From aa717b0f5c33d9d4e5002693ba89819cfb57bbe3 Mon Sep 17 00:00:00 2001
From: Krishan Kant Agnihotri
 <60218702+KrishanKantAgnihotri@users.noreply.github.com>
Date: Mon, 11 Oct 2021 18:32:30 +0530
Subject: [PATCH] chore(CPlusPlus): add Fenwick Tree (#542)

Co-authored-by: Ming Tsai <37890026+ming-tsai@users.noreply.github.com>
---
 algorithms/CPlusPlus/README.md              |   1 +
 algorithms/CPlusPlus/Trees/Fenwick_Tree.cpp | 102 ++++++++++++++++++++
 2 files changed, 103 insertions(+)
 create mode 100644 algorithms/CPlusPlus/Trees/Fenwick_Tree.cpp

diff --git a/algorithms/CPlusPlus/README.md b/algorithms/CPlusPlus/README.md
index 01a71993..b376d2a7 100644
--- a/algorithms/CPlusPlus/README.md
+++ b/algorithms/CPlusPlus/README.md
@@ -114,6 +114,7 @@
 - [Finding the elements of a tree visible from top view](Trees/Top-View-Of-A-Tree.cpp)
 - [Binary Tree Implementation](Trees/binary-tree-implementation.cpp)
 - [Iterative Segment Tree](Trees/IterativeSegmentTree.cpp)
+- [Fenwick Tree](Trees/Fenwick_Tree.cpp)
 
 # Maths
 - [Kaprekar Number](Maths/Kaprekar-number.cpp)
diff --git a/algorithms/CPlusPlus/Trees/Fenwick_Tree.cpp b/algorithms/CPlusPlus/Trees/Fenwick_Tree.cpp
new file mode 100644
index 00000000..3aa13069
--- /dev/null
+++ b/algorithms/CPlusPlus/Trees/Fenwick_Tree.cpp
@@ -0,0 +1,102 @@
+#include <bits/stdc++.h>
+using namespace std;
+//BIT with 1 based indexing
+template <typename T>
+struct BIT
+{
+    T N;
+    vector<T> tree;
+    void init(int n)
+    {
+        N = n;
+        tree.assign(n + 1, 0);
+    }
+    //point update in O(log(n))
+    void update(int idx, T val)
+    {
+
+        while (idx <= N)
+        {
+            tree[idx - 1] += val;
+            idx += (idx & (-idx));
+        }
+    }
+    //query in O(log(n))
+    T query(int idx)
+    {
+        T sm = 0;
+        while (idx > 0)
+        {
+            sm += tree[idx - 1];
+            idx -= (idx & (-idx));
+        }
+        return sm;
+    }
+    //sum function to find sum of values [l,r]
+    T sum(int l, int r)
+    {
+        return query(r) - query(l - 1);
+    }
+};
+
+int main()
+{
+
+    int n;
+    cin >> n;
+    vector<int> v(n);
+    for (int i = 0; i < n; i++)
+    {
+        cin >> v[i];
+    }
+    BIT<int> f;
+    f.init(n + 1); //1 base indexing
+    //Building of Fenwick Tree in O(n*(log(n)))
+    for (int i = 0; i < n; i++)
+    {
+        f.update(i + 1, v[i]);
+    }
+    //queries
+    int q;
+    cin >> q;
+    while (q--)
+    {
+        int t;
+        //two types of queries
+        //1) t = 1 change element at index i to u
+        //2) t = 2 print the sum of elements in range [l,r]
+        cin >> t;
+        if (t == 1)
+        {
+            int id, u;
+            cin >> id >> u;
+            id--; //changing to zero base
+            int initial = v[id];
+            f.update(id + 1, u - initial); //updating the delta
+            v[id] = u;
+        }
+        else
+        {
+            int l, r;
+            cin >> l >> r;
+            cout << f.sum(l, r) << endl;
+        }
+    }
+}
+
+// Time Complexity:
+// O(nlogn)
+// Space Complexity:
+// O(n)
+
+// Test Cases:
+// Input:
+// 5
+// 1 3 4 7 -15
+// 3
+// 2 2 5
+// 1 3 -5
+// 2 2 5
+// Output:
+// -1
+// -10