Help with recursive algorithm

This is a discussion on Help with recursive algorithm within the C Programming forums, part of the General Programming Boards category; I have to do a program that reads a list of positive numbers (5,3,6...) and a target. The program should ...

  1. #1
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    Help with recursive algorithm

    I have to do a program that reads a list of positive numbers (5,3,6...) and a target. The program should find the target value (if posible) through combinations of sums and differences of the given number list. Also it should store in an array the combination of numbers and its sign. This is what I have:

    Code:
     void findobj(int j) 
    { 
        int i,temp; 
    
        i = 0; 
    
        do{ 
            i++; 
            if (numbers[i] != KEY) 
            { 
                   //the variable "sum" stores the sum of the combination numbers 
                sum+= numbers[i]; 
                 
            //stores solution numbers 
                solution[j] = numbers[i]; 
                temp = numbers[i]; 
    
               //KEY is a macro wich value is -1,  
              //it  prevents the program from selecting  
              //the same number twice 
                numbers[i] = KEY; 
                 
                if (j < N) 
                { 
                    findobj(j+1); 
                    numbers[i] = temp; 
    
                    if (sum != objetive) 
                    { 
                        sum-=numbers[i]; 
                        solution[j] =  -(numbers[i]); 
                         
                    } 
                } 
            } 
        }while ((i < N) && (sum != objetive)); 
    
        return; 
    }
    The problem is that the program doesnt find all the combinations, for example, given the following list (2,3,10,4,8) and target = 16, the variable sum never reaches the target, (the combination of numbers to reach the target is 2,10,4) but if the target = 15, the variable sum reaches the target.

    Thanks.

  2. #2
    Frequently Quite Prolix dwks's Avatar
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    So in other words you don't implement code to skip over numbers.
    dwk

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    "Simplicity does not precede complexity, but follows it." -- Alan Perlis
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  3. #3
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    I tried to read the code, but I must admit I don't understand well how it works
    For instance, you use some variables defined elsewhere and not in the same function, numbers, solution, N, etc(I guess global variables)
    Also I see you use recursivity, but, you use it in a way hard to understand and prone to errors, instead to make the function returns some value, you make the function modify a global array. So it's not clear what is the END condition.
    You have here a problem of path finding, if I understood well, you have a list of numbers (n1,n2,n3..nN) and a target T, you have to sum them to get the final T (make combinations)
    There are algorithms to do that like the Tree Search (I guess the variant InDepth would fit for you)

    I would advise to review your algorithm more than try to tune this one.

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  4. #4
    Frequently Quite Prolix dwks's Avatar
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    I think this is known as the "backpack problem"; you might want to try googling it: http://www.google.ca/search?hl=en&q=...e+Search&meta=

    [edit] The first hit has a solution or two: http://www.edm2.com/0601/backpack.html [/edit]
    dwk

    Seek and ye shall find. quaere et invenies.

    "Simplicity does not precede complexity, but follows it." -- Alan Perlis
    "Testing can only prove the presence of bugs, not their absence." -- Edsger Dijkstra
    "The only real mistake is the one from which we learn nothing." -- John Powell


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  5. #5
    Fear the Reaper...
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    I believe this is actually called the 0-1 Knapsack problem. You can look up that along with recursion...but I think you'll probably just find dynamic programming solutions to that one.
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