How can we receive on element with a given rank? Give the procedure to determine the rank of element.

To retrieve an element with a specified rank, you can follow these steps:

1. Determine the Rank of the Element:

• The rank of an element in a matrix or array is typically determined by its position relative to other elements. In a 1D array, the rank of an element is simply its index. In a 2D array, the rank is determined by its row and column indices, and so on.

• To find the rank of an element in a multidimensional array, you can use the following formula:

    rank = (i1 - 1) * n2 * n3 * ... * nK + (i2 - 1) * n3 * ... * nK + ... + (iK - 1) * nK + iK
  

  where i1, i2, ..., iK are the indices of the element in the respective dimensions, and n2, n3, ..., nK are the sizes of the respective dimensions.

1. Accessing the Element with the Given Rank:

• Once you have determined the rank of the element, you can use this rank to access the element in the array.
• In a 1D array, you can directly access the element using its index.

• In a multidimensional array, you can use the following formula to calculate the indices of the element from its rank:

    i1 = 1 + (rank - 1) / (n2 * n3 * ... * nK)
    i2 = 1 + ((rank - 1) % (n2 * n3 * ... * nK)) / (n3 * ... * nK)
    ...
    iK = 1 + ((rank - 1) % (n2 * n3 * ... * nK)) % ... % nK
  

• Once you have calculated the indices, you can use them to access the element in the array.

Here is an example to illustrate the process:

Consider a 3D array A with dimensions (3, 4, 5). The total number of elements in the array is 3 * 4 * 5 = 60.

To find the rank of the element at A[1, 2, 3], we can use the formula:

rank = (1 - 1) * 4 * 5 + (2 - 1) * 5 + (3 - 1) + 1 = 19

Therefore, the rank of the element A[1, 2, 3] is 19.

To access this element using its rank, we can calculate the indices:

i1 = 1 + (19 - 1) / (4 * 5) = 2
i2 = 1 + ((19 - 1) % (4 * 5)) / 5 = 3
i3 = 1 + ((19 - 1) % (4 * 5)) % 5 = 3

Therefore, the element A[1, 2, 3] can be accessed using the indices i1 = 2, i2 = 3, and i3 = 3.

By following these steps, you can efficiently retrieve an element with a given rank in a multidimensional array.