用于查找大小为n的列表中的哪些数字与另一个数字相加的算法

我有一个十进制数字(让我们称之为目标)和一个其他十进制数字的数组(让我们调用数组元素)我需要找到总和为目标的元素的所有数字组合.

我倾向于使用C#(.Net 2.0)中的解决方案,但最好的算法可能无论如何都会获胜.

您的方法签名可能类似于:

public decimal[][] Solve(decimal goal, decimal[] elements)

Sam Meldrum.. 11

有趣的答案.感谢您指向维基百科 - 虽然有趣 - 他们实际上并没有解决问题,因为我正在寻找完全匹配 - 更多的会计/书籍问题比传统的bin-packing /背包问题.

我一直关注堆栈溢出的开发,并且想知道它会有多大用处.这个问题出现在工作中,我想知道堆栈溢出是否能够比我自己编写的更快地提供现成的答案(或更好的答案).还要感谢评论提示这是标记的作业 - 我认为鉴于上述情况,这是相当准确的.

对于那些感兴趣的人,这里是我的解决方案,使用递归(自然)我也改变了我的方法签名的思路,并去了List>而不是decimal [] []作为返回类型:

public class Solver {

    private List> mResults;

    public List> Solve(decimal goal, decimal[] elements) {

        mResults = new List>();
        RecursiveSolve(goal, 0.0m, 
            new List(), new List(elements), 0);
        return mResults; 
    }

    private void RecursiveSolve(decimal goal, decimal currentSum, 
        List included, List notIncluded, int startIndex) {

        for (int index = startIndex; index < notIncluded.Count; index++) {

            decimal nextValue = notIncluded[index];
            if (currentSum + nextValue == goal) {
                List newResult = new List(included);
                newResult.Add(nextValue);
                mResults.Add(newResult);
            }
            else if (currentSum + nextValue < goal) {
                List nextIncluded = new List(included);
                nextIncluded.Add(nextValue);
                List nextNotIncluded = new List(notIncluded);
                nextNotIncluded.Remove(nextValue);
                RecursiveSolve(goal, currentSum + nextValue,
                    nextIncluded, nextNotIncluded, startIndex++);
            }
        }
    }
}

如果您希望应用测试此功能,请尝试此控制台应用代码:

class Program {
    static void Main(string[] args) {

        string input;
        decimal goal;
        decimal element;

        do {
            Console.WriteLine("Please enter the goal:");
            input = Console.ReadLine();
        }
        while (!decimal.TryParse(input, out goal));

        Console.WriteLine("Please enter the elements (separated by spaces)");
        input = Console.ReadLine();
        string[] elementsText = input.Split(' ');
        List elementsList = new List();
        foreach (string elementText in elementsText) {
            if (decimal.TryParse(elementText, out element)) {
                elementsList.Add(element);
            }
        }

        Solver solver = new Solver();
        List> results = solver.Solve(goal, elementsList.ToArray());
        foreach(List result in results) {
            foreach (decimal value in result) {
                Console.Write("{0}\t", value);
            }
            Console.WriteLine();
        }


        Console.ReadLine();
    }
}

我希望这有助于其他人更快地得到答案(无论是作业还是其他).

干杯...

有趣的答案.感谢您指向维基百科 - 虽然有趣 - 他们实际上并没有解决问题,因为我正在寻找完全匹配 - 更多的会计/书籍问题比传统的bin-packing /背包问题.

我一直关注堆栈溢出的开发,并且想知道它会有多大用处.这个问题出现在工作中,我想知道堆栈溢出是否能够比我自己编写的更快地提供现成的答案(或更好的答案).还要感谢评论提示这是标记的作业 - 我认为鉴于上述情况,这是相当准确的.

对于那些感兴趣的人,这里是我的解决方案,使用递归(自然)我也改变了我的方法签名的思路,并去了List>而不是decimal [] []作为返回类型:

public class Solver {

    private List> mResults;

    public List> Solve(decimal goal, decimal[] elements) {

        mResults = new List>();
        RecursiveSolve(goal, 0.0m, 
            new List(), new List(elements), 0);
        return mResults; 
    }

    private void RecursiveSolve(decimal goal, decimal currentSum, 
        List included, List notIncluded, int startIndex) {

        for (int index = startIndex; index < notIncluded.Count; index++) {

            decimal nextValue = notIncluded[index];
            if (currentSum + nextValue == goal) {
                List newResult = new List(included);
                newResult.Add(nextValue);
                mResults.Add(newResult);
            }
            else if (currentSum + nextValue < goal) {
                List nextIncluded = new List(included);
                nextIncluded.Add(nextValue);
                List nextNotIncluded = new List(notIncluded);
                nextNotIncluded.Remove(nextValue);
                RecursiveSolve(goal, currentSum + nextValue,
                    nextIncluded, nextNotIncluded, startIndex++);
            }
        }
    }
}

如果您希望应用测试此功能,请尝试此控制台应用代码:

class Program {
    static void Main(string[] args) {

        string input;
        decimal goal;
        decimal element;

        do {
            Console.WriteLine("Please enter the goal:");
            input = Console.ReadLine();
        }
        while (!decimal.TryParse(input, out goal));

        Console.WriteLine("Please enter the elements (separated by spaces)");
        input = Console.ReadLine();
        string[] elementsText = input.Split(' ');
        List elementsList = new List();
        foreach (string elementText in elementsText) {
            if (decimal.TryParse(elementText, out element)) {
                elementsList.Add(element);
            }
        }

        Solver solver = new Solver();
        List> results = solver.Solve(goal, elementsList.ToArray());
        foreach(List result in results) {
            foreach (decimal value in result) {
                Console.Write("{0}\t", value);
            }
            Console.WriteLine();
        }


        Console.ReadLine();
    }
}

我希望这有助于其他人更快地得到答案(无论是作业还是其他).

干杯...