List comprehension Practice Problems Online

Use list comprehension to generate the list of all perfect numbers less than 10,000, $\{P_1,P_2,\ldots,P_N\}$ .

What is their sum $\sum_i P_i$ ?

Assumptions and Details

A perfect number is any integer which is equal to the sum of its proper divisors (all its divisors except for itself).

Suppose you're working on code for a molecular dynamics visualization. You need to represent various matrices, like the 3d rotation matrix, using Python lists. We can do so by using lists of lists.

For example, the matrix

$A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$

is represented by

1	`A = [[1,0,0], [0,1,0], [0,0,1]]`

and the matrix

$B= \begin{bmatrix} 1 \\ 2 \\ 3 \\ \end{bmatrix}$

would be

1	`B = [[1],[2],[3]]`

The fragments below are designed to perform operations on matrices. Your task is to match the function bodies with the correct function definitions.

A:

1 2	`def getcolumn(matrix, i): # Given a matrix named 'matrix' this method should return the ith column`

B:

1
2
3

def add(A, B):
    # Given two matrices (A and B) of the same dimensions,
    # this should return the sum of the two matrices

C:

1
2
3

def mult1D(row, col):
    # Given a row matrix[a1,a2..an] and a column[[r1],[r2]..[rn]]
    # matrix, this should return the 0D product [a1*r1 + a2*r2 .. an*rn]

The function bodies are given by the following

1:

1 2	`[[A[j][i] + B[j][i] for i in range(len(A[0]))] for j in range(0, len(A))]`

2:

1	`[sum([row[i] * col[i][0] for i in range(len(row))])]`

3:

1	`[[r[i]] for r in matrix]`

In scientific computing, it is a common task to take the transpose of a matrix. The transpose of a matrix $A$ , $A^T$ , is found by turning all the rows of a matrix into columns and vice versa. More formally the transpose of a matrix $A$ is found by reflecting $A$ over its main diagonal.

For example, the transpose of

$A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 1 & 9 \\ 8 & 0 & 1 \\ \end{bmatrix}$

is given by

$A^T = \begin{bmatrix} 1 & 4 & 8 \\ 2 & 1 & 0 \\ 3 & 9 & 1 \\ \end{bmatrix}$

Which of the following snippets of code would correctly transpose the $30 \times 20$ matrix $A$ ?

A:

1 2	`transpose = [[a[i][j] for i in range(0, 30 + 1)] for j in range(0, 20 + 1)]`

B:

1 2	`transpose = [[a[i][j] for j in range(0, 30)] for i in range(0, 20)]`

C::

1 2	`transpose = [[a[j][i] for j in range(0, 30)] for i in range(0, 20)]`

D::

1 2	`transpose = [[a[i][j] for i in range(0, 30+1)] for j in range(0, 20+1)]`

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