## MonotoneMatrixSearchTraits

### 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>