A Sparse Array refers to a data structure optimized for situations where the majority of its elements are zero or have a default null value. Unlike dense arrays, where elements are contiguous and start at index 0, sparse arrays are characterized by non-contiguous indexes and can have "holes" or gaps in the sequence of their indices. This makes sparse arrays particularly useful in scenarios where storing and manipulating large arrays with predominantly zero values would otherwise be inefficient in terms of both space and computational resources.
Sparse arrays are implemented through specialized algorithms and data structures that only store non-zero elements, significantly reducing memory usage and improving performance for certain operations. They are commonly represented in two main ways:
Array Representation: This involves using a 2D array with three rows to represent non-zero elements, where the first row stores the row number, the second row stores the column number, and the third row stores the value of the non-zero elements. The total number of columns in this matrix equals the total number of non-zero elements.
Linked List Representation: In this approach, each non-zero element is represented as a node in a linked list, with each node containing information about the row number, column number, and value of the non-zero element, as well as a pointer to the next node representing ...
