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Shift values in array [C#]

I would like to shift values in an array to the corners.
This is my 2-dimensional array:
4, 8, 0, 2
0, 6, 1, 9
7, 0, 5, 3
I want to shift all 0 values to the corners so it looks like:
0, 4, 8, 0
2, 6, 1, 9
0, 7, 5, 3
0, 4, 8, 0
2, 6, 1, 9
7, 5, 3, 0
0, 4, 8, 2
6, 1, 9, 7
0, 5, 3, 0
4, 8, 2, 0
6, 1, 9, 7
0, 5, 3, 0
There is an easy way to do it? Thanks a lot!

How can I get "thinner" graph for my coordinate system?

Following up with this, I have a bunch of coordinates and I draw them on a bitmap image as a coordinate system. Now, I would like to get rid of all the noise, and filter coordinates to give a "clearer" or "cleaner" path and "less" or "better" data to work on. To explain more, I will need to expose my awesome painting skills as follows:
Current:
Desired:
Notice:
I will need to delete coordinates
I might need to add coordinates
I might need to ignore shortest neighbor in some cases
The only thing I can think of, is to use a shortest path algorithm such as A* and Dijkstra. And populate data in some sort of data structure to contain neighbors and costs for every node and then to execute the algorithm. I don't want to start something that might be wrong or waste. I would love to see a pseudo code if possible on how could I solve such a problem?
P.S I am currently on Wpf C# but I am open to use C# or C++ for any task. Thanks

You are looking for an operation called thinning or skeletonization, possibly followed by some post-processing to remove small components. There are different algorithms for this that offer different properties. For example Guo and Hall's and Zhang and Suen's.

What you're after is a path finding application. There are several ways to approach this, but one of the simpler ways is to:
Pick a starting point, add to list
While True:
For each border_pt bordering last point on list:
Count number of points bordering border_pt
If count > best_count:
Mark border_pt as best
if border_pt is empty:
break
Add border_pt to list
Here's some C# code that does just that, it generates a simple list based on your cloud:
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Drawing;
using System.Linq;
using System.Threading.Tasks;
using System.Windows.Forms;
namespace WindowsFormsApplication1
{
class ExampleProgram : Form
{
const int GridWidth = 24;
const int GridHeight = 15;
List<Point> m_points = new List<Point>();
List<Point> m_trail = new List<Point>();
[STAThread]
static void Main()
{
Application.EnableVisualStyles();
Application.SetCompatibleTextRenderingDefault(false);
Application.Run(new ExampleProgram());
}
ExampleProgram()
{
// Simple little tool to add a bunch of points
AddPoints(
0, 4, 1, 3, 1, 4, 1, 5, 2, 4, 2, 5, 2, 6, 3, 4, 3, 5, 4, 5, 4, 6, 5, 5, 6, 5,
6, 4, 5, 4, 7, 4, 7, 3, 8, 3, 8, 4, 8, 5, 8, 6, 9, 6, 9, 5, 9, 4, 9, 3, 10, 2,
10, 3, 10, 4, 10, 5, 10, 6, 11, 5, 11, 4, 11, 3, 11, 2, 12, 4, 12, 5, 13, 5,
13, 6, 13, 8, 14, 8, 14, 7, 14, 6, 15, 7, 15, 8, 15, 9, 14, 9, 14, 10, 13, 10,
12, 10, 11, 10, 13, 11, 14, 11, 15, 11, 15, 12, 16, 12, 17, 12, 18, 12, 19,
12, 18, 11, 17, 11, 17, 10, 18, 10, 19, 10, 19, 9, 19, 8, 20, 8, 21, 8, 18,
7, 19, 7, 20, 7, 21, 7, 21, 6, 22, 6, 23, 6, 21, 5, 20, 5, 19, 5, 19, 4, 18,
4, 17, 4, 20, 3, 21, 3, 22, 3, 20, 2, 19, 2, 18, 2, 19, 1, 20, 1, 21, 1, 19,
0, 18, 0, 10, 0, 4, 1);
// Very basic form logic
ClientSize = new System.Drawing.Size(GridWidth * 20, GridHeight * 20);
DoubleBuffered = true;
Paint += ExampleProgram_Paint;
// Add a new point to the form (commented out)
// MouseUp += ExampleProgram_MouseUp_AddPoint;
// Draw the trail we find
MouseUp += ExampleProgram_MouseUp_AddTrail;
// Pick a starting point to start finding the trail from
// TODO: Left as an excersize for the reader to decide how to pick
// the starting point programatically
m_trail.Add(new Point(0, 4));
}
IEnumerable<Point> Border(Point pt)
{
// Return all points that border a give point
if (pt.X > 0)
{
if (pt.Y > 0)
{
yield return new Point(pt.X - 1, pt.Y - 1);
}
yield return new Point(pt.X - 1, pt.Y);
if (pt.Y < GridHeight - 1)
{
yield return new Point(pt.X - 1, pt.Y + 1);
}
}
if (pt.Y > 0)
{
yield return new Point(pt.X, pt.Y - 1);
}
if (pt.Y < GridHeight - 1)
{
yield return new Point(pt.X, pt.Y + 1);
}
if (pt.X < GridWidth - 1)
{
if (pt.Y > 0)
{
yield return new Point(pt.X + 1, pt.Y - 1);
}
yield return new Point(pt.X + 1, pt.Y);
if (pt.Y < GridHeight - 1)
{
yield return new Point(pt.X + 1, pt.Y + 1);
}
}
}
void AddPoints(params int[] points)
{
// Helper to add a bunch of points to our list of points
for (int i = 0; i < points.Length; i += 2)
{
m_points.Add(new Point(points[i], points[i + 1]));
}
}
void ExampleProgram_MouseUp_AddTrail(object sender, MouseEventArgs e)
{
// Calculate the trail
while (true)
{
// Find the best point for the next point
int bestCount = 0;
Point best = new Point();
// At the current end point, test all the points around it
foreach (var pt in Border(m_trail[m_trail.Count - 1]))
{
// And for each point, see how many points this point borders
int count = 0;
if (m_points.Contains(pt) && !m_trail.Contains(pt))
{
foreach (var test in Border(pt))
{
if (m_points.Contains(test))
{
if (m_trail.Contains(test))
{
// This is a point both in the original cloud, and the current
// trail, so give it a negative weight
count--;
}
else
{
// We haven't visited this point, so give it a positive weight
count++;
}
}
}
}
if (count > bestCount)
{
// This point looks better than anything we've found, so
// it's the best one so far
bestCount = count;
best = pt;
}
}
if (bestCount <= 0)
{
// We either didn't find anything, or what we did find was bad, so
// break out of the loop, we're done
break;
}
m_trail.Add(best);
}
Invalidate();
}
void ExampleProgram_MouseUp_AddPoint(object sender, MouseEventArgs e)
{
// Just add the point, and dump it out
int x = (int)Math.Round((((double)e.X) - 10.0) / 20.0, 0);
int y = (int)Math.Round((((double)e.Y) - 10.0) / 20.0, 0);
m_points.Add(new Point(x, y));
Debug.WriteLine("m_points.Add(new Point(" + x + ", " + y + "));");
Invalidate();
}
void ExampleProgram_Paint(object sender, PaintEventArgs e)
{
// Simple drawing, just draw a grid, and the points
e.Graphics.Clear(Color.White);
for (int x = 0; x < GridWidth; x++)
{
e.Graphics.DrawLine(Pens.Black, x * 20 + 10, 0, x * 20 + 10, ClientSize.Height);
}
for (int y = 0; y < GridHeight; y++)
{
e.Graphics.DrawLine(Pens.Black, 0, y * 20 + 10, ClientSize.Width, y * 20 + 10);
}
foreach (var pt in m_points)
{
e.Graphics.FillEllipse(Brushes.Black, (pt.X * 20 + 10) - 5, (pt.Y * 20 + 10) - 5, 10, 10);
}
foreach (var pt in m_trail)
{
e.Graphics.FillEllipse(Brushes.Red, (pt.X * 20 + 10) - 6, (pt.Y * 20 + 10) - 6, 12, 12);
}
}
}
}

You might want to consider treating your coordinates as a binary image and apply some Morphological techniques to the image.
Thinning might give you good results, but processing like this can be tricky to get working well in a wide range of cases.

Log of a very large number

I'm dealing with the BigInteger class with numbers in the order of 2 raised to the power 10,000,000.
The BigInteger Log function is now the most expensive function in my algorithm and I am desperately looking for an alternative.
Since I only need the integral part of the log, I came across this answer which seems brilliant in terms of speed but for some reason I am not getting accurate values. I do not care about the decimal part but I do need to get an accurate integral part whether the value is floored or ceiled as long as I know which.
Here is the function I implemented:
public static double LogBase2 (System.Numerics.BigInteger number)
{
return (LogBase2(number.ToByteArray()));
}
public static double LogBase2 (byte [] bytes)
{
// Corrected based on [ronalchn's] answer.
return (System.Math.Log(bytes [bytes.Length - 1], 2) + ((bytes.Length - 1) * 8));
}
The values are now incredibly accurate except for corner cases. The values 7 to 7.99999, 15 to 15.9999, 23 to 23.9999 31 to 31.9999, etc. return -Infinity. The numbers seem to revolve around byte boundaries. Any idea what's going on here?
Example:
LogBase2( 1081210289) = 30.009999999993600 != 30.000000000000000
LogBase2( 1088730701) = 30.019999999613300 != 30.000000000000000
LogBase2( 2132649894) = 30.989999999389400 != 30.988684686772200
LogBase2( 2147483648) = 31.000000000000000 != -Infinity
LogBase2( 2162420578) = 31.009999999993600 != -Infinity
LogBase2( 4235837212) = 31.979999999984800 != -Infinity
LogBase2( 4265299789) = 31.989999999727700 != -Infinity
LogBase2( 4294967296) = 32.000000000000000 != 32.000000000000000
LogBase2( 4324841156) = 32.009999999993600 != 32.000000000000000
LogBase2( 545958373094) = 38.989999999997200 != 38.988684686772200
LogBase2( 549755813887) = 38.999999999997400 != 38.988684686772200
LogBase2( 553579667970) = 39.009999999998800 != -Infinity
LogBase2( 557430119061) = 39.019999999998900 != -Infinity
LogBase2( 561307352157) = 39.029999999998300 != -Infinity
LogBase2( 565211553542) = 39.039999999997900 != -Infinity
LogBase2( 569142910795) = 39.049999999997200 != -Infinity
LogBase2( 1084374326282) = 39.979999999998100 != -Infinity
LogBase2( 1091916746189) = 39.989999999998500 != -Infinity
LogBase2( 1099511627775) = 39.999999999998700 != -Infinity

Try this:
public static int LogBase2(byte[] bytes)
{
if (bytes[bytes.Length - 1] >= 128) return -1; // -ve bigint (invalid - cannot take log of -ve number)
int log = 0;
while ((bytes[bytes.Length - 1]>>log)>0) log++;
return log + bytes.Length*8-9;
}
The reason for the most significant byte being 0 is because the BigInteger is a signed integer. When the most significant bit of the high-order byte is 1, an extra byte is tacked on to represent the sign bit of 0 for positive integers.
Also changed from using the System.Math.Log function because if you only want the rounded value, it is much faster to use bit operations.
If you have Microsoft Solver Foundation (download at http://msdn.microsoft.com/en-us/devlabs/hh145003.aspx), then you can use the BitCount() function:
public static double LogBase2(Microsoft.SolverFoundation.Common.BigInteger number)
{
return number.BitCount;
}
Or you can use the java library. Add a reference to the vjslib library (found in the .NET tab - this is the J# implementation of the java library).
You can now add "using java.math" in your code.
java.math.BigInteger has a bitLength() function

BigInteger bi = new BigInteger(128);
int log = bi.Log2();
public static class BigIntegerExtensions
{
static int[] PreCalc = new int[] { 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1};
public static int Log2(this BigInteger bi)
{
byte[] buf = bi.ToByteArray();
int len = buf.Length;
return len * 8 - PreCalc[buf[len - 1]] - 1;
}
}

Years late but maybe this will help someone else...
.Net Core 3 added the .GetBitLength() that is basically log2. (but just one increment too high) Since it is built-in to .net I think this is about as fast as we can get.
// Create some example number
BigInteger myNum= (BigInteger)32;
// Get the Log2
BigInteger myLog2 = myNum.GetBitLength() - 1;
https://dotnetfiddle.net/7ggy4D

Bit counting arbitrarily large positive integers in C#

There are many implementations of bit counting out there but in my case, I need to test if an arbitrarily large number contains at most two set bits.
I wrote the following function that does the job and seems to be quite fast but I wanted to find out if it can be further optimized for C#. This function gets called in a loop a few million times.
public static byte [] BitCountLookupArray = new byte []
{
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8
};
// The parameter [number] will NEVER be negative.
public static bool HasSetBitCountOfLessThenThree (System.Numerics.BigInteger number)
{
int sum = 0;
byte [] bytes = null;
bytes = number.ToByteArray();
for (int i=0; i < bytes.Length; i++)
{
sum += BitCountLookupArray [bytes [i]];
}
return (sum < 3);
}
IMPORTANT: The argument [number] sent to the function will NEVER be negative.
Some points I thought of were:
Making the function static. Done.
Using a static lookup array. Done.
Using pointers instead of array indexes since the number of bytes often crosses 100,000. Not sure how much this would help.
Forcing an inline function which sadly cannot be guaranteed in .NET.
Open to other suggestions.

This way you can optimise it further
for (int i=0; i < bytes.Length; i++)
{
sum += BitCountLookupArray [bytes [i]];
if(sum >= 3)
{
return false // This will stop the execution of unnecessary lines
// as we need to know whether sum is less than 3 or not.
}
}
return true;

Since you only need to know whether you have fewer than 3 set bits, I would suggest this:
// remove two bits
number &= number - 1;
number &= number - 1;
// if number != 0, then there were 3 or more bits set
return number.IsZero;
Of course Rain's method works too, and I'm not sure which strategy will be faster.
Alternative:
//remove one bit
number &= number - 1;
// if the number of bits left is 0 or 1, there were < 3 bits set
return number.IsZero || number.IsPowerOfTwo;
It's probably faster to test first, and remove the bit later:
return number.IsZero || // zero bits?
number.IsPowerOfTwo || // one bit?
(number & (number - 1)).IsPowerOfTwo; // two bits?

The most obvious optimisation is to drop out of the loop as soon as sum == 3, since any further matches past that point are immaterial.
There's also no need to set bytes twice; simply use byte [] bytes = number.ToByteArray();, but the benifit here is miniscule.

How to search an array with array?

I have 2 byte arrays:
Dim A() As Byte = {1, 2, 3, 4, 5, 6, 7, 8, 9}
Dim B() As Byte = {5, 6, 7}
Now I want to find the occurance of the full B in A. I tried Array.IndexOf(A, B) with no luck. Is there a simple way to search an array by array without the need to use any loops?
It should find the index (position) of 5,6,7 in the same order as in B().
If A() contains {1,2,3,4,7,6,5,9} it should return false or -1 because they are not in the same order.

The following Linq statement will give an IEnumerable<int> containing the positions of b in a (or an empty set if none occur):
Enumerable
.Range( 0, 1 + a.Length - b.Length )
.Where( i => a.Skip(i).Take(b.Length).SequenceEqual(b) );
I have no idea how to translate to VB.NET.

This might work, but it's C# and uses a loop:
private static int[] GetIndicesOf(byte[] needle, byte[] haystack)
{
int[] foundIndices = new int[needle.Length];
int found = 0;
for (int i = 0; i < haystack.Length; i++)
{
if (needle[found] == haystack[i])
{
foundIndices[found++] = i;
if (found == needle.Length)
return foundIndices;
}
else
{
i -= found; // Re-evaluate from the start of the found sentence + 1
found = 0; // Gap found, reset, maybe later in the haystack another occurrance of needle[0] is found
continue;
}
}
return null;
}
Tested with input:
Byte[] haystack = { 5, 6, 7, 8, 9, 0, 5, 6, 7 };
Byte[] needle = { 5, 6, 7 };
// Returns {0, 1, 2}
Byte[] haystack = { 5, 6, 0, 8, 9, 0, 5, 6, 7 };
Byte[] needle = { 5, 6, 7 };
// Returns {6, 7, 8}
Byte[] haystack = { 5, 6, 0, 7, 9, 0, 5, 6, 8 };
Byte[] needle = { 5, 6, 7 };
// Returns null
Byte[] haystack = { 1, 2, 1, 2, 2 };
Byte[] needle = { 1, 2, 2 };
// Returns {2, 3, 4}
Byte[] haystack = { 1, 2, 1, 2, 1, 2, 3 };
Byte[] needle = { 1, 2, 1, 2, 3 };
// Returns {2, 3, 4, 5, 6}
Byte[] haystack = { 1, 1, 1, 1, 2 };
Byte[] needle = { 1, 2 };
// Returns {3, 4}
But the Linq implementation of #spender looks nicer. :-P

How about creating a method that:
Concatinates the elements of the searched list to one string
Concatinates the elements of the list to search for to one string
Looks in the first string for the precense of the second string
Like so:
public bool IsSubSetOf(IList<int> list1, IList<int> list2){
var string1 = string.Join("", list1);
var string2 = string.Join("", list2);
return string1.Contains(string2);
}
Not tested...

An efficient way of solving this problem in general is the KMP algorithm. Quick googling suggest that a .NET implementation may be found here. It's implementational pseudocode is availible from Wikipedia.
An inefficient, but harmlessly easy to code way is presented in one of the links above as follows:
int[] T = new[]{1, 2, 3, 4, 5};
int[] P = new[]{3, 4};
for (int i = 0; i != T.Length; i++)
{
int j = 0
for (;i+j != T.Length && j != P.Length && T[i+j]==P[j]; j++);
if (j == P.Length) return i;
}

My take would be:
public static int Search<T>(T[] space, T[] searched) {
foreach (var e in Array.FindAll(space, e => e.Equals(searched[0]))) {
var idx = Array.IndexOf(space, e);
if (space.ArraySkip(idx).Take(searched.Length).SequenceEqual(searched))
return idx;
}
return -1;
}
public static class Linqy {
public static IEnumerable<T> ArraySkip<T>(this T[] array, int index) {
for (int i = index; i < array.Length; i++) {
yield return array[i];
}
}
}
As always, it depends on your data whether this is "good enough" or you will have to resort to more complex yet efficient algorithms. I introduced an arrayskip as the Linq skip does indeed only assume the IEnumerable interface and would enumerate up to the index.