Finding the largest product of four consecutive numbers in a grid

Question

Project Euler #11 asks to find the largest product of four numbers of a grid, where the four numbers occur consecutive to each other vertically, horizontally, or diagonally.

Here is my solution in Python. In addition to the usual code review, I have 2 extra questions (actually confessions of my laziness):

1. Would it be better if I compared products as in traditional way instead of using max(list)? Like:

   if (current > max_product):
       max_product = current
   

2. Would it be better if I used proper for loops instead of relying on try? Because in certain cases it gives KeyError.

Because of these two shortcuts, I feel like I have cheated. Shall I worry about them or just ignore them?

yy = """08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"""

rows = yy.splitlines()
d = {}
x = 0
for row in rows:
    row_cels = row.split()
    y = 0
    d[x] = {}
    for cell in row_cels:
        d[x].update({y: int(cell)})
        y+=1
    x+=1


def product(a, b, al="hori", r=4):
    try:
        res = 1
        for xx in xrange(r):
            if al == "hori": #        -
                res *= d[a][b+xx]
            elif al == "verti": #     |
                res *= d[b+xx][a]
            elif al == "dia": #       \
                res *= d[a+xx][b+xx]
            elif al == "diarev": #    /
                res *= d[a+xx][19-(b+xx)]
        return res
    except:
        return 0

hori = []
verti = []
dia = []
diarev = []

for x in xrange(0, 20):
    for y in xrange(0, 20):
        hori.append(product(x,y))
        verti.append(product(x, y, "verti"))
        dia.append(product(x, y, "dia"))
        diarev.append(product(x, y, "diarev"))

print max(max(hori), max(verti), max(dia), max(diarev))

Answer 1

1. It's OK to use max(), reimplementing it yourself won't save time, especially since the Python version is possibly faster if it's written in C. It's possible to be more concise and clearer though: max(hori + verti + dia + diarev).
2. You should use a list of list to represent a matrix, not a list of dictionaries. As cat_baxter points out, d = [map(int, row.split()) for row in open('20x20.txt').read().splitlines()] is enough to populate d. However if you're not familiar with list comprehensions and map, it's OK to use normal loops.
3. Python doesn't really have constants, but a convention is to do VERTI = "verti" and then use VERTI everywher, denoting that it is a constant ("verti" is not a good name, by the way, "vertical" is better. Use code completion.)
4. try: ... except: ... is bad practice, you need to catch specific exceptions (KeyError in this case). And you need to understand why those errors are thrown! This could be a bug in your code.

Answer 2

The problem is pretty trivial and you should only check the index ranges and don't use

for x in xrange(0, 20):
    for y in xrange(0, 20):

but

for x in xrange(16):
    for y in xrange(16):

My version:

d = [map(int, row.split()) for row in open('20x20.txt').read().splitlines()]
value = 0
for m in xrange(16):
    for n in xrange(16):
        value = max(value,
            # rows
            d[m][n] * d[m][n + 1] * d[m][n + 2] * d[m][n + 3],
            d[m + 1][n] * d[m + 1][n + 1] * d[m + 1][n + 2] * d[m + 1][n + 3],
            d[m + 2][n] * d[m + 2][n + 1] * d[m + 2][n + 2] * d[m + 2][n + 3],
            d[m + 3][n] * d[m + 3][n + 1] * d[m + 3][n + 2] * d[m + 3][n + 3],
            # cols
            d[m][n] * d[m + 1][n] * d[m + 2][n] * d[m + 3][n],
            d[m][n + 1] * d[m + 1][n + 1] * d[m + 2][n + 1] * d[m + 3][n + 1],
            d[m][n + 2] * d[m + 1][n + 2] * d[m + 2][n + 2] * d[m + 3][n + 2],
            d[m][n + 3] * d[m + 1][n + 3] * d[m + 2][n + 3] * d[m + 3][n + 3],
            # diag
            d[m][n] * d[m + 1][n + 1] * d[m + 2][n + 2] * d[m + 3][n + 3],
            d[m + 3][n] * d[m + 2][n + 1] * d[m + 1][n + 2] * d[m][n + 3])
print('Max value = %d' % value)