5.1.3 Characteristics of a Two-Dimensional Array Notes

Two-Dimensional Arrays

Understanding Two-Dimensional Arrays

Formally speaking, a two-dimensional array is an array of arrays.

arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

arr = [
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]
]

Two-dimensional arrays are useful for:

1. Matrices: Used in mathematical computations and simulations.
2. Grids and Maps: Ideal for representing game boards, pixel grids, and geographical maps.
3. Data Tables: Useful for storing tabular data, such as spreadsheets or databases.
4. Image Processing: Useful for representing pixels in digital images.

Key Characteristics of Two-Dimensional Arrays

1. Structure:
   1. Each element in the main array is a sub-array representing a row.
2. Indexing:
   1. Two indices are used to access elements: first for the row and second for the column.
   2. Indices typically start at 0, so the first element is accessed as array[0][0].
3. Uniform Data Type:
   1. All elements in a two-dimensional array must be of the same data type, such as integers, strings, or objects.
4. Fixed Size:
   1. The size of a two-dimensional array is defined at the time of creation and cannot be changed.
   2. In strongly typed programming languages, you must specify the number of rows and columns when declaring the array.
5. Memory Layout:
   1. Elements are stored in contiguous memory locations, which allows for efficient access and manipulation.

arr = [
        [1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]
]
print(arr[0]) # Output 0th row
print(arr[1][1])

Algorithms with Two-Dimensional Arrays

Iterating Over a Two-Dimensional Array

Iterating over a two-dimensional array typically involves nested loops: one for the rows and another for the columns.

arr =[ # 2d array of strings
        ["A1", "A2", "A3", "A4"],
        ["B1", "B2", "B3", "B4"]
]

for y in range(2):# outer loop
  for x in range(4): # inner loop
    print(f"y = {y}, x = {x}, value = {arr[y][x]}")

With iteration of a two-dimensional array, you can construct different algorithms such as searching or calculating the sum of rows/columns.

Transposing a Matrix

1. Transposing a matrix involves swapping rows and columns.
2. For a matrix A, the transpose B is defined as B[j][i] = A[i][j].

// ARR is original NxM array (N and M given)
// NEWARR is new MxN array filled with 0
loop Y from 0 to N-1
  loop X from 0 to M-1
    NEWARR[X][Y] = ARR[Y][X]
  end loop
end loop

arr =[ # 2d array of strings
        ["A1", "A2", "A3", "A4"],
        ["B1", "B2", "B3", "B4"]
]

rows = len(arr)
cols = len(arr[0])
result = [[0 for y in range(rows)] for x in range(cols)] # Python list comprehension, fill 4x2 array with 0

for y in range(rows):
  for x in range(cols):
    result[x][y] = arr[y][x]

for row in result: # Print every sub-array
  print(row)