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Let A be a two-dimensional array declared as follows:
A : array [1 ... 10] [1... 15] of integer;
Assuming that each integer takes one memory location. The array is stored in row-major order and the first element of the array is stored at location 100, what is the address of the element A [i] [j] ?
A : array [1 ... 10] [1... 15] of integer;
Assuming that each integer takes one memory location. The array is stored in row-major order and the first element of the array is stored at location 100, what is the address of the element A [i] [j] ?
- a)15i + j + 84
- b)15j + i + 84
- c)10i + j + 89
- d)10j + i + 89
Correct answer is option 'A'. Can you explain this answer?
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Let A be a two-dimensional array declared as follows:A : array [1 ... ...
Let r be number of elements in a row. Address of the element A[i] [j]
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Let A be a two-dimensional array declared as follows:A : array [1 ... ...
Address of the element A[i][j]
To find the address of the element A[i][j], we need to consider that the array is stored in row-major order and the first element of the array is stored at location 100.
Row-Major Order
In row-major order, the elements of the array are stored consecutively in memory row by row. This means that the elements of each row are stored one after another in memory.
Calculating the address
Let's break down the given array declaration: A : array [1 ... 10] [1 ... 15] of integer.
The array has 10 rows (from index 1 to 10) and 15 columns (from index 1 to 15).
The size of each integer element is 1 memory location.
The first element of the array is stored at location 100.
To calculate the address of the element A[i][j], we can use the formula:
Address = Base Address + (Row Size * (i - 1)) + (Column Size * (j - 1))
In this case, the base address is 100, the row size is 15, and the column size is 1.
So, the address of the element A[i][j] can be calculated as:
Address = 100 + (15 * (i - 1)) + (1 * (j - 1))
Simplifying further:
Address = 100 + 15i - 15 + j - 1
Address = 15i + j - 16 + 100
Address = 15i + j + 84
Therefore, the correct answer is option 'A': 15i + j + 84.
To find the address of the element A[i][j], we need to consider that the array is stored in row-major order and the first element of the array is stored at location 100.
Row-Major Order
In row-major order, the elements of the array are stored consecutively in memory row by row. This means that the elements of each row are stored one after another in memory.
Calculating the address
Let's break down the given array declaration: A : array [1 ... 10] [1 ... 15] of integer.
The array has 10 rows (from index 1 to 10) and 15 columns (from index 1 to 15).
The size of each integer element is 1 memory location.
The first element of the array is stored at location 100.
To calculate the address of the element A[i][j], we can use the formula:
Address = Base Address + (Row Size * (i - 1)) + (Column Size * (j - 1))
In this case, the base address is 100, the row size is 15, and the column size is 1.
So, the address of the element A[i][j] can be calculated as:
Address = 100 + (15 * (i - 1)) + (1 * (j - 1))
Simplifying further:
Address = 100 + 15i - 15 + j - 1
Address = 15i + j - 16 + 100
Address = 15i + j + 84
Therefore, the correct answer is option 'A': 15i + j + 84.
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