Multi-Dimensional Arrays: Basics and Traversal Quiz Quiz

Explore the concepts and common operations of multi-dimensional arrays, focusing on their structure, element access, and traversal techniques. Enhance your understanding of how to work with two-dimensional arrays in programming and apply efficient array manipulation strategies.

1. Understanding Multi-Dimensional Arrays

   Which statement best describes a two-dimensional array such as int array[3][4] in most programming languages?

   1. It consists of four arrays with three elements each.
   2. It is an array containing three arrays, each of which has four elements.
   3. It is a collection of seven elements organized in a single row.
   4. It is a single array that stores twelve variables in no particular order.

   Explanation: In most programming languages, a two-dimensional array like int array[3][4] is an array of arrays, specifically three arrays with four elements each. 'A collection of seven elements' is incorrect because the total number of elements is three times four, not seven. 'Four arrays with three elements each' reverses the dimensions. 'A single array that stores twelve variables in no particular order' fails to represent the structured, row-and-column format of a two-dimensional array.

2. Element Access in 2D Arrays

   Given a two-dimensional array matrix[5][6], which expression accesses the element in the fourth row and second column assuming zero-based indexing?

   1. matrix[2][4]
   2. matrix[1][3]
   3. matrix[4][2]
   4. matrix[3][1]

   Explanation: Zero-based indexing means counting starts at zero, so the fourth row is index 3 and the second column is index 1, making matrix[3][1] correct. matrix[4][2] would refer to the fifth row and third column, while matrix[2][4] selects the third row and fifth column. matrix[1][3] corresponds to the second row and fourth column, all of which are incorrect positions.

3. Length Calculation in Multi-Dimensional Arrays

   For an array defined as arr[2][5], how many total elements can be stored in this two-dimensional array?

   1. 25
   2. 12
   3. 10
   4. 7

   Explanation: The total number of elements in a two-dimensional array is the product of its dimensions, so arr[2][5] holds 2 times 5, which is 10 elements. 7 and 12 are incorrect as they do not result from multiplying the dimensions. 25 would be the result if both dimensions were 5, which is not the case here.

4. Row-Major Order Traversal

   When using nested loops to traverse a two-dimensional array in row-major order, which loop structure is typically used?

   1. Both loops iterate through columns only.
   2. Both loops iterate through rows only.
   3. The outer loop iterates through columns and the inner loop iterates through rows.
   4. The outer loop iterates through rows and the inner loop iterates through columns.

   Explanation: Row-major order traversal means processing every column of a row before moving to the next row, typically achieved by having the outer loop go over rows and the inner loop go over columns. Swapping the loops (columns first, rows second) does not follow row-major order. Both loops limited to rows or columns do not allow proper traversal of all elements.

5. Modifying Elements in a Multi-Dimensional Array

   If you have a 2D array grades[4][3], how would you update the value at the last row and last column (assuming zero-based indexing)?

   1. grades[4][3] = value;
   2. grades[3][2] = value;
   3. grades[1][4] = value;
   4. grades[2][3] = value;

   Explanation: Since indexing starts at zero, the last row is index 3 and the last column is index 2 for grades[4][3], so grades[3][2] correctly accesses the last element. grades[4][3] tries to access indices beyond the array's size, which would typically cause an error. grades[2][3] and grades[1][4] use invalid indices for either the row or the column.