c++

3 41 42 43 44 45 So the value at row:2, column:3 is 34 (rows and columns both start at 0) However, there is a fairly easy way to translate between a 2D vector as shown above and a ID vector. Below is a 1D vector representation of the matrix above with the 1D indicies in bold. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 The question is really, how to translate row:2, column:3 to a 1D vector index and how to translate a ID vector index back to a row/column format. To do this we have to know the number of columns in the 2D vector. In this particular case, 5 columns. row-index/5 (integer division), where 5 is the number of columns. column index%5 (modulus), where 5 is the number of columns index- row 5+column, where 5 is the number of columns For the example, row: 2 column: 3 is index (2 * 5) + 3 13 index 13 is row-13/5 2. column 13%5 3 Program Specifications Each of the functions below is doing calculations on a 2D vector using a 1D vector as the underlying parameter that is passed. The parameters are passed as const references: references to prevent copying but const to prevent modification of the parameter function: ostreams print_vector (const vector&v, ostream& out) print the vector to the provided stream, returning that stream. Each element of the vector is separated from the next by a comma, no comma after the last element. You print out to the provide ostream, not cout! Look at the Mimir tests for examples. You return the stream you passed in!! function: long four_corner_sum (const vectorlong> v, int rows, int cols) return the sum of the 4 corners of the provided 1D vector, interpreted as a 2D matrix with provided row and column count. For the matrix above, it would return 11+15+41+45112 Error Check: if there are less than either two rows or two columns (thus no corners), return 0 function: column vector& rows, int cols) vector order (const v, int return a new vector that is a reordering of the original 1D vector in column order. Collect each column, first to last, and within the column in row order 0 11 12 13 14 15 1 21 22 23 24 25 11,21,31,41,12, 22, 32,42,13,23, 33, 43, 14, 24, 34,44, 15, 25, 35, 45 2 31 32 33 34 35 3 41 42 43 44 45 function: vector rotaterows_up (const vector& v, int rows, int cols) return a new vector that is a rotation of the 2D matrix rows up by one. Here, the 2d row becomes the 1, the 3d the 2d etc. and the 1st row becomes the last