Updating a Fenwick Tree

To update the value of an element in a Fenwick Tree, we can use the update method. This method takes two parameters: index and value. Starting from the given index, we update the corresponding values in the tree by adding the value. We continue updating until we reach the end of the tree or go out of bounds.

Here's an example of how to implement the update method in C++:

1void update(int index, int value) {
2  while (index < tree.size()) {
3    tree[index] += value;
4    index += index & (-index);
5  }
6}

In the above code, we iterate through the tree starting from the given index and update the values by adding the value. We update the index by adding the least significant bit (obtained by using the & operator with the two's complement of the index). This process continues until we reach the end of the tree or go out of bounds.

Let's create a Fenwick Tree with a size of 10 and perform an update operation at index 5 with a value of 3. Then, we'll perform a query operation at index 8 and print the result.

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}

#include <iostream>

using namespace std;

​

// Class for Fenwick Tree

class FenwickTree {

private:

  vector<int> tree;

public:

  // Constructor

  FenwickTree(int size) {

    tree.resize(size + 1, 0);

  }

​

  // Update method

  void update(int index, int value) {

    while (index < tree.size()) {

      tree[index] += value;

      index += index & (-index);

    }

  }

​

  // Query method

  int query(int index) {

    int sum = 0;

    while (index > 0) {

      sum += tree[index];

      index -= index & (-index);

    }

    return sum;