折腾两个壶的面试题怎么做？

问：

两个任意容量水壶，能否恰好量出目标分量的水？

相当经典面试题，小学的时候就开始在寒假作业里折腾我了，想不到现在还成了面试的拦路虎。所以决定彻底的解决掉。

如果实际问题的核心就是最大公约数

见代码中：GCD 函数

然后就很简单了。

using System;

namespace Algorithm.BottleAndBottle
{
    class Program
    {
        static void Main(string[] args)
        {
            var x = Ask("Please Input First The Bottle Capacity");
            var y = Ask("Please Input Second The Bottle Capacity");
            var max = x + y;

            var z = Ask("Please Input Target Request Capacity");
            if (z > max) { Console.WriteLine(" Target Is Overload!"); return; }

            //GET GCD
            var gcd = GCD(x, y);

            if (z % gcd > 0)
            {
                Console.WriteLine("Can't Not Load");
                Console.ReadLine();
                return;
            }

            int a, b;
            //z=a*x+b*y;

            int[,] aLine = ValueLine(x, y), bLine = ValueLine(y, x);
            a = 2 * y - 1;
            b = 2 * x - 1;

            for (int xi = 0; xi < a; xi++)
            {
                var xIndex = aLine[0, xi];
                var xValue = aLine[1, xi];

                for (int yi = 0; yi < b; yi++)
                {
                    var yIndex = bLine[0, yi];
                    var yValue = bLine[1, yi];

                    var sum = xValue + yValue;

                    if (sum > 0 && sum <= max)
                    {
                        var s = $"a:{xIndex};b:{yIndex}=>{sum}";
                        if (sum == z)
                        {
                            Console.WriteLine(s + " <<== LIKE THIS");
                        }
                        else
                        {
                            Console.WriteLine(s);
                        }
                    }
                }
            }
        }

        static int[,] ValueLine(int v, int c)
        {
            int[,] Line = new int[2, 2 * c - 1];
            int index = 1 - c;
            int vs = v * index;
            int count = 2 * c - 1;

            for (int i = 0; i < count; i++)
            {
                Line[0, i] = index++;
                Line[1, i] = vs;
                vs += v;
            }
            return Line;
        }

        static int GCD(int a, int b)
        {
            return (a == b) ? a : ((a > b) ? GCD(a - b, b) : GCD(b - a, a));
        }


        static int Ask(string question)
        {
            int value;
            string input;
            bool isOk;
            do
            {
                Console.WriteLine(question);
                input = Console.ReadLine();
                isOk = (int.TryParse(input, out value) && value > 0);
            } while (!isOk);

            return value;
        }
    }

}