Why are Tries an Efficient Choice for Implementing Sparse Matrices?

Sparse matrices are efficient data structures for representing data that has a high proportion of zero values. They store only the non-zero elements, which can significantly reduce memory usage and improve performance.

Tries, a type of tree data structure, are commonly used to implement sparse matrices. They map coordinates to a position in a vector, where segments are distributed. This allows for efficient access to elements, with only two array indexing operations required to determine if an element is present or absent.

Unlike hashmaps, which require complex hashing functions and handle collisions, tries provide read-only access to elements with no collisions. This makes them significantly faster than hashmaps, especially for frequently read data.

The code demonstrates how to build a sparse matrix using a trie. It uses integer indexing to access elements and can be flexibly resized to accommodate different matrix sizes. The code includes methods for setting and getting values, as well as a compact() method to optimize data storage by detecting and merging common subranges.

Tries are a powerful data structure for implementing sparse matrices, offering advantages in terms of memory usage, performance, and flexibility.

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