MyPoint MoveCursor(int maxDepth, int numMoves, MyPoint startingPoint)
{
int k = 0; //number of moves
MyPoint p = startingPoint; //[x,y]; 32x,
/* From Problem 220:
* Let D0 be the two-letter string "Fa". For n≥1, derive Dn from Dn-1 by the string-rewriting rules:
* "a" → "aRbFR"
* "b" → "LFaLb"
* Thus, D0 = "Fa", D1 = "FaRbFR", D2 = "FaRbFRRLFaLbFR", and so on.
* "These strings can be interpreted as instructions to a computer graphics program,
* with "F" meaning "draw forward one unit", "L" meaning "turn left 90 degrees",
* "R" meaning "turn right 90 degrees", and "a" and "b" being ignored.
* The initial position of the computer cursor is (0,0), pointing up towards (0,1)."*/
//Insight: It is not necessary to know the full instruction string before we start moving.
//every time we encounter 'a' or 'b' we replace it, adding to each instruction a parameter 'depth'
//that represents how many replacements took place that originate such instruction.
//Thus: thus every time we pop an instruction a[i] from the stack, we push instructions
//R[i+1], F[i+1], b[i+1], R[i+1], a[i+1] (inverted order of "aRbFR")
//onto the stack if i < maxDepth, otherwise we ignore the instruction and move on to the next one. (similar for 'b' instructions).
Stack <MyInstruction> s = new Stack <MyInstruction>();
s.Push(new MyInstruction(InstructionValue.a, 0)); //a
s.Push(new MyInstruction(InstructionValue.F, 0)); //f
while (k < numMoves)
{
//pop next instruction:
MyInstruction i = s.Pop();
if (i.instruction == InstructionValue.F)
{
p.Move();
k++; //count move
}
else if (i.instruction == InstructionValue.L)
{
p.RotateLeft(); //rotate left
}
else if (i.instruction == InstructionValue.R)
{
p.RotateRight(); //rotate right
}
else
{
//should a|b be replaced or ignored?
//if depth < maxdepth, replace and go deeper one level, otherwise ignore
if (i.depth < maxDepth)
{
//TOO SLOW
//string replaceString = i.instruction == InstructionValue.a ? "aRbFR" : "LFaLb";
//foreach (string newInst in replaceString.Reverse().Select(x => x.ToString()))
//{
// InstructionValue auxInst = (InstructionValue)Enum.Parse(typeof(InstructionValue), newInst, false);
// s.Push(new MyInstruction(auxInst, (byte)(i.depth + 1)));
//}
if (i.instruction == InstructionValue.a)
{
//RFbRa
s.Push(new MyInstruction(InstructionValue.R, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.F, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.b, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.R, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.a, (byte)(i.depth + 1)));
}
else
{
//bLaFL
s.Push(new MyInstruction(InstructionValue.b, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.L, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.a, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.F, (byte)(i.depth + 1)));
s.Push(new MyInstruction(InstructionValue.L, (byte)(i.depth + 1)));
}
}
}
}
return(p); //return the point we reached after moving 'numMoves' times
}