Added fenwick tree class

src/classes/tree/fenwick_tree.h

@@ -0,0 +1,63 @@
+#ifndef FENWICK_TREE_H
+#define FENWICK_TREE_H
+
+#ifdef __cplusplus
+#include <iostream>
+#include <vector>
+#endif
+
+/**
+* @brief fenwick tree class
+*/
+template <typename T>
+struct fenwick_tree {
+    std::vector<T> tree;
+    int n;
+
+    /**
+    * @brief default constructor of fenwick tree class
+    * @param v: the input vector
+    */
+    explicit fenwick_tree(const std::vector<T> &v) noexcept : n(int(v.size())) {
+        tree = std::vector<T>(n, 0);
+        for(int i = 0; i<n; i++) {
+            this->update(i, v[i]);
+        }
+    }
+
+    /**
+    * @brief sum query function
+    * @param k: the ending index of the query
+    * @return T: the sum of range [0, k]
+    */
+    T sum(int k) {
+        T sum = 0;
+        for(; k >= 0; k = (k & (k + 1)) - 1) {
+            sum += tree[k];
+        }
+        return sum;
+    }
+
+    /**
+    * @brief sum query function(from index a to b)
+    * @param a: starting index
+    * @param b: ending index
+    * @returns T: the sum of range [a, b]
+    */
+    T sum(int a, int b) {
+        return sum(b) - sum(a - 1);
+    }
+
+    /**
+    * @brief update query function
+    * @param k: the index
+    * @param x: the value that will be added to data[k]
+    */
+    void update(int k, int x) {
+        for(; k < n; k = k | (k + 1)) {
+            tree[k] += x;
+        }
+    }
+};
+
+#endif

tests/tree/fenwick_tree.cc

@@ -0,0 +1,37 @@
+#include "../../src/classes/tree/fenwick_tree.h"
+#include "../../third_party/catch.hpp"
+
+
+TEST_CASE("Testing fenwick tree default constructor") {
+    std::vector<int> v = {1, 4, 5, 6, 7};
+    CHECK_NOTHROW(fenwick_tree<int>(v));
+}
+
+TEST_CASE("Testing fenwick tree sum query [1]") {
+    std::vector<int> v = {1, 2, 3, 4, 5};
+    fenwick_tree<int> f(v);
+    REQUIRE(f.sum(2) == 6);
+    REQUIRE(f.sum(1) == 3);
+    REQUIRE(f.sum(4) == 15);
+    REQUIRE(f.sum(0) == 1);
+}
+
+TEST_CASE("Testing fenwick tree sum query [2]") {
+    std::vector<int> v = {1, 2, 3, 4, 5};
+    fenwick_tree<int> f(v);
+    REQUIRE(f.sum(2) == 6);
+    REQUIRE(f.sum(4) == 15);
+    REQUIRE(f.sum(1, 2) == 5);
+    REQUIRE(f.sum(3, 4) == 9);
+    REQUIRE(f.sum(1, 3) == 9);
+}
+
+TEST_CASE("Testing update query [1]") {
+    std::vector<int> v = {1, 2, 3, 4, 5};
+    fenwick_tree<int> f(v);
+
+    f.update(0, 2);
+    REQUIRE(f.sum(0, 1) == 5);
+    f.update(0, -5);
+    REQUIRE(f.sum(0, 2) == 3);
+}

tutorial/tree/fenwick_tree.md

@@ -0,0 +1,25 @@
+### Mini tutorial for fenwick tree class
+
+-- fenwick_tree<T> creates a fenwick tree with nodes of type T
+
+### *default constructor*:
+```cpp
+vector<int> v = {1, 2, 3, 4, 5};
+fenwick_tree<int> f(v); // this creates the fenwick tree
+                        // with the passed vector v
+```
+
+### *sum query*:
+```cpp
+...
+cout << f.sum(2) << '\n'; // this should return 6
+cout << f.sum(0, 2) << '\n'; // this should return 6 as well
+```
+
+### *update query*:
+```cpp
+...
+f.update(0, -5); // updates the value of index 0 to -4(1 + -5)
+cout << f.sum(2) << '\n'; // this should return 1 now
+cout << f.sum(0, 2) << '\n'; // this should return 1 as well
+```