Fenwick Tree Optimization

Fenwick Trees are a powerful data structure for efficiently computing prefix sums and performing range queries on an array. However, there are several optimization techniques that can further enhance the performance of Fenwick Trees. Let's explore some of these optimization techniques:

1. Zero-Based Indexing

By default, Fenwick Trees use one-based indexing, where the first element has index 1. However, for optimization purposes, it is often beneficial to use zero-based indexing, where the first element has index 0. Zero-based indexing can simplify the implementation of Fenwick Trees and eliminate the need for certain adjustments when accessing array elements.

1// Fenwick Tree with zero-based indexing
2int fenwickTree[10];

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#include <iostream>

using namespace std;

​

int main() {

  // Fenwick Tree Optimization techniques

  // 1. Zero-Based Indexing

  // 2. Compression

  // 3. Precompute Sum

  // 4. Range Update

  // 5. Range Query

  // 6. Binary Indexed Tree

  // 7. Sparse Fenwick Tree

  // 8. 2D Fenwick Tree

  return 0;

}