Performing Queries on a Fenwick Tree

In this lesson, we will learn how to perform queries on a Fenwick Tree. A query on a Fenwick Tree allows us to calculate the sum of a range of values efficiently.

To perform a query on a Fenwick Tree, we follow a similar process as updating a value, but in reverse. Starting from the given index, we traverse the Fenwick Tree using bitwise operations until we reach index 0. At each step, we add the value at the current index to a running sum.

Here's an example code snippet in C++ that demonstrates how to perform a query on a Fenwick Tree:

1#include <iostream>
2using namespace std;
3
4int main() {
5  int n;
6  cin >> n;
7
8  int fenwick[n + 1];
9  for (int i = 0; i <= n; i++) {
10    fenwick[i] = 0;
11  }
12
13  int idx;
14  cin >> idx;
15
16  int sum = 0;
17  while (idx > 0) {
18    sum += fenwick[idx];
19    idx -= idx & -idx;
20  }
21
22  cout << sum << endl;
23
24  return 0;
25}

In the code snippet, we first create an array to store the Fenwick Tree and initialize all elements to 0. Then, we input the index at which we want to perform the query.

Next, we initialize a running sum variable to 0 and start traversing the Fenwick Tree from the given index. At each step, we add the value at the current index to the running sum and update the index using bitwise operations.

Finally, we output the sum of the range of values.

Keep in mind that this code snippet serves as an example implementation, and you may need to modify it based on your specific use case.

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#include <iostream>

using namespace std;

​

int main() {

  // Replace with your Fenwick Tree implementation

  int n;

  cin >> n;

​

  // Create an array to store the Fenwick Tree

  int fenwick[n + 1];

  for (int i = 0; i <= n; i++) {

    fenwick[i] = 0;

  }

​

  // Perform a query on the Fenwick Tree

  int idx;

  cin >> idx;

​

  int sum = 0;

  while (idx > 0) {

    sum += fenwick[idx];

    idx -= idx & -idx;

  }

​

  // Output the query result

  cout << sum << endl;

​

  return 0;

}