Two Dimensional Arrays

CSE202: Lecture 16 The Ohio State University 1

Two Dimensional Arrays


Two-dimensional Arrays

• A two-dimensional array consists of both rows and columns of elements. It is essentially a matrix.

• To declare a two-dimensional array, we merely use two sets of square brackets.– The first contains the number of rows– The second contains the number of columns

//Creates a 2D array with 3 rows and 4 columnsint vals[3][4];


Indices in 2D arrays

• Assume that the two dimensional array called val is declared and looks like the following:

• To access the cell containing 6, we reference val[1][3], that is, row 1, column 3.

val Col 0 Col 1 Col 2 Col 3

Row 0 8 16 9 52

Row 1 3 15 27 6

Row 2 14 25 2 10


Using 2D arrays

• Just like 1D arrays, once you have specified the index, you are just working with a single variable of the given data type.

• Assignments and usage is still the same:

sumRow0 = val[0][0] + val[0][1] + val[0][2] + val[0][3];

//assigns 72 to cell at row 2, column 3val[2][3] = 72;


Initializing 2D arrays

• You can use additional braces to indicate when rows start and end, but you don’t have to do that.int val[3][4] = { {8,16,9,52},

{3,15,27,6}, {14,25,2,10}

};

• Orint val[3][4] = {8,16,9,52,

3,15,27,6, 14,25,2,10};

• Or (correct, but not as clear as the first two):int val[3][4] = {8,16,9,52,3,15,27,6,14,25,2,10};


More on 2D arrays

• Initialization of 2D arrays is done in row order.

• 2D arrays work well with (for) loops like 1D arrays. However, to access all elements, typically you will need nested loops for 2D arrays. Can you see why?


Example Program...int main(){ const int NUM_ROW(3); const int NUM_COL(4); int vals[NUM_ROW][NUM_COL] = { {11, 12, 13, 14}, {21, 22, 23, 24}, {31, 32, 33, 34} };

// output the array for (int row = 0; row < NUM_ROW; row++) { for (int col = 0; col < NUM_COL; col++) { cout << vals[row][col] << " "; } cout << endl; }...


Example Program... int vals[NUM_ROW][NUM_COL] = { {11, 12, 13, 14}, {21, 22, 23, 24}, {31, 32, 33, 34} };

// output the array for (int row = 0; row < NUM_ROW; row++) { for (int col = 0; col < NUM_COL; col++) { cout << vals[row][col] << " "; } cout << endl; }...

> array2DExample.exe11 12 13 1421 22 23 2431 32 33 34


Example Program (2)...int main(){ const int NUM_ROW(3); const int NUM_COL(4); int vals[NUM_ROW][NUM_COL] = { {11, 12, 13, 14}, {21, 22, 23, 24}, {31, 32, 33, 34} };

// output the transpose of the array for (int col = 0; col < NUM_COL; col++) { for (int row = 0; row < NUM_ROW; row++) { cout << vals[row][col] << " "; } cout << endl; }...


Matrix Addition Algorithm

• Add two n x m matrices A, B;

• for each row i of A do

– for each column j of A do

° C[i][j] = A[i][j] + B[i][j];

• Output matrices A, B and C.


matrixAdd.cpp...int main(){ const int NUM_ROWS(3); // number of matrix rows const int NUM_COLS(2); // number of matrix columns

// Note: A, B and C have the same dimensions double A[NUM_ROWS][NUM_COLS] = { {3, 3}, {1, 1}, {2, 0} }; double B[NUM_ROWS][NUM_COLS] = { {3, 0}, {3, 0}, {0, 1} }; double C[NUM_ROWS][NUM_COLS];

// C = A + B for (int i=0; i<NUM_ROWS; i++) { for (int j=0; j<NUM_COLS; j++) { C[i][j] = A[i][j] + B[i][j]; } }...


matrixAdd.cpp (2)... // display A cout << "A =" << endl; for (int i=0; i<NUM_ROWS; i++) { for (int j=0; j<NUM_COLS; j++) { cout << " " << A[i][j] << " "; } cout << endl; } cout << endl;...


Distance Matrix Algorithm

• Compute a matrix D storing distances to a point (x,y);

• Input: x, y

• for each row i of D do

– for each column j of D do

° D[i][j] = distance from (x,y) to (i,j)

• Output matrix D.


distanceMatrix.cpp... // dimensions of distance matrix const int N_ROWS(8); const int N_COLS(12); double A[N_ROWS][N_COLS]; double x(0.0), y(0.0);

cout << "Enter (x,y) coordinates of center: "; cin >> x >> y;

for (int i=0; i<N_ROWS; i++) { for (int j=0; j<N_COLS; j++) { double dx = j-x; // Note: x represents columns double dy = i-y; // Note: y represents rows double dist = sqrt(dx*dx+dy*dy); A[i][j] = dist; } }...


X Matrix Algorithm

• Compute a character matrix A representing an X;• Input: h (height of the X)

• Initialize the first h columns in the first h rows of A to ‘-’;

• Set all elements of A on the diagonal from A[0][0] to A[h-1][h-1] to ‘X’;

• Set all elements of A on the diagonal from A[0][h-1] to A[h-1][0] to ‘X’.


X.cpp... // dimensions of matrix A const int N_ROWS(50); const int N_COLS(N_ROWS); char A[N_ROWS][N_COLS]; int height(0);

cout << "Enter height of X: "; cin >> height;

while (height > N_ROWS) { cout << "Input error. Input must be less than or equal to " << N_ROWS << ". " << endl;

cout << "Enter height of X: "; cin >> height; }...


X.cpp (2) // initialize elements of A to '-' for (int i=0; i<height; i++) { for (int j=0; j<height; j++) { A[i][j] = '-'; } }

// draw diagonal \ in A for (int k=0; k<height; k++) { A[k][k] = 'X'; }

// draw diagonal / in A for (int k=0; k<height; k++) { A[k][height-k-1] = 'X'; }


X.cpp... // dimensions of matrix A const int N_ROWS(50); const int N_COLS(N_ROWS); char A[N_ROWS][N_COLS]; int height(0.0);

cout << "Enter height of X: "; cin >> height;

while (height > N_ROWS) { cout << "Input error. Input must be less than or equal to " << N_ROWS << ". " << endl;

cout << "Enter height of X: "; cin >> height; }...


Two Dimensional Arrays as Parameters


Matrix Addition Algorithm

• Add two n x m matrices A, B;

• for each row i of A do

– for each column j of A do

° C[i][j] = A[i][j] + B[i][j];

• Output matrices A, B and C.


matrixAdd2.cpp...int main(){ // Note: A, B and C have the same dimensions double A[NUM_ROWS][NUM_COLS] = { {3, 3}, {1, 1}, {2, 0} }; double B[NUM_ROWS][NUM_COLS] = { {3, 0}, {3, 0}, {0, 1} }; double C[NUM_ROWS][NUM_COLS];

add(A, B, C); cout << "A = " << endl; display(A); cout << "B = " << endl; display(B); cout << "C = " << endl; display(C);

return 0;}...


matrixAdd2.cpp...// GLOBAL CONSTANTSconst int NUM_ROWS(3); // number of matrix rowsconst int NUM_COLS(2); // number of matrix columns

// Function prototypesvoid add(const double M1[NUM_ROWS][NUM_COLS], const double M2[NUM_ROWS][NUM_COLS], double M3[NUM_ROWS][NUM_COLS]);void display(const double M[NUM_ROWS][NUM_COLS]);

int main(){ // Note: A, B and C have the same dimensions // Matrices double A[NUM_ROWS][NUM_COLS] = { {3, 3}, {1, 1}, {2, 0} }; double B[NUM_ROWS][NUM_COLS] = { {3, 0}, {3, 0}, {0, 1} }; double C[NUM_ROWS][NUM_COLS];...


Function add()// Add two matrices// M1[][] = First matrix// M2[][] = Second matrix// M3[][] = M1[][] + M2[][]// Note: M1, M2 and M3 must have the same dimensionsvoid add(const double M1[NUM_ROWS][NUM_COLS], const double M2[NUM_ROWS][NUM_COLS], double M3[NUM_ROWS][NUM_COLS]){ // M3 = M1 + M2 for (int i=0; i < NUM_ROWS; i++) { for (int j=0; j<NUM_COLS; j++) { M3[i][j] = M1[i][j] + M2[i][j]; } }}


Function display()// Output matrix// M[][] = Matrixvoid display(const double M[NUM_ROWS][NUM_COLS]){ for (int i=0; i < NUM_ROWS; i++) { for (int j=0; j < NUM_COLS; j++) { cout << " " << setw(3) << M[i][j]; } cout << endl; } cout << endl;}


matrixAdd2.cpp...int main(){ // Note: A, B and C have the same dimensions double A[NUM_ROWS][NUM_COLS] = { {3, 3}, {1, 1}, {2, 0} }; double B[NUM_ROWS][NUM_COLS] = { {3, 0}, {3, 0}, {0, 1} }; double C[NUM_ROWS][NUM_COLS];

add(A, B, C); cout << "A = " << endl; display(A); cout << "B = " << endl; display(B); cout << "C = " << endl; display(C);

return 0;}...


Passing 2D Arrays into Functions

• 2D arrays are always passed by reference.• To declare a 2D array parameter,

– Define global constants NUM_ROWS and NUM_COLS;– Parameter is: type array2D[NUM_ROWS][NUM_COLS]

For instance,

void f(int array2D[NUM_ROWS][NUM_COLS])

• No way to declare a variable length 2D array parameter.

For instance, void f(int array2D[][]) is illegal and will generate a syntax error.


Multi-Dimensional Arrays

• Arrays can have higher dimensions.

• Definitions, intialization, indexing, function parameters are similar to 2D arrays.

• Note multidimensional arrays can have quite a few elements so you must be mindful of your memory capacity:

int big[1000][1000][1000]; //a billion ints


Common Programming Errors

• Addressing indices that are out of bounds of the array range. This will run-time crash or at the very least a logical error. Be careful especially when using expressions to compute the indices.– Remember, indexing starts with 0, not 1!!!

• Forgetting to declare the array (either altogether or forgetting the [])

• Assuming the array is initialized (to zero.)

Documents

Two Dimensional Arrays