Column Major Order

If elements of an array are stored in a column-major fashion means moving across the column and then to the next column then it’s in column-major order. To find the address of the element using column-major order use the following formula:

Address of A[I][J] = B + W * ((J – LC) * M + (I – LR))  

I = Row Subset of an element whose address to be found, 
J = Column Subset of an element whose address to be found, 
B = Base address, 
W = Storage size of one element store in any array(in byte), 
LR = Lower Limit of row/start row index of matrix(If not given assume it as zero), 
LC = Lower Limit of column/start column index of matrix(If not given assume it as zero), 
M = Number of rows given in the matrix.

Row Major Order and Column Major Order

When it comes to organizing and accessing elements in a multi-dimensional array, two prevalent methods are Row Major Order and Column Major Order. These approaches define how elements are stored in memory and impact the efficiency of data access in computing.

Table of Content

  • Row Major Order
  • How to find address using Row Major Order? 
  • Column Major Order
  • How to find address using Column Major Order?
  • Row Major Order vs Column Major Order

Let us discuss them in detail one by one.

Similar Reads

Row Major Order

Row major ordering assigns successive elements, moving across the rows and then down the next row, to successive memory locations. In simple language, the elements of an array are stored in a Row-Wise fashion.To find the address of the element using row-major order uses the following formula:...

How to find address using Row Major Order?

Given an array, arr[1………10][1………15] with base value 100 and the size of each element is 1 Byte in memory. Find the address of arr[8][6] with the help of row-major order....

Column Major Order

If elements of an array are stored in a column-major fashion means moving across the column and then to the next column then it’s in column-major order. To find the address of the element using column-major order use the following formula:...

How to find address using Column Major Order?

Given an array arr[1………10][1………15] with a base value of 100 and the size of each element is 1 Byte in memory find the address of arr[8][6] with the help of column-major order....

Row Major Order vs Column Major Order

Aspect Row Major Order Column Major Order Memory Organization Elements are stored row by row in contiguous locations. Elements are stored column by column in contiguous locations. Memory Layout Example For a 2D array A[m][n]: [A[0][0], A[0][1], …, A[m-1][n-1]] For the same array: [A[0][0], A[1][0], …, A[m-1][n-1]] Traversal Direction Moves through the entire row before progressing to the next row. Moves through the entire column before progressing to the next column. Access Efficiency Efficient for row-wise access, less efficient for column-wise access. Efficient for column-wise access, less efficient for row-wise access. Common Use Cases Commonly used in languages like C and C++. Commonly used in languages like Fortran. Applications Suitable for row-wise operations, e.g., image processing. Suitable for column-wise operations, e.g., matrix multiplication....