Be yourself; Everyone else is already taken.
— Oscar Wilde.
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Rotation of Matrix
Problem Statement
Rotate a matrix so that each loops do a rotation by 1.
If the input is :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
The output should be :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Solution
Matrix in c# can be stored in multi-dimensional array or a jagged array. We are considering the solution using multi-dimensional array.The optimal solution would be to rotate each loop just once. So if the array size in MxN then the number of element in outer loop would be : M + M + N + N – 4. We reduced 4 because the corner got included twice.
To get the element in inner loop, the same formula can be used but now with reduction in size of M and N by 2. So the count would be (M-2) + (M-2) + (N-2) + (N-2) -4. We reduced two since the inner loop would have 1 less element on both end of the array.
As you can see from the diagram, we need to loop 4 times in this case. The number of element in each loop can be derived by adding rows and column and removing duplicate. The other thing to notice is that the number of loop will be the MIN(M,N)/2 + 1. This is pretty obvious because the number loop will be the half of the shortest side.
Below is the C# code. The code accept any array and rotates it. The display function has some formatting display logic which can be ignored:
using System;
namespace LGO
{
class Program
{
static void Main(string[] args)
{
int [,] matrix = new int[,] { {01,02,03,04,05,06,07},
{26,30,31,32,33,34,35},
{25,47,50,51,52,53,36},
{24,46,59,60,61,54,37},
{23,45,58,57,56,55,38},
{22,44,43,42,41,40,39},
{21,20,19,18,17,16,15}
};
display(matrix);
rotate(matrix);
display(matrix);
}
public static void rotate(int[,] matrix)
{
int numberofLoops = matrix.GetLength(0) > matrix.GetLength(1) ? (matrix.GetLength(1)+1)/2 : (matrix.GetLength(0)+1)/2;
int row=0, col=0, toVal=0, fromVal = 0 , maxInLoop, maxCol , maxRow , nextCol = 0, nextRow = 0;
for(int i = 0; i<numberofLoops; i++)
{
maxCol = matrix.GetLength(1)-1-i;
maxRow = matrix.GetLength(0)-1-i;
row = col = i;
toVal = matrix[row, col];
maxInLoop = 2*(matrix.GetLength(0)-2*i) + 2*(matrix.GetLength(1)-2*i) - 4;
for(int j=0; j< maxInLoop; j++)
{
fromVal = toVal;
if(row == i && col < maxCol)
{
nextCol = col + 1;
toVal = matrix[row, nextCol];
matrix[row, nextCol] = fromVal;
col++;
}
else if(row < maxRow && col == maxCol)
{
nextRow = row + 1;
toVal = matrix[nextRow, col];
matrix[nextRow, col] = fromVal;
row++;
}
else if(row == maxRow && col > i)
{
nextCol = col - 1;
toVal = matrix[row, nextCol];
matrix[row, nextCol] = fromVal;
col--;
}
else if(row > 0 && col == i)
{
nextRow = row - 1;
toVal = matrix[nextRow, col];
matrix[nextRow, col] = fromVal;
row--;
}
}
}
}
public static void display(int[,] matrix)
{
for(int i = 0; i< matrix.GetLength(0); i++)
{ for(int j=0; j< matrix.GetLength(1);j++)
{
Console.Write(matrix[i,j]);
int length = matrix[i,j]/10 < 1 ? 3 : (matrix[i,j]/10 < 10 ? 2 : 1);
for(int k=0;k<length;k++)
Console.Write(" ");
}
Console.WriteLine();
}
}
}
}
Introduce Yourself (Example Post)
This is an example post, originally published as part of Blogging University. Enroll in one of our ten programs, and start your blog right.
You’re going to publish a post today. Don’t worry about how your blog looks. Don’t worry if you haven’t given it a name yet, or you’re feeling overwhelmed. Just click the “New Post” button, and tell us why you’re here.
Why do this?
- Because it gives new readers context. What are you about? Why should they read your blog?
- Because it will help you focus you own ideas about your blog and what you’d like to do with it.
The post can be short or long, a personal intro to your life or a bloggy mission statement, a manifesto for the future or a simple outline of your the types of things you hope to publish.
To help you get started, here are a few questions:
- Why are you blogging publicly, rather than keeping a personal journal?
- What topics do you think you’ll write about?
- Who would you love to connect with via your blog?
- If you blog successfully throughout the next year, what would you hope to have accomplished?
You’re not locked into any of this; one of the wonderful things about blogs is how they constantly evolve as we learn, grow, and interact with one another — but it’s good to know where and why you started, and articulating your goals may just give you a few other post ideas.
Can’t think how to get started? Just write the first thing that pops into your head. Anne Lamott, author of a book on writing we love, says that you need to give yourself permission to write a “crappy first draft”. Anne makes a great point — just start writing, and worry about editing it later.
When you’re ready to publish, give your post three to five tags that describe your blog’s focus — writing, photography, fiction, parenting, food, cars, movies, sports, whatever. These tags will help others who care about your topics find you in the Reader. Make sure one of the tags is “zerotohero,” so other new bloggers can find you, too.
algorithm in C# 