Overview of Multi-Dimensional Arrays

What are Multi-Dimensional Arrays?

MULTI-DIMENSIONAL ARRAYS

• Multi-dimensional array can have 2 dimensions, 3 dimensions, etc.
• You can think, a multi-dimensional array is an array of arrays.
• We can create up to 12-dimensional arrays but arrays above 2D are rarely used.

A two-dimensional array is also known as MATRIX. A matrix can be represented as a table of rows andcolumns

CONCEPTUAL VIEW OF MULTI-DIMENSIONAL ARRAYS

DECLARING MULTI-DIMENSIONAL ARRAYS

GENERAL FORM OF DECLARATION

dataType arrayName [size1][size2]...[sizeN];, this is declaring N-dimensional array. Where N is the number of dimensions, dataType is the data type of the array elements.

SIZE OF MULTI-DIMENSIONAL ARRAYS

• Total number of elements in a multidimensional array = multiply size of all the dimensions.

• Example:

  1. 2D: int myArray1[10][20] = 200 elements
  2. 3D: int myArray1[10][20][30] = 6,000 elements

DECLARING 2D ARRAY

• The total number of elements in a 2-D array is ROW*COLUMN

DECLARING AND INITIALIZING 2D ARRAY

Method 1:

int A[3][2] = {1, 2, 3, 4, 5, 6}; its gona look like this:

1 | 2
3 | 4
5 | 6

Method 2:

int B[2][4] = { {1, 2, 3, 4}, {5, 6, 7, 8} }; //less confusing its gona look like this:

1 | 2 | 3 | 4
5 | 6 | 7 | 8

Method 3:

int C[3][4];
// Use nested FOR loop to input value
// from user input
for(int i = 0; i < 3; i++){
    for(int j = 0; j < 4; j++){
        cin >> C[i][j];
    }
} // will create a 3 row 4 column matrix

SAMPLE DECLARING AND INITIALIZING 2D ARRAY

#include <iostream>
#define ROW 4
#define COL 2
using namespace std;
int main(){
    // use constant for row and column sizes
    int myArray[ROW][COL] ={
        {9,8},
        {7,6},
        {2,3},
        {4,5}};
    // use nested FOR loop for initializing
    // same value for all elements
    // example assign value 5 to all elements
    int row, col;
    for (row=0; row <ROW; row++)
        for (col=0; col<COL; col++) myArray[row][col]=5;
    return 0;
}

PRACTISE

1. Determine sizes of below arrays: a) int tool[5][40]

   int tool[5][40];
   // 5 rows, 40 columns
   // 5 * 40 = 200 elements
   

b) float students[3][4][7]

float students[3][4][7];
// 3 rows, 4 columns, 7 elements
// 3 * 4 * 7 = 84 elements

1. Is there error in below array declarations?

a) int Quiz1[3][4] = { {1,2,3,4}, {5,6,7,8}, {9,10,11} };, // missing a element since 3rd row has 3 elements only

b) int Quiz2[4][2]={1,2,3,4}; // missing 2 elements

Two-Dimensional (2D) Arrays

ASSESSING 2D ARRAY ELEMENTS

• To access elements, use the row indexes and column indexes.

• Generally, require two FOR loops.

  1. One to traverse the rows
  2. Another to traverse columns

Example:

int row, col;
for (row=0; row < 3; row++) {
    for (col=0; col < 4; col++) {
        cout << myArray[row][col] << " ";
    }
    cout << endl;
}

TRAVERSAL OF MATRIX (2D ARRAYS)

Row wise traversal:

for (row=0; row < 3; row++) {
    for (col=0; col < 2; col++) {
        cout << myArray[row][col] << " ";
    }
    cout << endl;
}

Column wise traversal:

for (col=0; col < 2; col++) {
    for (row=0; row < 3; row++) {
        cout << myArray[row][col] << " ";
    }
    cout << endl;
}

MANIPULATING ALL ELEMENTS

Row wise traversal:

for (row=0; row<3; row++) {
    for (col=0; col<2; col++) {
        cout<<myArray[row][col] << " ";
        total += myArray[row][col];
    }
    cout << '\n';
}

cout<<< "Total values= " << total <<<< '\n'; // 21

Column wise traversal:

for (col=0; col<2; col++) {
    for (row=0; row<3; row++) {
        cout<<myArray[row][col] << " ";
        total += myArray[row][col];
    }
    cout << '\n';
}

cout<<< "Total values= " << total <<<< '\n'; // 21

MANIPULATING ROW-BASED ELEMENTS

#include <iostream>
#define TEAM 4
#define GAME 2
using namespace std;

int main(){
    int myTeam[TEAM] [GAME]={
        {1,2},
        {3,4},
        {5,6},
        {7,8}};

    int row, col, totalTeam [TEAM]={0};
    for (row=0; row <TEAM; row++){
        for (col=0; col<GAME; col++){
            cout<<<myTeam [row][col] <<< " ";
            totalTeam[row] += myTeam [row][col];
        }
        cout << '\n';
        cout << "Total team "<< row+1 <<  " = " <<totalTeam[row]<<< '\n';
    }
    return 0;
}

output:

1 2
Total team 1 = 3
3 4
Total team 2 = 7
5 6
Total team 3 = 11
7 8
Total team 4 = 15

MANIPULATING COLUMN-BASED ELEMENTS

#include <iostream>
#define TEAM 4
#define GAME 2
using namespace std;

int main(){
    int myTeam[TEAM] [GAME]={
        {1,2},
        {3,4},
        {5,6},
        {7,8}};

    int row, col, totalGame [GAME]={0};
    for (col=0; col < 2; col++){
        for (row=0; row < 3; row++){
            cout<<<myTeam [row][col] <<< " ";
            totalGame[col] += myTeam [row][col];
        }
        cout << '\n';
        cout << "Total game "<< col+1 <<  " = " <<totalGame[col]<<< '\n';
    }
    return 0;
}

output:

1 3 5 
Total game 1 = 9
2 4 6
Total game 2 = 12

PASSING 2D ARRAY TO FUNCTIONS

1. Passing Copy of Array

#include <iostream>
#define TEAM 4
#define GAME 2
using namespace std;

int totalMarks (int myTeam[][GAME]) { //leave the row -size empty
    int row=0, col=0, total=0;
    for (row=0; row<TEAM; row++) {
        for (col=0; col<GAME; col++){
            cout<<< myTeam[row][col] << " ";
            total myTeam[row][col];
        }
        cout << '\n';
    }
    return total;
}

int main(){
    int theTeam[TEAM] [GAME]={
        {1,2},
        {3,4},
        {5,6},
        {7,8}};

    cout << "Total marks" << totalMarks(theTeam) << '\n';

    return 0;
}

1. Passing its Reference

#include <iostream>
#define TEAM 4
#define GAME 2
using namespace std;

int totalMarks (int (&myTeam)[TEAM][GAME]) {
    int row=0, col=0, total=0;
    for (row=0; row<TEAM; row++) {
        for (col=0; col<GAME; col++){
            cout<<< myTeam[row][col] << " ";
            total += myTeam[row][col];
        }
        cout << '\n';
    }
    //change the value of myTeam array
    myTeam[2][1] = 100;
    return total;
}

int main(){
    int theTeam[TEAM] [GAME]={
        {1,2},
        {3,4},
        {5,6},
        {7,8}};

    cout << "Total marks" << totalMarks(theTeam) << '\n';
    cout << "New value of myTeam[2][1] = " << theTeam[2][1] << '\n';

    return 0;
}

1. Passing by Pointers*

2. Decaying the Pointer to the Array*