fenwick tree

A Fenwick tree, also known as a Binary Indexed Tree (BIT), is a data structure that efficiently supports prefix sum queries and updates in an array of numbers. Here are the steps to implement a Fenwick tree:

  1. Initialization: Create an array BIT[] of size n+1, where n is the number of elements in the input array. Initialize all elements of BIT[] to 0.

  2. Construction: For each index i from 1 to n, update BIT[] as follows:

  3. Set index j = i
  4. While j is within the range of BIT[], add the value of the input array at index j to BIT[j]

  5. Update j to j + (j & -j)

  6. Prefix Sum Query: To compute the prefix sum of the input array up to index i:

  7. Initialize the variable sum to 0
  8. Set index j = i
  9. While j is greater than 0, add the value of BIT[j] to sum and update j to j - (j & -j)

  10. Return the value of sum as the prefix sum

  11. Range Update: To update the value of the input array at index i by a given value val:

  12. Set index j = i
  13. While j is within the range of BIT[], add val to BIT[j] and update j to j + (j & -j)

These steps illustrate the process of implementing a Fenwick tree in C++ to efficiently support prefix sum queries and updates in an array of numbers.