gistfile1.py

# -*- coding: utf-8 -*-
nums = [1, 1, 7, 7]

from operator import add, sub, mul, div

ops = {"*": mul, "+": add, "-": sub, "/": div}


def split(nums):
    N = len(nums)
    if nums:
        head = nums[0]
        if N > 1:
            for n1, n2 in split(nums[1:]):
                yield n1, [head] + n2
                yield [head] + n1, n2
        else:
            yield [], [head]
            yield [head], []
    
eqs = {}

for n in nums:
    eqs[(n, )] = {}
    eqs[(n, )][float(n)] = n

def solve(nums):
    """
    与えられたnumsと加減乗除の組み合わせでできる式を返す
    """
    if len(nums) == 1:
        return eqs[tuple(nums)]

    key = tuple(sorted(nums))
    if eqs.has_key(key):
        return eqs[key] # memoize

    result = {}
    for n1, n2 in split(nums):
        if not n1 or not n2: continue # []の場合はスキップ
        eq_lhs = solve(n1)
        eq_rhs = solve(n2)
        for lhs in eq_lhs:
            for rhs in eq_rhs:
                for op in ops:
                    try:
                        value = ops[op](lhs, rhs)
                    except ZeroDivisionError:
                        continue
                    result[value] = (op, eq_lhs[lhs], eq_rhs[rhs])

    eqs[key] = result
    return result

for line in sorted(solve(nums).items()):
    print line

"""
output:
...
(0.12244897959183675, ('/', ('-', 1, ('/', 1, 7)), 7))
(0.125, ('-', 1, ('/', 7, ('+', 7, 1))))
(0.13999999999999999, ('/', 1, ('+', ('/', 1, 7), 7)))
(0.14285714285714279, ('-', ('/', ('+', 7, 1), 7), 1))
(0.14285714285714285, ('/', ('+', 1, 1), ('+', 7, 7)))
...
"""