ndim_ds 0.1.4

Generalized N-dimensional data structures

N-Dimensional Data Structures (Python)

A pure-Python library providing generalized N-dimensional data structures. These structures use 1D list-flattening mathematics under the hood to improve cache locality without relying on C-extensions or Numpy.

Installation

The package is officially available on PyPI:

pip install ndim_ds

Data Structures Included

1. Static N-Dim Prefix Sum (StaticNDimPrefixSum) Answers range sum queries offline. After all initial values are added, a sweep() computes prefix sums in $O(V)$ time, allowing subsequent $O(1)$ queries of any hyper-rectangular region.

2. Static N-Dim Difference Array (StaticNDimDifferenceArray) Applies many range additions offline. After deferred $O(1)$ updates are queued, a sweep() runs in $O(V)$ time to finalize the grid, allowing subsequent $O(1)$ point queries.

3. Dynamic N-Dim Fenwick Tree (DynamicNDimFenwickTree) Also known as a Binary Indexed Tree. Supports $O(\log^N(V))$ point updates and prefix sum queries across $N$ dimensions.

4. Dynamic N-Dim Difference Fenwick Tree (DynamicNDimDiffFenwickTree) A Fenwick tree modified to support $O(\log^N(V))$ range updates and point queries across $N$ dimensions.

5. Dynamic N-Dim Range Fenwick Tree (DynamicNDimRangeFenwickTree) Supports $O(\log^N(V))$ range updates and range sum queries across $N$ dimensions. Internally uses $2^N$ algebraic Fenwick trees to correctly scale the range updates.

6. Dynamic N-Dim Segment Tree (DynamicNDimSegTree) Supports $O(\log^N(V))$ point updates and range queries across $N$ dimensions for any associative operation (e.g., min, max, gcd).

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Global Usage

Once installed globally via pip, you can directly import the data structures into any Python script on your machine.

Example

from ndim_ds import StaticNDimPrefixSum, DynamicNDimRangeFenwickTree

# --- Static Example ---
# Initialize a 10x10x10 static grid
grid = StaticNDimPrefixSum([10, 10, 10])

grid.add([1, 1, 1], 50)
grid.add([5, 5, 5], 25)
grid.sweep() # Finalize the grid in O(V) time

# Query the volume sum from (0, 0, 0) to (3, 3, 3) in O(1) time
total_static = grid.query_range([0, 0, 0], [3, 3, 3])

# --- Dynamic Example ---
# Initialize a 10x10x10 dynamic range tree
tree = DynamicNDimRangeFenwickTree([10, 10, 10])

# Add 50 to the bounding box from (1, 1, 1) to (5, 5, 5) in O(log^N(V)) time
tree.add_range([1, 1, 1], [5, 5, 5], 50)

# Query the volume sum from (0, 0, 0) to (3, 3, 3) in O(log^N(V)) time
total_dynamic = tree.query_range([0, 0, 0], [3, 3, 3])

Testing

The codebase is tested with randomized operations across 5-dimensional constraints using pytest. To run tests locally from source:

uv run pytest test/