An abitrary sparse matrix can be represented as a doubly linked list. Non-zero terms (and only non-zero terms) are stored in this linked list in row-major order. The class `DLLSparseMatrixTerm` defines the terms of the sparse matrix (similar to the relationship between `ChainNode` and `Chain`). Develop a Java class `DLLSparseMatrix` that implements `insert`, `clear`, and `transpose` of the sparse matrix. The transpose should be done in O(n2) time and O(1) space. Row-major representation means we store terms row by row. For example, the non-zero terms of the following sparse matrix
| 1 | 2 | | | |
| | 3 | 4 | | |
| 5 | | | 6 | |
| | 7 | | | |
can be represented in this sequence [1, 2, 3, 4, 5, 6, 7] in a row-major ordering.
When `transpose()` is invoked, the result matrix is
| 1 | | 5 | |
| 2 | 3 | | 7 |
| | 4 | | |
| | | 6 | |
| | | | |
So the terms are represented in this sequence [ 1, 5, 2, 3, 7, 4, 6] in row-major ordering.
The code for the class `DLLSparseMatrixTerm` is given in the [url removed, login to view] file in the codes.zip.
1. Write the code for the new class. (Import the dataStructures package from [url removed, login to view]).
2. Show that your transpose method takes *O*(*n*2) time and *O*(1) space. Be as precise as possible.
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