求算法,知道总额和单价,求数量

Question

例子1
已知有一批货物，有各种不同的型号：单价分别是：1336；975，800，482，647，307，742，
472，每种型号若干台之后，总数是33605元。
请问如何得知这批货物各多少台，可以对应上33605这个总数？例子2
我要开出来一个总金额为5万的发票，明细的型号单价有：235，500，300，822，523
，447，285等这种价格，每种型号多少数量，总数刚好对成5万就OK数量上分布要比较平均请问此类题目是什么类型的问题,对应的是什么算法呢.

Answer 1

第一个例子的答案可以是
307单价15个，742单价20个，472单价30个。
307*15+742*20+472*30=33605第二个例子的答案还可以是
523单价2个，447单价77个，285单价51个。
523*2+447*77+285*51=50000用穷举能算出来。我写的循环如下，但是这个没法均匀分布，一有结果就结算计算了。
不知道有没有更好的方法
int a = 0, b = 0, c = 0, d = 0, e = 0, f = 0, g = 0, h = 0;
            bool state = false;            
            for (int i = 0; i <= 33605 / 1336; i++)
            {
                a = i;
                Console.WriteLine("a={0}", a);
                if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                {
                    state = true;
                    break;
                }
                else
                {
                    #region
                    for (int j = 0; j <= (33605 - a * 1336) / 975; j++)
                    {
                        b = j;
                        Console.WriteLine("b={0}", b);
                        if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                        {
                            state = true;
                            break;
                        }
                        else
                        {
                            #region
                            for (int k = 0; k <= (33605 - a * 1336 - b * 975) / 800; k++)
                            {
                                c = k;
                                if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                                {
                                    state = true;
                                    break;
                                }
                                else
                                {
                                    #region
                                    for (int l = 0; l <= (33605 - a * 1336 - b * 975 - c * 800) / 482; l++)
                                    {
                                        d = l;
                                        if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                                        {
                                            state = true;
                                            break;
                                        }
                                        else
                                        {
                                            #region
                                            for (int m = 0; m <= (33605 - a * 1336 - b * 975 - c * 800 - d * 482) / 647; m++)
                                            {
                                                e = m;
                                                if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                                                {
                                                    state = true;
                                                    break;
                                                }
                                                else
                                                {
                                                    #region
                                                    for (int n = 0; n <= (33605 - a * 1336 - b * 975 - c * 800 - d * 482 - e * 647) / 307; n++)
                                                    {
                                                        f = n;
                                                        if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                                                        {
                                                            state = true;
                                                            break;
                                                        }
                                                        else
                                                        {
                                                            #region
                                                            for (int o = 0; o <= (33605 - a * 1336 - b * 975 - c * 800 - d * 482 - e * 647 - f * 307) / 742; o++)
                                                            {
                                                                g = o;
                                                                if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                                                                {
                                                                    state = true;
                                                                    break;
                                                                }
                                                                else
                                                                {
                                                                    for (int p = 0; p <= (33605 - a * 1336 - b * 975 - c * 800 - d * 482 - e * 647 - f * 307 - g * 742) / 472; p++)
                                                                    {
                                                                        h = p;
                                                                        if (a * 1336 + b * 975 + c * 800 + d * 482 + e * 647 + f * 307 + g * 742 + h * 472 == 33605)
                                                                        {
                                                                            state = true;
                                                                            break;
                                                                        }
                                                                    }                                                                    
                                                                }
                                                                if (state == true)
                                                                {
                                                                    break;
                                                                }
                                                            }
                                                            #endregion                                                            
                                                        } 
                                                        if (state == true)
                                                        {
                                                            break;
                                                        }
                                                    }
                                                    #endregion                                                    
                                                } 
                                                if (state == true)
                                                {
                                                    break;
                                                }
                                            }
                                            #endregion
                                        }
                                        if (state == true)
                                        {
                                            break;
                                        }
                                    }
                                    #endregion
                                }
                                if (state == true)
                                {
                                    break;
                                }
                            }
                            #endregion
                        }
                        if (state == true)
                        {
                            break;
                        }
                    }
                    #endregion                   
                }
                if (state == true)
                {
                    break;
                }
            }
            if (state == true)
            {
                Console.WriteLine("has get the result");
                Console.WriteLine("{0}*1336+{1}*975+{2}*800+{3}*482+{4}*647+{5}*307+{6}*742+{7}*472=33605", a, b, c, d, e, f, g, h);
            }
            else
            {
                Console.WriteLine("no result");
            }
            Console.ReadLine();