Applications of Fenwick Tree

Fenwick Trees find use in a wide range of applications. Here are a few notable ones:

• Range Sum Queries: Fenwick Trees can efficiently answer range sum queries on arrays or sequences. They provide a flexible and efficient way to calculate and update the sum of elements in a given range.

• Inversion Count: Inversion count is the measure of how far an array is from being sorted. Fenwick Trees can be used to efficiently calculate the inversion count of an array, making it useful in sorting and ranking problems.

• Frequency Count: Fenwick Trees can also be used to efficiently count the frequency of occurrences of elements in an array or a sequence. This is particularly useful in problems where you need to track the frequency of elements as you traverse the array.

Do you want to see an example of how a Fenwick Tree can be implemented in C++ to update values and calculate prefix sums?

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#include <iostream>

using namespace std;

​

int main() {

  // Fenwick Tree implementation

  int n = 10;

  int fenwickTree[11] = {0};

​

  // Update value at index

  int indexToUpdate = 5;

  int valueToUpdate = 8;

  while (indexToUpdate <= n) {

    fenwickTree[indexToUpdate] += valueToUpdate;

    indexToUpdate += indexToUpdate & -indexToUpdate;

  }

​

  // Get prefix sum

  int prefixSum = 0;

  int index = 10;

  while (index > 0) {

    prefixSum += fenwickTree[index];

    index -= index & -index;

  }

​

  cout << "Prefix Sum: " << prefixSum << endl;

​

  return 0;

}