0, 6);
+    assert(fenwick_tree.sum_range(0, 0) == 6);
+    assert(fenwick_tree.sum_range(0, 1) == 8);
+    assert(fenwick_tree.sum_range(0, 2) == 11);
+    return 0;
+}