ISRO2020-18

Question

Consider a $2$-dimensional array $x$ with $10$ rows and $4$ columns, with each element storing a value equivalent to the product of row number and column number. The array is stored in row-major format. If the first element $x[0][0]$ occupies the memory location with address $1000$ and each element occupies only one memory location, which all locations (in decimal) will be holding a value of $10$?

1. $1018,1019$
2. $1022,1041$
3. $1013,1014$
4. $1000,1399$

Comments

Address of [Lr........n][Lc......m]th element in row major order =B+W[n(I−Lr)+[J−Lc]]

B-Base address

W=element size

n=number of rows

Lr is the first row number, Lc is the first column number.

10 =10*1

10=5*2

In 10*1, i=10 and j=1

1000+1((10-0)*4+(1-0))=1041

In 5*2 i=5 and j=2

1000+1((5-0)*4+(2-0))=1022

hence B is correct

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If you're considering starting index from 0 then row will go upto 9 .

So 2 possibilities 5*2 and 2*5

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But, there is only 4 column in question .so 5*2 is not possible

Answer 1

Locations holding value 10 is only (5,2) because all other possibilities like (2, 5), (1, 10), (10, 1) lead to array overflows as this array has 10 rows, 4 columns which are 0-indexed.

As the array is stored in row-major format, We have to travel 5 rows of 4 columns from the base address and then in that row travel 2 columns to get the required location.

Now, Address of arr[5][2] = 1000 + 5 * 4 + 2 = 1022.

So (b) options has 1022, but 1041 location is incorrect because it lies outside the array as 1041 = 1000 + 10 * 4 + 1,  where 1040 = 1000 + 10 * 4 is the last location in array.

So no option is correct.

Answer 2

as given in the questions there is 2 options so you can take 10*1 also and there must be 5*2 too. so there correct option is B.