Diagonal difference

Question

Given

You are given a square matrix of size \$N×N\$. Calculate the absolute difference of the sums across the two main diagonals.

Input Format

The first line contains a single integer N. The next N lines contain N integers (each) describing the matrix.

Constraints

\$1\leq N \leq 100\$

\$−100 \leq A_{i} \leq 100\$

Solution

def diagonal_difference(matrix):
    l = sum(matrix[i][i] for i in range(N))
    r = sum(matrix[i][N-i-1] for i in range(N))
    return abs(l - r)

matrix = []
N = input()
for _ in range(N):
    matrix.append(map(int, raw_input().split()))

print diagonal_difference(matrix)

Is there more elegant solution for the given problem. Also, I am getting intuition that I can use reduce, is that possible?

Answer 1

Instead of indexing to access the rows, you could use iteration:

l = sum(row[i] for i, row in enumerate(matrix))

Instead of doing two passes over matrix to calculate l and r, you could accumulate the difference in one pass: (note also negative indexing from end of list)

difference = sum(row[i] - row[-i-1] for i, row in enumerate(matrix))
return abs(difference)

The single-pass approach would also allow you to process input line by line, instead of storing the whole matrix in memory.

Answer 2

My big concern with this approach is that you store the entire matrix before doing any processing. Since the size of the matrix is \$O(N^2)\$, you could run into occupancy problems for large \$N\$.

A simpler approach would be to get the contribution to the difference with each row of the matrix, as you read it. You're only ever storing a single row at once.

That is:

N = int(raw_input())
difference = 0
for i in xrange(N):
    row = raw_input().split()
    difference += (int(row[i]) - int(row[N-1-i]))
print abs(difference)

A few other items of note here:

• I'm getting N via a raw_input() call, not input(). In general you should be wary of using input() and evaluating arbitrary code from the user.

  (Although that advice only applies to Python 2; in Python 3 the names have changed.)

• In Python 2, using xrange() is preferable to range() because it doesn't create a list for the entire range.

• I'm being lazy about the coercion to int(), and reducing from \$N^2\$ calls to \$2N\$ calls.

Answer 3

You don't pass N to diagonal_difference, that's bad practice. You should either be passing it as a parameter, or at least determining it within the function since it's just len(matrix). Also N isn't a good name, just because the question used that doesn't mean you need to. Code has different requirements than a brief. Maybe matrix_size or some other explicit name.

It's also odd to have raw_input() when you're actually expecting input. Putting at least ">" is recommended so that the user can see that the script is waiting for input, not just running code silently.