/// <summary>
/// Performs the multiplication and prints a detailed solution.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="stepByStep">Indicates whether the operation should be performed in step-by-step mode controlled by user.</param>
public static void Multiplication(double x, double y, bool stepByStep)
{
// Make the numbers whole.
int degree = NumberWork.GetMostRoundingDegree(x, y);
long xArg = (long)(x * NumberWork.Pow(10, degree));
long yArg = (long)(y * NumberWork.Pow(10, degree));
int maxLength = NumberWork.NumLength(xArg) + NumberWork.NumLength(yArg);
if (NumberWork.NumLength(xArg) < NumberWork.NumLength(yArg))
{
Swap(ref xArg, ref yArg);
}
// Write them.
Console.Write(String.Join("", Enumerable.Repeat(' ', maxLength - NumberWork.NumLength(xArg))));
Console.WriteLine($" {xArg}");
Console.Write(String.Join("", Enumerable.Repeat(' ', maxLength - NumberWork.NumLength(yArg))));
Console.WriteLine($" {yArg}");
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
// Get the components of the numbers.
long[] xComps = NumberWork.GetNumberComponents(xArg);
long[] yComps = NumberWork.GetNumberComponents(yArg);
// Multiply each digit by each other.
foreach (var xComp in xComps)
{
foreach (var yComp in yComps)
{
var result = xComp * yComp;
var strResult = result.ToString();
// Skip zeroes.
if (result != 0)
{
if (stepByStep)
{
Control.WaitForUserKey();
}
// Write interim result.
Console.Write(String.Join("", Enumerable.Repeat(' ', 3 + maxLength - strResult.Length)));
Console.WriteLine(strResult + $" = {xComp} * {yComp}");
}
}
}
// Write the final result.
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
Console.Write(String.Join("", Enumerable.Repeat(' ', maxLength - NumberWork.NumLength(xArg * yArg))));
Console.WriteLine($" {xArg * yArg * Math.Pow(10, -degree * 2)}");
}
/// <summary>
/// Performs the subtraction and prints a detailed solution.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="stepByStep">Indicates whether the operation should be performed in step-by-step mode controlled by user.</param>
public static void Subtraction(double x, double y, bool stepByStep)
{
// Make the numbers whole.
int degree = NumberWork.GetMostRoundingDegree(x, y);
long xArg = (long)(x * NumberWork.Pow(10, degree));
long yArg = (long)(y * NumberWork.Pow(10, degree));
int maxLength = NumberWork.GetMaxLength(xArg, yArg);
if (NumberWork.NumLength(xArg) < NumberWork.NumLength(yArg))
{
Swap(ref xArg, ref yArg);
}
Console.Write(String.Join("", Enumerable.Repeat(' ', maxLength - NumberWork.NumLength(xArg))));
Console.WriteLine($" {xArg}");
Console.Write(String.Join("", Enumerable.Repeat(' ', maxLength - NumberWork.NumLength(yArg))));
Console.WriteLine($" {yArg}");
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
long[] yComps = NumberWork.GetNumberComponents(yArg);
Console.Write(String.Join("", Enumerable.Repeat(' ', 3 + maxLength - NumberWork.NumLength(xArg))));
Console.WriteLine(xArg);
// Subtract each digit (component) from x and write interim results.
foreach (var comp in yComps)
{
if (stepByStep)
{
Control.WaitForUserKey();
}
Console.Write(String.Join("", Enumerable.Repeat(' ', 3 + maxLength - NumberWork.NumLength(comp))));
Console.WriteLine(comp);
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
Console.Write(String.Join("", Enumerable.Repeat(' ', 3 + maxLength - NumberWork.NumLength(xArg - comp))));
Console.WriteLine(xArg - comp);
xArg -= comp;
}
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
Console.Write(String.Join("", Enumerable.Repeat(' ', 3 + maxLength - NumberWork.NumLength(xArg) - 1)));
Console.WriteLine(xArg * Math.Pow(10, -degree));
}
/// <summary>
/// Performs the addition and prints a detailed solution.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="stepByStep">Indicates whether the operation should be performed in step-by-step mode controlled by user.</param>
public static void Addition(double x, double y, bool stepByStep)
{
// Make the arguments whole.
int degree = NumberWork.GetMostRoundingDegree(x, y);
long xArg = (long)(x * NumberWork.Pow(10, degree));
long yArg = (long)(y * NumberWork.Pow(10, degree));
int maxLength = NumberWork.GetMaxLength(xArg, yArg);
if (NumberWork.NumLength(xArg) < NumberWork.NumLength(yArg))
{
Swap(ref xArg, ref yArg);
}
Console.WriteLine($" {xArg}");
Console.WriteLine($" " + String.Join("", Enumerable.Repeat(" ", maxLength - NumberWork.NumLength(yArg))) + yArg);
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
// Get components of the digits (see GetNumberComponents documentstion).
long[] xComps = NumberWork.GetNumberComponents(xArg);
long[] yComps = NumberWork.GetNumberComponents(yArg);
for (int i = 0; i < maxLength; i++)
{
if (stepByStep)
{
Control.WaitForUserKey();
}
// Add two digits (components).
var result = xComps[i] + (i < yComps.Length ? yComps[i] : 0);
var strResult = result.ToString();
// Write the result of the addition.
Console.Write(String.Join("", Enumerable.Repeat(' ', 3 + maxLength - strResult.Length)));
Console.WriteLine(strResult);
}
// Write the shrinked result.
Console.WriteLine(" " + String.Join("", Enumerable.Repeat("-", maxLength)));
Console.WriteLine(" " + (xArg + yArg) * Math.Pow(10, -degree));
}
/// <summary>
/// Computes the composite expression with a detailed solution.
/// </summary>
/// <param name="expression"></param>
/// <param name="stepByStep"></param>
public static void ComputeExpression(string expression, bool stepByStep)
{
// Cast the expression to reverse polish notation and remove all meaningless spaces.
string reversed = ReversePolishNotation.GetExpression(expression).Trim();
// Get all the tokens delimited by spaces.
string[] tokens = reversed.Split(' ');
// Stack to store operands and results.
Stack <double> stack = new Stack <double>();
// Stage counter.
var i = 0;
// Traverse all tokens in the expression.
foreach (var token in tokens)
{
if (token == "")
{
continue;
}
// If token is a number, push it to the stack right away.
if (NumberWork.IsDouble(token))
{
stack.Push(double.Parse(token));
continue;
}
// If token is an operation.
// Retrieve operaands from the stack.
var second = stack.Pop();
var first = stack.Pop();
double result = default;
switch (token)
{
case "+":
Console.WriteLine($"Stage {i}: {first} + {second}");
Console.WriteLine();
Addition(first, second, stepByStep);
result = first + second;
break;
case "-":
Console.WriteLine($"Stage {i}: {first} - {second}");
Console.WriteLine();
Subtraction(first, second, stepByStep);
result = first - second;
break;
case "*":
Console.WriteLine($"Stage {i}: {first} * {second}");
Console.WriteLine();
Multiplication(first, second, stepByStep);
result = first * second;
break;
case "/":
Console.WriteLine($"Stage {i}: {first} / {second}");
Console.WriteLine();
Division(first, second, stepByStep);
result = first / second;
break;
}
// Push the interim result to the stack.
stack.Push(result);
Console.WriteLine();
i++;
if (stepByStep)
{
Control.WaitForUserKey();
}
}
// Retrireve the final result from the stack.
var answer = stack.Pop();
Console.WriteLine($"Result: {answer}");
}
/// <summary>
/// Performs the division and prints a detailed solution.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="stepByStep">Indicates whether the operation should be performed in step-by-step mode controlled by user.</param>
public static void Division(double x, double y, bool stepByStep)
{
Console.Write($"{x} / {y} = ");
int degree = NumberWork.GetMostRoundingDegree(x, y);
// Make the operands whole.
long xArg = (long)(x * NumberWork.Pow(10, degree));
long yArg = (long)(y * NumberWork.Pow(10, degree));
Console.WriteLine($"{xArg} / {yArg}");
Console.WriteLine();
Console.WriteLine($" {xArg}|{yArg}");
// Get cursor position for the result.
var(answerI, answerJ) = (Console.CursorLeft + 3 + NumberWork.NumLength(xArg), Console.CursorTop);
// Get an initial value for division.
var(div, remaining) = NumberWork.GetSufficientPartForDivision(xArg, yArg);
Console.SetCursorPosition(answerI, answerJ);
Console.Write("|");
answerI++;
var position = 3;
// For putting a dot.
var trigger = false;
for (int i = 0; i < DivisionLimit; i++)
{
if (stepByStep)
{
Control.WaitForUserKey();
}
// Compute the next digit of the result and write to the result position.
var result = div / yArg;
var(savedI, savedJ) = (Console.CursorLeft, Console.CursorTop + (i == 0 ? 0 : 1));
Console.SetCursorPosition(answerI, answerJ);
Console.Write(result);
answerI++;
Console.SetCursorPosition(savedI, savedJ);
var rev = result * yArg;
var divLength = NumberWork.NumLength(div);
var revLength = NumberWork.NumLength(rev);
Console.SetCursorPosition(position + divLength - revLength, Console.CursorTop);
Console.Write(rev);
Console.SetCursorPosition(position, Console.CursorTop + 1);
Console.Write(String.Join("", Enumerable.Repeat("-", divLength)));
// Compute and write difference.
div -= rev;
position += divLength - NumberWork.NumLength(div);
// If it's zero, quit the loop.
if (div == 0)
{
Console.SetCursorPosition(position, Console.CursorTop + 1);
Console.Write(div);
break;
}
while (true)
{
if (stepByStep)
{
Control.WaitForUserKey();
}
long firstDigit;
if (remaining == -1)
{
firstDigit = 0;
// If it's time to put a dot in the result.
if (!trigger)
{
(savedI, savedJ) = (Console.CursorLeft, Console.CursorTop);
Console.SetCursorPosition(answerI, answerJ);
Console.Write('.');
answerI++;
Console.SetCursorPosition(savedI, savedJ);
trigger = true;
}
}
else
{
(firstDigit, remaining) = NumberWork.GetFirstDigit(remaining);
}
// Add the next digit (or zero if there's no unused digits anymore).
div = NumberWork.Concat(div, firstDigit);
if (div / yArg == 0)
{
(savedI, savedJ) = (Console.CursorLeft, Console.CursorTop);
Console.SetCursorPosition(answerI, answerJ);
Console.Write(0);
answerI++;
Console.SetCursorPosition(savedI, savedJ);
i++;
if (i >= DivisionLimit)
{
break;
}
}
else
{
break;
}
}
Console.SetCursorPosition(position, Console.CursorTop + 1);
Console.Write(div);
}
}