 ## MonotoneMatrixSearchTraits advanced ### Definition

The concept MonotoneMatrixSearchTraits is a refinement of BasicMatrix and defines types and operations needed to compute the maxima for all rows of a totally monotone matrix using the function monotone_matrix_search.

### Types

 MonotoneMatrixSearchTraits::Value The type of a matrix entry.

### Operations

 int m.number_of_columns () const returns the number of columns. int m.number_of_rows () const returns the number of rows. Entry m.operator() ( int row, int column) const returns the entry at position (row, column). Precondition: 0 row < number_of_rows() and 0 column < number_of_columns(). void m.replace_column ( int old, int new) replace column old with column number new. Precondition: 0 old, new < number_of_columns(). Matrix* m.extract_all_even_rows () const returns a new Matrix consisting of all rows of m with even index, (i.e. first row is row 0 of m, second row is row 2 of m etc.). Precondition: number_of_rows() > 0. void m.shrink_to_quadratic_size () deletes the rightmost columns, such that m becomes quadratic. Precondition: number_of_columns() number_of_rows(). Postcondition: number_of_rows() == number_of_columns().

### Notes

• For the sake of efficiency (and in order to achieve the time bounds claimed for monotone_matrix_search), all these operations have to be realized in constant time - except for extract_all_even_rows which may take linear time.
• There is an adaptor Dynamic_matrix that can be used to add most of the functionality described above to arbitrary matrix classes.

### Has Models

CGAL::Dynamic_matrix<M> advanced 