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])