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Multi-Dimensional Arrays

✅ Multi-Dimensional Arrays (Detailed BCA Exam Answer)

✅ 1. Definition of Multi-Dimensional Array

A Multi-Dimensional Array is an array that contains more than one dimension (more than one index is required to access an element).

✅ In simple words:
If an array needs two or more subscripts/indexes to represent elements, it is called a multi-dimensional array.

📌 Examples:

  • 2D Array → A[i][j]
  • 3D Array → A[i][j][k]
  • 4D Array → A[i][j][k][l] (rare)

✅ 2. Types of Multi-Dimensional Arrays

Multi-dimensional arrays can be:

✅ 1. Two-Dimensional Array (2D Array)
✅ 2. Three-Dimensional Array (3D Array)
✅ 3. Higher Dimensional Arrays (4D, 5D…)

✅ 3. Two-Dimensional Array (2D Array) – Quick View

A 2D array stores data in rows and columns like a matrix.

✅ Declaration:

int A[3][4];

✅ Access:

A[i][j]

📌 Example:

10 20 30
40 50 60

✅ 4. Three-Dimensional Array (3D Array)

✅ Definition

A 3D array is an array of 2D arrays.
It stores data in the form of layers (tables).

✅ Declaration:

datatype array_name[x][y][z];

✅ Example:

int A[2][3][4];

Means:

  • 2 blocks/layers
  • 3 rows
  • 4 columns

✅ Total elements:
[
2 \times 3 \times 4 = 24
]

✅ Accessing 3D Array Elements

A[i][j][k]

Where:

  • i = layer number
  • j = row number
  • k = column number

✅ Example:

A[0][1][2]

✅ Example Representation (3D)

Example: A[2][2][2]

Layer 0:

A[0][0][0]  A[0][0][1]
A[0][1][0]  A[0][1][1]

Layer 1:

A[1][0][0]  A[1][0][1]
A[1][1][0]  A[1][1][1]

✅ 5. Memory Representation of Multi-Dimensional Arrays

Even though multi-dimensional arrays look like tables or cubes, memory is linear, so elements are stored in a sequence.

✅ In C/C++, arrays are stored in Row-Major Order.

✅ Row Major Order (for 2D)

Row 0 → Row 1 → Row 2…

✅ For 3D Arrays

First all elements of:

  • Layer 0 (row by row)
    then
  • Layer 1 (row by row)

✅ 6. Traversing Multi-Dimensional Arrays

✅ Traversing 2D Array

Uses 2 loops:

for(i=0; i<rows; i++)
{
    for(j=0; j<cols; j++)
        printf("%d ", A[i][j]);
}

✅ Traversing 3D Array

Uses 3 loops:

for(i=0; i<x; i++)
{
    for(j=0; j<y; j++)
    {
        for(k=0; k<z; k++)
            printf("%d ", A[i][j][k]);
    }
}

✅ 7. Applications of Multi-Dimensional Arrays

✅ Used in:

  1. Matrix operations (2D)
  2. Image processing (2D pixels)
  3. 3D Graphics and games (3D arrays)
  4. Scientific and engineering calculations
  5. Weather forecasting data
  6. Representation of graphs (Adjacency Matrix)

✅ 8. Advantages of Multi-Dimensional Arrays

✅ Benefits:

  • Organizes complex data in structured form
  • Useful for mathematical operations
  • Easy representation of tables, matrices, and cubes
  • Fast access using index values

✅ 9. Disadvantages of Multi-Dimensional Arrays

❌ Limitations:

  • Fixed size (static allocation)
  • Memory wastage if size is large
  • Complex handling for insertion and deletion
  • Requires contiguous memory allocation
  • More nested loops → more time complexity

✅ Conclusion

Multi-dimensional arrays store data using more than one index and are useful for representing tables (2D), cubes (3D), and complex structures. They are widely used in matrix operations, graphics, and scientific applications. In C/C++, they are stored in memory using Row-Major order.