n-dim-data-structures 0.1.0

A collection of optimized N-dimensional data structures in Python

N-Dimensional Data Structures

A blazing-fast, polyglot (Python & C++) library providing generalized $N$-dimensional data structures.

Whether you are working in Python for data science and backend engineering, or you need highly-optimized header-only C++ templates to copy-paste into competitive programming platforms like Codeforces and LeetCode, this repository has you covered.

Data Structures Included

All structures support $O(1)$ or $O(\log^N(V))$ operations scaled effortlessly across any arbitrary number of dimensions.

1. Static N-Dim Prefix Sum (static_n_dim_prefix_sum)
2. Static N-Dim Difference Array (static_n_dim_difference_array)
3. Dynamic N-Dim Fenwick Tree (dynamic_n_dim_fenwick_tree)
4. Dynamic N-Dim Difference Fenwick Tree (dynamic_n_dim_diff_fenwick_tree)
5. Dynamic N-Dim Range Fenwick Tree (dynamic_n_dim_range_fenwick_tree)
6. Dynamic N-Dim Segment Tree (dynamic_n_dim_seg_tree)

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C++ (Competitive Programming)

The cpp/include/ndim/ directory contains highly optimized, header-only C++17 templates designed specifically for competitive programming.

They use standard <bits/stdc++.h> format with using namespace std; to ensure they are instantly copy-pasteable into online judges without causing scope or header errors. Memory is maintained via flat, contiguous 1D vectors mapped algebraically to $N$ dimensions, preventing memory scattering and ensuring maximum CPU cache efficiency.

Example Usage

#include "dynamic_n_dim_seg_tree.hpp"

// Example: 3D Segment Tree using std::min
auto min_func = [](int64_t a, int64_t b) { return min(a, b); };
int64_t def = 1e18; // infinity

// 4x4x4 grid
DynamicNDimSegTree<int64_t, decltype(min_func)> tree({4, 4, 4}, min_func, def);

tree.update({1, 1, 1}, 5);
tree.update({2, 2, 2}, 10);

int64_t val = tree.query_range({0, 0, 0}, {3, 3, 3}); // 5

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Python (Data Science / General)

The python/src/ directory contains the pure-Python implementations. They use 1D list-flattening mathematics similar to numpy under the hood, but operate purely on standard library primitives, ensuring maximum portability without heavy C-extension dependencies.

Installation

The library is configured using uv via pyproject.toml.

cd python
uv sync

Example Usage

from dynamic_n_dim_range_fenwick_tree import DynamicNDimRangeFenwickTree

# 10x10x10 grid
tree = DynamicNDimRangeFenwickTree([10, 10, 10])

# Add 50 to the bounding box from (1, 1, 1) to (5, 5, 5)
tree.add_range([1, 1, 1], [5, 5, 5], 50)

# Query the volume sum from (0, 0, 0) to (3, 3, 3)
total = tree.query_range([0, 0, 0], [3, 3, 3])

Testing

Both ecosystems are rigorously tested with aggressive $10^3$ iteration stress tests across $5$-dimensional constraints.

• Python: Uses pytest. Run uv run pytest test/
• C++: Uses doctest. Compile the files in cpp/test/ using g++ -std=c++17 and run the resulting executables.