CSCI 1110 - C++ Lecture Notes
Chapter 13 - Multidimensional Arrays

Two-Dimensional Arrays

Processing Two-Dimensional Arrays

Passing Two-Dimensional Arrays as Parameters

Arrays of Arrays

Higher Dimensional Arrays

Two-Dimensional Arrays

• One-dimensional arrays represent lists of homogeneous items.
  
  
• Two-dimensional arrays are collections of components, all of the same type, structured in two dimensions. Each component is accessed by a pair of indices that represent the component's position in each dimension.
  
  

	[0]	[1]	[2]
[0]
[1]
[2]
[3]



The above table represents a two-dimensional array with 4 rows and 3 columns. This is refered to as a 4 X 3 array. 


• To declare a multidimensional array, specify the size of each of the dimensions enclosed in square brackets:

 
 

    const int NUM_ROWS = 4;
    const int NUM_COLS = 3;

    float alpha[NUM_ROWS][NUM_COLS];



• References to individual members of the array are made just like one-dimensional array references, except that two index values are used:

 

    alpha[1][2] = 12.8;



• Example:

 enum Colors
   {RED, YELLOW, GREEN, BLUE, N_COLORS};
 enum Makes
   {FORD, TOYOTA, BMW, VW, GMC, N_MAKES};

 float ticket[N_COLORS][N_MAKES];

 ticket[BLUE][VW] = 0.75;
 ticket[RED][BMW] = 1.46;

Processing Two-Dimensional Arrays

• Most two-dimensional array processing consists of accessing the data either by rows or by columns.
  
  
• Example - Sum the rows and columns of an array:

 

  const int NUM_ROWS = 40;
  const int NUM_COLS = 35;
  int table[NUM_ROWS][NUM_COLS];
  long rowSum[NUM_ROWS];
  long colSum[NUM_COLS];
  int row;
  int col;

  // sum the rows
  for (row = 0; row < NUM_ROWS; row++)
  {
     rowSum[row] = 0;
     for (col = 0; col < NUM_COLS; col++)
        rowSum[row] += table[row][col];
  }

  // sum the columns
  for (col = 0; col < NUM_COLS; col++)
  {
     colSum[col] = 0;
     for (row = 0; row < NUM_ROWS; row++)
        colSum[col] += table[row][col];
}



• To initialize a two-dimensional table, use a declaration similar to the following:

 

 int table[2][3]
 {
    {14, 3, -5},
    {0, 46, 65}
 };

---

Passing Two-Dimensional Arrays as Parameters

• When a one-dimensional array is defined as a formal parameter, the side of the array may be omitted.

 

  void Fun(float list[], int size)
  {
    . . .
  }



• With two-dimensional arrays, the first dimension (number of rows) may be omitted, but not the second dimension (number of columns).

  void Fun(float table[][5], int rows, int cols)
  {
    . . .
  }

You can specify both dimensions if you choose to.

 void Fun(float table[2][5], int rows, int cols)
  {
    . . .
  }



•  When a function is called with an array as an argument, the base address (memory location of the first element) is passed to the function. C++ computes the actual address of each element from this base address plus the number of elements in each column:

 
 

  int table[4][2];

table[0][0]	1
table[0][1]	2
table[1][0]	7
table[1][1]	3
table[2][0]	56
table[2][1]	-6
table[3][0]	99
table[3][1]	-54

 

C++ computes the actual memory location for the elements from its indices and the number of items in each row. table[2][1]is at 6th location in the array, starting with the base address.

Arrays of Arrays

• Another way to visualize a two-dimensional array is as a one-dimensional array whose members are one-dimensional arrays.
  
  
• Example:

 

  const int MAX_STUDENTS = 150;
  typedef char String20[21];

  String20 student[MAX_STUDENTS];

which is equivalent to:

  char student[MAX_STUDENTS][21];

Higher Dimensional Arrays

• Sometimes data needs to be indexed in more than two ways. For example, suppose we wanted to collect weather data for a number of locations (x, y positions), altitudes, and hour of the day. We could define an array to keep track of temperatures as follows:

 
 

  float temp[100][100][10][24];
 

This would allow for 240,000 readings. Each reading would be indexed by an x position (0 - 99), a y position (0 - 99), an altitude (0 - 9), and an hour (0-23).
 



• The example above could also be done as:

 
 

 typedef float Day[24];
 typedef DayTemp Altitude[10];
 Altitude temp[100][100];