● Row Major Order: Think of searching row by row. You start at the very top left corner and read across the entire first row. Then, you move down to the second row and read across again. You keep going down, row by row, until you find the treasure (or the specific number you're looking for).
● Column Major Order: This is like searching column by column. You start at the very top left corner and read down the first column. Then, you move to the second column and read down again. You keep going right, column by column, until you find the treasure.
Row Major and Column Major Order in 2D Arrays
1. Introduction
● A 2D array is a collection of elements arranged in rows and columns.
● Elements in a 2D array can be accessed using two indices: row index and column index.
● Two primary methods for storing elements in memory:
○ Row Major Order
○ Column Major Order
2. Row Major Order
Elements within the same row are stored consecutively in memory.
Example:
○ Consider a 3x3 array:
1 2 3
4 5 6
7 8 9
○ In Row Major, the order of elements in memory would be: 1, 2, 3, 4, 5, 6,
7, 8, 9.
3. Column Major Order
Elements within the same column are stored consecutively in memory.
Example:
○ For the same 3x3 array:
1 2 3
4 5 6
7 8 9
○ In Column Major, the order would be: 1, 4, 7, 2, 5, 8, 3, 6, 9.
4. Implications
● Memory Allocation:
○ Row Major is often the default due to its efficiency in accessing elements within the same row.
● Array Traversal:
○ The order of traversal can significantly impact algorithm performance.
○ Traversing in the same order as the memory storage can improve cache efficiency.
5. Example in C/C++
Row Major:
C++
int arr[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
Column Major (requires manual handling):
Typically, you would need to manage memory manually or use specific data structures.
6. Conclusion
● Understanding Row Major and Column Major is crucial for efficient memory management and array traversal in 2D arrays.
● The choice of storage order can impact algorithm performance and memory usage.
Can add below optional topics to this theory :
● Cache Memory and its impact on array access.
● Implementation of 2D arrays in different programming languages.
● Applications of Row Major and Column Major in real-world scenarios (e.g., image processing, game development).