element address in 3 dimensional array

Question

I am looking for the formulas to find the memory location of an element in a 3-D Array for row major and for column major. After using my logic I end up with the following formulas. say array is A[L][M][N].

row-major:Loc(A[i][j][k])=base+w(M*N(i-x)+N*(j-y)+(k-z))
column-major:Loc(A[i][j][k])=base+w(M*n(i-x)+M*(k-z)+(j-y))

where x, y, z are lower bounds of 1st(L) 2nd(M) and 3rd(N) index. I tried this formula and got the correct result but when I applied this formula on a Question in the book then the answer did not match. Please can anyone help me out with this.

Answer 1

Formula for 3D Array

Row Major Order:

Address of

A[I, J, K] = B + W * [(D - Do)*RC + (I - Ro)*C + (J - Co)]

Column Major Order:

Address of

A[I, J, K] = B + W * [(D - Do)*RC + (I - Ro) + (J - Co)*R]

Where:

• B = Base Address (start address)
• W = Weight (storage size of one element stored in the array)
• R = Row (total number of rows)
• C = Column (total number of columns)
• D = Width (total number of cells depth-wise)
• R_o = Lower Bound of Row
• C_o = Lower Bound of Column
• D_o = Lower Bound of Width

Answer 2

Right one is:

row-major:Loc(A[i][j][k])=base+w(N*(i-x)+(j-y)+M*N(k-z))
column-major:Loc(A[i][j][k])=base+w((i-x)+M*N(k-z)+M*(j-y))