Multidimensional Arrays Notes

Multidimensional Arrays

  • A more complex data structure that enforces correlation rules.
  • Used for sophisticated problems like time series data analysis.
  • Commonly used in machine learning algorithms.
  • Can have thousands or millions of dimensions, but we'll focus on two-dimensional arrays.

Task Update: Employee Hours

  • Goal: Record the number of hours each of the five employees work each day from Monday to Thursday.
  • Segmentation:
    • Getting the data.
    • Implementing the algorithm.
  • Updates:
    • Update the data to handle a multidimensional array.
    • Update the algorithm: for each employee, for each day, print the hours.

Representing Data with Two-Dimensional Arrays

  • One-dimensional arrays are insufficient for representing rows and columns.
  • Two-dimensional arrays allow specifying the number of rows (employees) and columns (days).
  • Number of rows = 5 (employees).
  • Number of columns = 4 (days).
  • Theoretically and implementation wise, swapping rows and columns can make a difference.

Creating Multidimensional Arrays

1. Creating an Empty Array and Adding Elements

  • Specify the array type, followed by square brackets and the identifier.

  • The number of commas within the square brackets indicates the number of dimensions minus one.

    • Two-dimensional array: one comma.
    • Three-dimensional array: two commas.

  • Syntax:

    type[,] identifier = new type[length1, length2];

  • Example:

    int[,] hours = new int[5, 4];

  • Default Values:

    • Numeric types: 0
    • Characters: Unicode null character
    • Booleans: false

  • Setting Values:

    • Use the array name followed by indices to set values for each element.
    • Can be done individually or via loops.
    • Example: hours[0, 0] = 6; (Jenny's hours on Monday set to 6).
2. Setting Values During Array Creation (with new keyword)

  • Specify values upon creation using the new keyword and compound type.

  • Syntax:

    type[,] identifier = new type[,] {{val1, val2, ...}, {val3, val4, ...}, ...};

  • The compiler infers array lengths from the provided values.

3. Setting Values During Array Creation (without new keyword)

  • Similar to the previous method but without using the new keyword or specifying the type on the right-hand side.

  • Syntax:

    type[,] identifier = {{val1, val2, ...}, {val3, val4, ...}, ...};

  • This method is used for the test case example.

Visualizing Two-Dimensional Arrays

  1. Table: Rows and columns (employees x days).
  2. Array within an Array: An array of employees, where each employee has an array of days.
  • hours[employeeIndex, dayIndex] accesses the hours for a specific employee on a specific day.

Algorithm for Printing Values

  • Uses nested for loops.
  • Outer loop: processes employees.
  • Inner loop: processes days.
Outer Loop
  • Iterates through each employee.
  • Initial value: 0.
  • Change statement: increments the value.
  • Condition statement: uses the length of the first index of the array (employees).
  • getLength(0) returns the number of employees.
Inner Loop
  • Iterates through each day for the current employee.
  • Initial value: 0.
  • Change statement: increments the value.
  • Condition statement: uses the length of the second index of the array (days).
  • getLength(1) returns the number of days.
Printing Hours
  • Prints the hours for each day within the inner loop.
  • Right and RightLine statements used for presentation.

Presentation Improvements

  1. Print Employee Names:
    • Arrays can only hold one type (names are strings).
    • Use a separate names array to print the name during the outer for loop execution.
  2. Calculate Total Hours per Week:
    • Useful for verification.
    • Sum the hours for each employee across all days.

Testing Considerations

  • Empty or single-element arrays.
  • Valid/invalid input.
  • Array lengths: ensure they are the same or handle different lengths.
  • Test cases with the outer array (employees) larger than the inner array (days) using different values.

Multidimensional vs. Parallel Arrays

  • Multidimensional array: Stricter controls about correlation.
  • Conceptually like a table with rows and columns.
  • Useful for complex datasets like time series.
  • Disadvantage: only supports data of the same type.
  • Choice depends on the context of the problem.