Advanced Fenwick Tree Variations

In this section, we will dive deeper into the advanced variations of Fenwick Trees. Fenwick Trees are a powerful data structure that can be modified and extended in various ways to solve different problems efficiently.

Binary Indexed Tree (BIT)

One of the most common variations of Fenwick Trees is the Binary Indexed Tree (BIT). BIT is a compact representation of Fenwick Trees designed to handle range updates and range queries efficiently.

The structure and operations of the BIT are similar to the standard Fenwick Tree, but with a few modifications. It uses a binary encoding scheme to represent the indices, and the update and query functions are adjusted accordingly to work with the encoded indices.

Here's an example of how to implement a Binary Indexed Tree (BIT) in C++:

1#include <iostream>
2using namespace std;
3
4class BinaryIndexedTree {
5  int* bit;
6  int size;
7
8public:
9  BinaryIndexedTree(int n) {
10    size = n + 1;
11    bit = new int[size];
12    for (int i = 0; i < size; i++) {
13      bit[i] = 0;
14    }
15  }
16
17  void update(int index, int value) {
18    while (index < size) {
19      bit[index] += value;
20      index += (index & -index);
21    }
22  }
23
24  int query(int index) {
25    int sum = 0;
26    while (index > 0) {
27      sum += bit[index];
28      index -= (index & -index);
29    }
30    return sum;
31  }
32};
33
34int main() {
35  int n;
36  cin >> n;
37
38  BinaryIndexedTree bit(n);
39
40  // Perform advanced Fenwick Tree variations operations
41
42  return 0;
43}

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#include <iostream>

using namespace std;

int main() {

  // Replace with your advanced Fenwick Tree variations logic here

}