void LateUpdate()
{
//no point moving if there are no waypoints
if (waypoints.length == 0)
{
return;
}
//perform a 2D lookat - change to 3D for things that moves in 3D.e.g.airplanes or birds - waypoints[currentWP].transform.position.y
Vector3 lookAtGoal = new Vector3(waypoints[currentWP].transform.position.x, this.transform.position.y, waypoints[currentWP].transform.position.z);
Vector3 direction = lookAtGoal - this.transform.position;
this.transform.rotation = Quarternion.Slerp(this.transform.rotation, Quarternion.LookRotation(direction), Time.deltaTime * rotSpeed);
//if close enough to a waypoint: increase goal waypoint by 1
if (direcion.magnitude < accuracy)
{
currentWP++;
//cycle around the waypoints
if (currentWP >= waypoints.Length)
{
currentWP = 0;
}
}
//never stop at anything
this.transform.Translate(0, 0, speed * Time.deltaTime);
}
static Quarternion[] copySegment(Quarternion[] input, int copies)
{
Quarternion[] result = new Quarternion[input.Length * copies];
for (int i = 0; i < copies; i++)
{
input.CopyTo(result, input.Length * i);
}
return(result);
}
static Quarternion BruteMultiply(params Quarternion[] input)
{
Quarternion result = Quarternion.one;
for (int i = 0; i < input.Length; i++)
{
result = BruteMultiply2(result, input[i]);
}
return(result);
}
static bool IsNegative(Quarternion x)
{
if (x == Quarternion.neg_i || x == Quarternion.neg_j || x == Quarternion.neg_k || x == Quarternion.neg_one)
{
return(true);
}
else
{
return(false);
}
}
protected void Move(Vector2 newPos, Quaternion newRot)
{
if (photonView.isMine)
{
rb.MovePosition(newPos);
rb.MoveRotation(newRot.eulerAngles.z);
}
else
{
Vector3 lerpPos = Vector3.Lerp(transform.position, newPos, Time.deltaTime * lerpSpeed);
rb.MovePosition(lerpPos);
Quaternion lerpRot = Quarternion.Lerp(transform.rotation, newRot, Time.deltaTime * lerpSpeed);
rb.MoveRotation(lerpRot.eulerAngles.z);
}
}
static Quarternion Abs(Quarternion x)
{
switch (x)
{
case Quarternion.neg_i: return(Quarternion.i);
case Quarternion.neg_j: return(Quarternion.j);
case Quarternion.neg_k: return(Quarternion.k);
case Quarternion.neg_one: return(Quarternion.one);
default:
return(x);
}
}
static void Main(string[] args)
{
Quarternion x = Quarternion.i;
Quarternion y = Quarternion.neg_one;
Quarternion result = BruteMultiply2(x, y);
// if (result == Quarternion.neg_i) { System.Console.WriteLine("Good");}
StreamReader myStream = File.OpenText(args[0]);
int numCases = Int32.Parse(myStream.ReadLine());
for (int i = 1; i <= numCases; i++)
{
System.Console.Write("Case #{0}: ", i);
string line1 = myStream.ReadLine();
string line2 = myStream.ReadLine();
RunCase(line1, line2);
}
}
static bool BruteForceCheck(Quarternion[] segment)
{
Quarternion[] segmentLeft = new Quarternion[segment.Length];
// Compute left products
segmentLeft[0] = segment[0];
for (int i = 1; i < segment.Length; i++)
{
segmentLeft[i] = BruteMultiply2(segmentLeft[i - 1], segment[i]);
}
if (segmentLeft[segment.Length - 1] != Quarternion.neg_one)
{
return(false);
}
// Compute right products
Quarternion[] segmentRight = new Quarternion[segment.Length];
segmentRight[segmentRight.Length - 1] = segment[segment.Length - 1];
for (int i = segmentRight.Length - 2; i >= 0; i--)
{
segmentRight[i] = BruteMultiply2(segment[i], segmentRight[i + 1]);
}
// Brute force for two concatenated segments
for (int i = 1; i < segment.Length - 1; i++)
{
if (segmentLeft[i - 1] == Quarternion.i) // if the left substring is i
{
for (int j = i + 1; j < segment.Length; j++)
{
if (segmentRight[j] == Quarternion.k &&
BruteMultiply(segment.Skip(i).Take(j - i).ToArray()) == Quarternion.j)
{
// System.Console.WriteLine("YES");
return(true);
}
}
}
}
return(false);
}
void LateUpdate()
{
Vector3 lookAtGoal = new Vector3(goal.position.x, this.transform.position.y, goal.position.z);
//work out the direction to face towards the goal vector
Vector3 direction = lookAtGoal - this.transform.position;
//snap to the right direction
//this.transform.LookAt(lookAtGoal);
//using quarternion - a complex data structure holding a rotation - to do fantastic things
//turning an angle from facing in one direction to another: takes the current character rotation, perform LookRotation on direction vector
//LookRotation gives the rotation that needs to occur to be facing in the direction
this.transform.rotation = Quarternion.Slerp(this.transform.rotation, Quarternion.LookRotation(direction), rotSpeed * Time.deltaTime);
//if using applied root motion: remove the code below - related to pushing the character forward with animation rather than code
if (Vector3.Distance(transform.position, lookAtGoal) > accuracy)
{
this.transform.Translate(0, 0, speed * Time.deltaTime);
}
}
private static Quarternion Negate(Quarternion x)
{
if (IsNegative(x))
{
return(Abs(x));
}
else
{
// positive
switch (x)
{
case Quarternion.i: return(Quarternion.neg_i);
case Quarternion.j: return(Quarternion.neg_j);
case Quarternion.k: return(Quarternion.neg_k);
case Quarternion.one: return(Quarternion.neg_one);
default:
throw new Exception();
}
}
}
static void RunCase(string line1, string line2)
{
string[] split = line1.Split(' ');
int L = Int32.Parse(split[0]);
long X = Int64.Parse(split[1]);
if (L*X < 3)
{
System.Console.WriteLine("NO");
return;
}
if (X%4 == 0) // if x mod 4 = 0, then the whole thing multiplies out to +1
{
System.Console.WriteLine("NO");
return;
}
Quarternion[] segment = new Quarternion[L];
for (int i = 0; i < segment.Length; i++)
{
segment[i] = Parse(line2[i]);
}
Quarternion segmentProduct = BruteMultiply(segment);
if (X%4 == 1 && segmentProduct != Quarternion.neg_one)
{
System.Console.WriteLine("NO");
return;
}
else if (X%4 == 2 && BruteMultiply2(segmentProduct, segmentProduct) != Quarternion.neg_one)
{
System.Console.WriteLine("NO");
return;
}
else if (X%4 == 3 && BruteMultiply(segmentProduct, segmentProduct, segmentProduct) != Quarternion.neg_one)
{
System.Console.WriteLine("NO");
return;
}
Quarternion[] criticalSegment = new Quarternion[1];
if (X <= 15)
{
criticalSegment = copySegment(segment, (int)X);
}
else
{
if (X%4 == 1)
{
criticalSegment = copySegment(segment, 17);
}
else if (X%4 == 2)
{
criticalSegment = copySegment(segment, 18);
}
else if (X % 4 == 3)
{
criticalSegment = copySegment(segment, 19);
}
}
if (BruteForceCheck(criticalSegment)) { System.Console.WriteLine("YES"); }
else { System.Console.WriteLine("NO"); }
return;
}
static Quarternion BruteMultiply2(Quarternion x, Quarternion y)
{
bool x_neg = IsNegative(x);
bool y_neg = IsNegative(y);
if (x_neg)
{
x = Abs(x);
}
if (y_neg)
{
y = Abs(y);
}
Quarternion z = Quarternion.one;
switch (x)
{
case Quarternion.one:
switch (y)
{
case Quarternion.one: z = Quarternion.one;
break;
case Quarternion.i: z = Quarternion.i;
break;
case Quarternion.j: z = Quarternion.j;
break;
case Quarternion.k: z = Quarternion.k;
break;
}
break;
case Quarternion.i:
switch (y)
{
case Quarternion.one: z = Quarternion.i;
break;
case Quarternion.i: z = Quarternion.neg_one;
break;
case Quarternion.j: z = Quarternion.k;
break;
case Quarternion.k: z = Quarternion.neg_j;
break;
}
break;
case Quarternion.j:
switch (y)
{
case Quarternion.one: z = Quarternion.j;
break;
case Quarternion.i: z = Quarternion.neg_k;
break;
case Quarternion.j: z = Quarternion.neg_one;
break;
case Quarternion.k:
z = Quarternion.i;
break;
}
break;
case Quarternion.k:
switch (y)
{
case Quarternion.one: z = Quarternion.k;
break;
case Quarternion.i: z = Quarternion.j;
break;
case Quarternion.j: z = Quarternion.neg_i;
break;
case Quarternion.k: z = Quarternion.neg_one;
break;
}
break;
}
if (x_neg && !y_neg || !x_neg && y_neg)
{
return Negate(z);
}
else
{
return z;
}
}
private static Quarternion Negate(Quarternion x)
{
if (IsNegative(x))
{
return Abs(x);
}
else
{
// positive
switch (x)
{
case Quarternion.i: return Quarternion.neg_i;
case Quarternion.j: return Quarternion.neg_j;
case Quarternion.k: return Quarternion.neg_k;
case Quarternion.one: return Quarternion.neg_one;
default:
throw new Exception();
}
}
}
static Quarternion Abs(Quarternion x)
{
switch (x)
{
case Quarternion.neg_i: return Quarternion.i;
case Quarternion.neg_j: return Quarternion.j;
case Quarternion.neg_k: return Quarternion.k;
case Quarternion.neg_one: return Quarternion.one;
default:
return x;
}
}
static bool IsNegative(Quarternion x)
{
if (x == Quarternion.neg_i || x == Quarternion.neg_j || x == Quarternion.neg_k || x == Quarternion.neg_one)
{
return true;
}
else
{
return false;
}
}
static bool BruteForceCheck(Quarternion[] segment)
{
Quarternion[] segmentLeft = new Quarternion[segment.Length];
// Compute left products
segmentLeft[0] = segment[0];
for (int i = 1; i < segment.Length; i++)
{
segmentLeft[i] = BruteMultiply2(segmentLeft[i - 1], segment[i]);
}
if (segmentLeft[segment.Length - 1] != Quarternion.neg_one)
{
return false;
}
// Compute right products
Quarternion[] segmentRight = new Quarternion[segment.Length];
segmentRight[segmentRight.Length - 1] = segment[segment.Length - 1];
for (int i = segmentRight.Length - 2; i >= 0; i--)
{
segmentRight[i] = BruteMultiply2(segment[i], segmentRight[i + 1]);
}
// Brute force for two concatenated segments
for (int i = 1; i < segment.Length-1; i++)
{
if (segmentLeft[i-1] == Quarternion.i) // if the left substring is i
{
for (int j = i + 1; j < segment.Length; j++)
{
if (segmentRight[j] == Quarternion.k &&
BruteMultiply(segment.Skip(i).Take(j - i).ToArray()) == Quarternion.j)
{
// System.Console.WriteLine("YES");
return true;
}
}
}
}
return false;
}
static Quarternion[] copySegment(Quarternion[] input, int copies)
{
Quarternion[] result = new Quarternion[input.Length*copies];
for (int i = 0; i < copies; i++)
{
input.CopyTo(result, input.Length*i);
}
return result;
}
static void RunCase(string line1, string line2)
{
string[] split = line1.Split(' ');
int L = Int32.Parse(split[0]);
long X = Int64.Parse(split[1]);
if (L * X < 3)
{
System.Console.WriteLine("NO");
return;
}
if (X % 4 == 0) // if x mod 4 = 0, then the whole thing multiplies out to +1
{
System.Console.WriteLine("NO");
return;
}
Quarternion[] segment = new Quarternion[L];
for (int i = 0; i < segment.Length; i++)
{
segment[i] = Parse(line2[i]);
}
Quarternion segmentProduct = BruteMultiply(segment);
if (X % 4 == 1 && segmentProduct != Quarternion.neg_one)
{
System.Console.WriteLine("NO");
return;
}
else if (X % 4 == 2 && BruteMultiply2(segmentProduct, segmentProduct) != Quarternion.neg_one)
{
System.Console.WriteLine("NO");
return;
}
else if (X % 4 == 3 && BruteMultiply(segmentProduct, segmentProduct, segmentProduct) != Quarternion.neg_one)
{
System.Console.WriteLine("NO");
return;
}
Quarternion[] criticalSegment = new Quarternion[1];
if (X <= 15)
{
criticalSegment = copySegment(segment, (int)X);
}
else
{
if (X % 4 == 1)
{
criticalSegment = copySegment(segment, 17);
}
else if (X % 4 == 2)
{
criticalSegment = copySegment(segment, 18);
}
else if (X % 4 == 3)
{
criticalSegment = copySegment(segment, 19);
}
}
if (BruteForceCheck(criticalSegment))
{
System.Console.WriteLine("YES");
}
else
{
System.Console.WriteLine("NO");
}
return;
}
static Quarternion BruteMultiply2(Quarternion x, Quarternion y)
{
bool x_neg = IsNegative(x);
bool y_neg = IsNegative(y);
if (x_neg)
{
x = Abs(x);
}
if (y_neg)
{
y = Abs(y);
}
Quarternion z = Quarternion.one;
switch (x)
{
case Quarternion.one:
switch (y)
{
case Quarternion.one: z = Quarternion.one;
break;
case Quarternion.i: z = Quarternion.i;
break;
case Quarternion.j: z = Quarternion.j;
break;
case Quarternion.k: z = Quarternion.k;
break;
}
break;
case Quarternion.i:
switch (y)
{
case Quarternion.one: z = Quarternion.i;
break;
case Quarternion.i: z = Quarternion.neg_one;
break;
case Quarternion.j: z = Quarternion.k;
break;
case Quarternion.k: z = Quarternion.neg_j;
break;
}
break;
case Quarternion.j:
switch (y)
{
case Quarternion.one: z = Quarternion.j;
break;
case Quarternion.i: z = Quarternion.neg_k;
break;
case Quarternion.j: z = Quarternion.neg_one;
break;
case Quarternion.k:
z = Quarternion.i;
break;
}
break;
case Quarternion.k:
switch (y)
{
case Quarternion.one: z = Quarternion.k;
break;
case Quarternion.i: z = Quarternion.j;
break;
case Quarternion.j: z = Quarternion.neg_i;
break;
case Quarternion.k: z = Quarternion.neg_one;
break;
}
break;
}
if (x_neg && !y_neg || !x_neg && y_neg)
{
return(Negate(z));
}
else
{
return(z);
}
}
