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copied!<p>Your best clue about how to approach this problem is the fact that your teacher/professor wants you to use recursion. That is, this <em>isn't a math problem</em> - it is a search problem. </p> <p>Not to give too much away (it is homework after all), but you have to spawn a call to the recursive function using an operator, a number and a list containing the remaining numbers. The recursive function will extract a number from the list and, using the operation passed in, combine it with the number passed in (which is your running total). Take the running total and call yourself again with the remaining items on the list (you'll have to iterate the list within the call but the sequence of calls is depth-first). Do this once for each of the four operators unless Success has been achieved by a previous leg of the search.</p> <p><strong>I updated this to use a list instead of a stack</strong></p> <p>When the result of the operation is your target number and your list is empty, then you have successfully found the set of operations (those that traced the path to the successful leaf) - set the Success flag and unwind. Note that the operators aren't on a list nor are they in the call: the function itself always iterates over all four. Your mechanism for "unwinding" the operator sequence from the successful leaf to get the sequence is to return the current operator and number prepended to the value returned by recursive call (only one of which will be successful since you stop at success - that, obviously, is the one to use). If none are successful, then what you return isn't important anyhow.</p> <p><strong>Update</strong> This is <em>much</em> harder when you have to consider expressions like the one that Daniel posted. You have combinatorics on the numbers <em>and</em> the groupings (numbers due to the fact that / and - are order sensitive even without grouping and grouping because it changes precedence). Then, of course, you also have the combinatorics of the operations. It is harder to manage the differences between (4 + 3) * 2 and 4 + (3 * 2) because grouping doesn't recurse like operators or numbers (which you can just iterate over in a breadth-first manner while making your (depth-first) recursive calls). </p>

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