A Practical Introduction to Data Structures and Algorithm Analysis

428 Chap. 12 Lists and Arrays RevisitedCols0 1 3 6Rows0A 00 A 06A 011A 11 A 13A 764A 40A 717Figure 12.7 The orthogonal list sparse matrix representation.One approach to representing a sparse matrix is to concatenate (or otherwisecombine) the row and column coordinates into a single value and use this as a keyin a hash table. Thus, if we want to know the value of a particular position in thematrix, we search the hash table for the appropriate key. If a value for this positionis not found, it is assumed to be zero. This is an ideal approach when all queries tothe matrix are in terms of access by specified position. However, if we wish to findthe first non-zero element in a given row, or the next non-zero element below thecurrent one in a given column, then the hash table requires us to check sequentiallythrough all possible positions in some row or column.Another approach is to implement the matrix as an orthogonal list, as illustratedin Figure 12.7. Here we have a list of row headers, each of which containsa pointer to a list of matrix records. A second list of column headers also containspointers to matrix records. Each non-zero matrix element stores pointers toits non-zero neighbors in the row, both following and preceding it. Each non-zero