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    <p>I think the problem can be approached by grouping the operands according to the operations performed on them. Example:</p> <pre><code>312 / 130 x 350 + 122 + 282 =&gt; (/, [312, 130]), (x, [350]), (+, [122, 282]) </code></pre> <p>You can then place certain constraints on the order of these groups:</p> <ol> <li><code>-</code> groups cannot occur directly before <code>+</code> groups</li> <li><code>/</code> groups cannot occur directly before <code>*</code> groups</li> <li>within each group, the order of the numbers must be ascending</li> </ol> <p>Possible groupings would thus look like this:</p> <ul> <li>"first 3 asc. operands connected with a <code>+</code>, then 2 asc. operands connected with a <code>*</code>"</li> <li>"first 1 asc. operand connected with a <code>+</code>, then 2 asc. operands connected with a <code>*</code>, then 2 asc. operands connected with <code>/</code>"</li> </ul> <p>Impossible would be something like this:</p> <ul> <li>"first 2 asc. operands connected with a <code>-</code>, then 3 asc. operands connected with <code>+</code>" (would collide with "first 3 asc. operands connected with a <code>+</code>, then 2 asc. operands connected with <code>-</code></li> </ul> <p>I tried a brute-force approach to create and fill such groupings, but it's unbearably slow. Maybe you can optimize it to be more efficient :) Could also be that there's some subtle bug in there, but unfortunately I don't have any more time to work on it:</p> <pre><code>import operator import fractions from itertools import permutations, product, count from functools import reduce vectors = [[87, 125, 209, 312], [29, 122, 254, 372], [15, 130, 277, 369], [142, 197, 282, 383], [64, 157, 256, 350]] vectors = [[fractions.Fraction(x) for x in v] for v in vectors] operators = { '+': operator.add, '-': operator.sub, '*': operator.mul, '/': operator.div, } def create_groupings(n, exclude = ()): if n &lt;= 0: yield () for i in range(1, n+1): if not '+' in exclude: for rest in create_groupings(n - i, ('+',)): yield ((i, '+'),) + rest if not '-' in exclude: for rest in create_groupings(n - i, ('+', '-')): yield ((i, '-'),) + rest if not '*' in exclude: for rest in create_groupings(n - i, ('*',)): yield ((i, '*'),) + rest if not '/' in exclude: for rest in create_groupings(n - i, ('/', '*')): yield ((i, '/'),) + rest def fill_grouping(groups, vectors): if len(groups) == 0: yield () return (group_size, op), grest = groups[0], groups[1:] for vv in permutations(vectors): vecs, vrest = vectors[:group_size], vectors[group_size:] for operands in map(list, product(*vecs)): # enforce ascending ordering to avoid collisions # like A + B == B + A if operands != sorted(operands): continue for rest in fill_grouping(grest, vrest): yield ((op, operands),) + rest groupings = create_groupings(5) for g in groupings: for groups in fill_grouping(g, vectors): evaluated = ((op, reduce(operators[op], x)) for (op, x) in groups) _, value = reduce(lambda (_, x), (op, y): (None, operators[op](x,y)), evaluated) if 1000 == value: print groups </code></pre> <p>Hope this helps (at least the idea :)</p>
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    1. POFind equivalent results under distributive and commutative laws
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    1. USNiklas B.
    1. USNiklas B.
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    1. POFind equivalent results under distributive and commutative laws
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    1. COFor a saturday night is great :) I'll take a look at it!
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      1. USRik Poggi
 

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