def euler85(target=2000000):
"""http://projecteuler.net/index.php?section=problems&id=85
By counting carefully it can be seen that a rectangular grid measuring 3 by
2 contains eighteen rectangles.
Although there exists no rectangular grid that contains exactly two million
rectangles, find the area of the grid with the nearest solution."""
return product(find_grid(target))
def euler8():
"""http://projecteuler.net/problem=8
Find the greatest product of five consecutive digits in the 1000-digit
number.
"""
digit_string = """\
73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450\
"""
digits = map(int, [c for c in digit_string if c.isdigit()])
max_product = -sys.maxint - 1
for i in xrange(len(digits) - 5):
p = product(digits[i:i + 5])
if max_product < p:
max_product = p
return max_product
def rad(n):
return product(set(factor(n)))
def rdiag(idx):
if xdim - idx < 4 or ydim - idx / xdim < 4:
return 0
return product(grid[idx + n * xdim + n] for n in range(4))
def down(idx):
if ydim - idx / xdim < 4:
return 0
return product(grid[idx + n * xdim] for n in range(4))
def right(idx):
if xdim - idx < 4:
return 0
return product(grid[idx:idx + 4])
