namespace practice
{
class homework2
{
static double findGreatestCommonDivisor(double CoefficientA, double CoefficientB)
{
if (CoefficientB > CoefficientA)//確保
{
double temp;
temp = CoefficientB;
CoefficientB = CoefficientA;
CoefficientA = temp;
}//(為確保較大的數字在前面，故需要交換位置)
double mod = CoefficientA % CoefficientB;//第一次輾轉相除
while (mod > 0)//若最大公因數==較小的數，直接回傳較小的數
{
CoefficientA = mod;//將第一次輾轉相除的餘數變成較小的係數
CoefficientB %= CoefficientA;/*準備第二次輾轉相除，讓第一次的餘數，對原本較小的係數相除。
處理過後做完重新回到開頭的情況 */
mod = CoefficientA % CoefficientB;//第二次輾轉相除
if (mod == 0)//判斷若mod==0則直接回傳第二次輾轉相除後較小的細數
return CoefficientB;
else
continue;//若不等於0則繼續做
}
return CoefficientB;
}//找最大公因數
static double [,]particularSolution(double CoefficientA, double CoefficientB, double CoefficientC, double gcd)
{
if (CoefficientC % gcd != 0)//若 c 不為最大公因數的倍數, 則無解。
{
Console.WriteLine("{0}x + {1}y = {2} : 此題無解", CoefficientA, CoefficientB, CoefficientC);
return null;
}
else if (CoefficientC % gcd == 0)//若 c 為最大公因數的倍數, 則同除最大公因數。
{
CoefficientA /= gcd;
CoefficientB /= gcd;
CoefficientC /= gcd;
}
double[,] particularSolution = new double[(int)CoefficientA + 1, (int)CoefficientA + 1];
//創一個放特解的假二維陣列
for (int i = 0; i <= CoefficientA; i++)
{
particularSolution[0, i] = (CoefficientC - (CoefficientB * i)) / (CoefficientA);
//在0<=y<=a的範圍內, 尋找 x 的整數解(x=(c'-b'y)/a必須為整數)
particularSolution[1, i] = i;
}
return particularSolution;
}//求特解
static double[, ,] generalSolution(double CoefficientA, double CoefficientB, double CoefficientC, double gcd,double[,] particularSolutionArr)
{
CoefficientA /= gcd;
CoefficientB /= gcd;
CoefficientC /= gcd;
double[, ,] generalSolution = new double[(int)CoefficientA + 1, (int)CoefficientA + 1, 21];
//創一個放通解的假二維陣列，一組特解配一組通解，故維度是一樣的
for (int i = 0; i <= CoefficientA; i++)
{
for (int t = 0; t <= 3; t++)
{
generalSolution[0, i,t] = particularSolutionArr[0, i] + CoefficientB * (t-10);
//x=x0+b't
generalSolution[1, i,t] = particularSolutionArr[1, i] - CoefficientA * (t-10);
} //y=y0-a't
}
return generalSolution;
}//求通解
static void jogPuzzle()
{
int bottleA = 0;
int bottleB = 0;
int delta = 0;//A跟B的差值
int clear = 0;
do
{
if (bottleA == 0)
{
bottleA += 3;
Console.WriteLine("A杯子裝滿3公升");
Console.WriteLine("目前狀態:({0},{1})",bottleA,bottleB);
}
else if (bottleB == 5)
{
bottleB = 0;
}
else if (bottleA == 3)
{
bottleA -= 3;
bottleB += 3;
if (bottleB > 5)
{
delta = bottleB - 5;
bottleB = 5;
bottleA = delta;
}
Console.WriteLine("A杯子往B杯倒水");
Console.WriteLine("目前狀態:({0},{1})", bottleA, bottleB);
}
else
{
bottleB += bottleA;
if (bottleB > 5)
{
delta = bottleB - 5;
bottleB = 5;
bottleA = delta;
}
else
{
bottleA = 0;
}
Console.WriteLine("A杯子往B杯倒水");
Console.WriteLine("目前狀態:({0},{1})", bottleA, bottleB);
}
} while (bottleB != 4);
Console.Read();
}
static void Main(string[] args)
{
string temp;
double CoefficientA;
double CoefficientB;
double CoefficientC;
double gcd;
double[,] particularSolutionArr;//特解的假二維陣列
double[, ,] generalSolutionArr;//通解的假三維陣列
do
{
Console.WriteLine("一、若 a,b 為整數, 求 ax + by = c 的整數解。");
Console.WriteLine("輸入參數a");
temp = Console.ReadLine();
CoefficientA = double.Parse(temp);
Console.WriteLine("輸入參數b");
temp = Console.ReadLine();
CoefficientB = double.Parse(temp);
Console.WriteLine("輸入參數c");
temp = Console.ReadLine();
CoefficientC = double.Parse(temp);
gcd = findGreatestCommonDivisor(CoefficientA, CoefficientB);//求最大公因數
particularSolutionArr = particularSolution(CoefficientA, CoefficientB, CoefficientC, gcd);//解特解之meothd
} while (particularSolutionArr == null);
generalSolutionArr = generalSolution(CoefficientA, CoefficientB, CoefficientC,gcd, particularSolutionArr);//解通解meothd
Console.WriteLine("{0}x + {1}y = {2}", CoefficientA, CoefficientB, CoefficientC);
for (int i = 0; i <= (CoefficientA/gcd); i++)//印出特解
{
Console.WriteLine("第{0}組特解(particularSolution):",i+1);
Console.WriteLine("x:{0},y:{1}\n",particularSolutionArr[0, i], particularSolutionArr[1, i]);//印特解
Console.WriteLine("第{0}組通解(particularSolution):",i+1);
for (int j = 0; j <= (CoefficientA / gcd); j++)//印出通解
{
for (int t = 0; t <= 3; t++)
{
Console.WriteLine("x:{0},y:{1}\n", generalSolutionArr[0, j, t], generalSolutionArr[1, j, t]);//印通解
}
}
}
Console.WriteLine("===============我是分隔線=================");
jogPuzzle();
Console.ReadKey();
}
}
}
2015年3月26日 星期四
[2015][Homework][Team03] - Hw02
[2015][Homework]Team02 - Hw02
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace Hw2
{
class Program
{
static void Main(string[] args)
{
int sele;
while (true)
{
Console.WriteLine("請輸入1或2執行第一題或第二題");
Console.WriteLine("若要結束程式請輸入其他數字");
sele = int.Parse(Console.ReadLine());
switch (sele)
{
case 1:
int kGcd;
Console.WriteLine("若 a, b 為整數, 求ax+by=c的整數解。");
Console.WriteLine("請輸入一個整數a");
int a = int.Parse(Console.ReadLine());
Console.WriteLine("請輸入一個整數b");
int b = int.Parse(Console.ReadLine());
Console.WriteLine("請輸入一個整數c");
int c = int.Parse(Console.ReadLine());
//演算步驟一 計算 a, b 的最大公因數
int aCopy = a;
int bCopy = b;
int temp;
if (a > b)
{
while(aCopy % bCopy != 0)
{
temp = aCopy % bCopy;
aCopy = bCopy;
bCopy = temp;
}
kGcd = bCopy;
}
else
{
while(bCopy % aCopy != 0)
{
temp = bCopy % aCopy;
bCopy = aCopy;
aCopy = temp;
}
kGcd = aCopy;
}
Console.WriteLine("最大公因數={0}",kGcd);
//演算步驟二 設(a, b) = k, 若 c 不為 k 的倍數, 則無解。
if (c % kGcd != 0)
{
Console.WriteLine("無解");
Console.ReadLine();
Console.Clear();
break;
}
//演算步驟三 若 c = kc’
a /= kGcd;
b /= kGcd;
c /= kGcd;
//演算步驟四 求特殊解
int x = 0;
int y = 0;
for (y = 0; y <= a; y++)
{
if ((c - b * y) % a == 0)
{
x = (c - b * y) / a;
break;
}
}
//演算步驟五 通解
int t;
for (t = 0; t < 10; t++)
{
Console.WriteLine("x={0,3},y={1,3}", x, y);
x += b;
y -= a;
}
Console.ReadKey();
Console.Clear();
break;
case 2:
int aContainer = 3;
int bContainer = 5;
int aWater = 0;
int bWater = 0;
int step = 0;
Console.WriteLine("一開始,A桶有水{0}公升,B桶有水{1}公升\n", aWater, bWater);
while (bWater != 4)
{
step++;
if (bWater == 0)
{
bWater = bContainer;
Console.WriteLine("step{0}:把B桶裝滿水\n此時,A桶有水{1}公升,B桶有水{2}公升\n", step, aWater, bWater);
}
else if (aWater >= 3)
{
aWater = 0;
Console.WriteLine("step{0}:A桶水滿,把A桶的水全部倒掉\n此時,A桶有水{1}公升,B桶有水{2}公升\n", step, aWater, bWater);
}
else if (aWater + bWater >= aContainer)
{
bWater = aWater + bWater - aContainer;
aWater = aContainer;
Console.WriteLine("step{0}:將B桶的水倒滿A桶\n此時,A桶有水{1}公升,B桶有水{2}公升\n", step, aWater, bWater);
}
else if (aWater + bWater != 4)
{
aWater = aWater + bWater;
bWater = 0;
Console.WriteLine("step{0}:將B桶的水倒滿A桶\n此時,A桶有水{1}公升,B桶有水{2}公升\n", step, aWater, bWater);
}
else//bWater+aWater=4
{
bWater = aWater + bWater;
aWater = 0;
Console.WriteLine("step{0}:將A桶的水倒回B桶\n此時,A桶有水{1}公升,B桶有水{2}公升\n", step, aWater, bWater);
}
}
Console.WriteLine("最後,A桶有水{0}公升,B桶有水{1}公升\n", aWater, bWater);
Console.WriteLine("B桶有水{0}公升放在啟動開關上,解除炸彈", bWater);
Console.ReadLine();
Console.Clear();
break;
default:
return;
}
}
}
}
}
2015年3月25日 星期三
2015年3月24日 星期二
2015年3月22日 星期日
訂閱：
文章 (Atom)