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 = []

eq0 = {} # no operators
for n in nums:
    eq0[float(n)] = n
eqs.append(eq0)

for num_op in range(1, 4): # 演算子の個数1〜3
    eq = {}
    # 使っていい合計の演算子はnum_op - 1
    for num_op_lhs in range(num_op):
        num_op_rhs = num_op - 1 - num_op_lhs
        eq_lhs = eqs[num_op_lhs]
        eq_rhs = eqs[num_op_rhs]
        for lhs in eq_lhs:
            for rhs in eq_rhs:
                for op in ops:
                    try:
                        value = ops[op](lhs, rhs)
                    except ZeroDivisionError:
                        continue
                    eq[value] = (op, eq_lhs[lhs], eq_rhs[rhs])

    eqs.append(eq)

for line in sorted(eqs[3].items()):
    print line

"""
output:
...
(0.125, ('/', ('/', 7, ('+', 7, 1)), 7))
(0.13999999999999999, ('/', 1, ('+', ('/', 1, 7), 7)))
(0.14000000000000001, ('/', 7, ('+', ('*', 7, 7), 1)))
(0.14285714285714279, ('-', ('+', ('/', 1, 7), 1), 1))
(0.14285714285714285, ('/', ('/', ('/', 1, 7), 1), 1))
...
"""