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A two-dimensional array named Arr is with the range Arr[10........20, 25......45]. The base address of the array is 10 and the size of each element is 2 bytes. What will be the location of Arr[15][30] using column major order?
  • a)
    35
  • b)
    130
  • c)
    230
  • d)
    70
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A two-dimensional array named Arr is with the range Arr[10........20, ...
Solution:

Given,
- Range of the 2D array Arr is Arr[10........20, 25......45]
- Base address of the array is 10
- Size of each element is 2 bytes

To find the location of Arr[15][30] using column major order,

Step 1: Find the total number of rows and columns in the array
- Number of rows = 20 - 10 + 1 = 11
- Number of columns = 45 - 25 + 1 = 21

Step 2: Calculate the offset of Arr[15][30] using column major order
- Offset = (30 - 25) * 11 + (15 - 10) = 5 * 11 + 5 = 60

Step 3: Calculate the location of Arr[15][30] using column major order
- Location = Base address + (Offset * Size of each element)
- Location = 10 + (60 * 2) = 130

Therefore, the location of Arr[15][30] using column major order is option B, which is 130.

Note: In column major order, the elements are stored column-wise. Hence, we first need to calculate the offset of the element in the column and then multiply it by the number of rows to get the total offset. Finally, we add the base address to get the location.
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Community Answer
A two-dimensional array named Arr is with the range Arr[10........20, ...
Column major order concept: 
  • Column major order means the element in a column is stored adjacent to each other. This basically works in a 2d and 3d array.
  • Now we are given the base address along with the size of each element and the construction of a 2d array(row and column number )
  • First, we have to calculate the no. of rows here = (Row upper limit - Row lower limit) + 1 = (20 - 10) + 1 = 11.
  • We need no. of the column if the ques will ask about Row major order.
  • There is a formula available to calculate it directly(Rather than going into deep how the formula came, it's better to remember the formula.)
Formula:-
Address of A[I][J] is can be calculated with the formula is A[I][J] = B + ((J – LC) * M + (I – LR))*W.
where;
  • I- Row subset of an element whose address is to be found ( 15 here)
  • J = Column Subset of an element whose address is to be found,(30 here)
  • B- Base address(10 here)
  • W- storage size of one element  (2 bytes here)
  • LR- the lower limit of row (u can take start index of the matrix)- (10 in this ques)
  • LC-Lower limit of column(start column index of the matrix) - (25 in this ques)
  • M- number of rows given in the matrix. (11 here)
 
Now solve the equation by solving the inner bracket first.
10+[5*11+5] *2  = 10+(60)*2 = 10+120= 130 will be the answer.
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A two-dimensional array named Arr is with the range Arr[10........20, 25......45]. The base address of the array is 10 and the size of each element is 2 bytes. What will be the location of Arr[15][30] using column major order?a)35b)130c)230d)70Correct answer is option 'B'. Can you explain this answer?
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