HackerRank Matrix Layer Rotation Problem Solution

HackerRank Matrix Layer Rotation Solution

Yashwant Parihar,

In this post, we will solve HackerRank Matrix Layer Rotation Problem Solution.

You are given a 2D matrix of dimension m x n and a positive integer r. You have to rotate the matrix r times and print the resultant matrix. Rotation should be in anti-clockwise direction.
Rotation of a 4×5 matrix is represented by the following figure. Note that in one rotation, you have to shift elements by one step only.

It is guaranteed that the minimum of m and n will be even.

As an example rotate the Start matrix by 2:

    Start         First           Second
     1 2 3 4       2  3  4  5      3  4  5  6
    12 1 2 5  ->   1  2  3  6 ->   2  3  4  7
    11 4 3 6      12  1  4  7      1  2  1  8
    10 9 8 7      11 10  9  8     12 11 10  9

Function Description

Complete the matrixRotation function in the editor below.

matrixRotation has the following parameter(s):

  • int matrix[m][n]: a 2D array of integers
  • int r: the rotation factor

Prints
It should print the resultant 2D integer array and return nothing. Print each row on a separate line as space-separated integers.

Input Format
The first line contains three space separated integers, m. n. and r, the number of rows and
columns in matrix, and the required rotation.
The next m lines contain n space-separated integers representing the elements of a row of
matrix.

Sample Input

Sample Input #01

STDIN        Function
-----        --------
4 4 2        rows m = 4, columns n = 4, rotation factor r = 2
1 2 3 4      matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
5 6 7 8
9 10 11 12
13 14 15 16

Sample Output #01

3 4 8 12
2 11 10 16
1 7 6 15
5 9 13 14

Explanation #01

The matrix is rotated through two rotations.

     1  2  3  4      2  3  4  8      3  4  8 12
     5  6  7  8      1  7 11 12      2 11 10 16
     9 10 11 12  ->  5  6 10 16  ->  1  7  6 15
    13 14 15 16      9 13 14 15      5  9 13 14

Sample Input #02

5 4 7
1 2 3 4
7 8 9 10
13 14 15 16
19 20 21 22
25 26 27 28

Sample Output #02

28 27 26 25
22 9 15 19
16 8 21 13
10 14 20 7
4 3 2 1

Explanation 02

The various states through 7 rotations:

    1  2  3  4      2  3  4 10    3  4 10 16    4 10 16 22
    7  8  9 10      1  9 15 16    2 15 21 22    3 21 20 28
    13 14 15 16 ->  7  8 21 22 -> 1  9 20 28 -> 2 15 14 27 ->
    19 20 21 22    13 14 20 28    7  8 14 27    1  9  8 26
    25 26 27 28    19 25 26 27    13 19 25 26   7 13 19 25

    10 16 22 28    16 22 28 27    22 28 27 26    28 27 26 25
     4 20 14 27    10 14  8 26    16  8  9 25    22  9 15 19
     3 21  8 26 ->  4 20  9 25 -> 10 14 15 19 -> 16  8 21 13
     2 15  9 25     3 21 15 19     4 20 21 13    10 14 20  7
     1  7 13 19     2  1  7 13     3  2  1  7     4  3  2  1

Sample Input #03

2 2 3
1 1
1 1

Sample Output #03

1 1
1 1

Explanation #03

All of the elements are the same, so any rotation will repeat the same matrix.

HackerRank Matrix Layer Rotation Problem Solution
HackerRank Matrix Layer Rotation Problem Solution

Matrix Layer Rotation C Solution

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int main() {

    /* Enter your code here. Read input from STDIN. Print output to STDOUT */    
    int row,col,rot;
    int i,j,current;
    int rIndex,cIndex;
    int min1,min2,frameNumber;
    int horRot,verRot,currentRot;
    int rotmat[300][300];
    scanf("%d %d %d",&row,&col,&rot);
    for(i=0;i<row;i++)
    {
        for(j=0;j<col;j++)
        {
            scanf("%d",&current);
            min1=fmin(i,j);
            min2=fmin(col-1-j,row-1-i);
            frameNumber=fmin(min1,min2);
            horRot=col-1-2*frameNumber;
            verRot=row-1-2*frameNumber;
            currentRot=rot%(2*(horRot+verRot));
            rIndex=i;
            cIndex=j;
            while(currentRot!=0)
            {
                if(rIndex==frameNumber && cIndex>frameNumber)
                {
                    cIndex--;
                }
                else if(cIndex==frameNumber && rIndex<(row-1-frameNumber))
                {
                    rIndex++;
                }
                else if(rIndex==(row-1-frameNumber) && cIndex<(col-1-frameNumber))
                {
                    cIndex++;
                }
                else if(cIndex==(col-1-frameNumber) && rIndex>frameNumber)
                {
                    rIndex--;
                }
                currentRot--;
            }
            rotmat[rIndex][cIndex]=current;
        }
    }
    
    for(i=0;i<row;i++)
    {
        for(j=0;j<col;j++)
        {
            printf("%d ",rotmat[i][j]); 
        }
         printf("\n");
    }
    
    return 0;
}

Matrix Layer Rotation C++ Solution

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;


int main() {
    int M,N,R; cin >> M >> N >> R;
    vector<vector<int>> v(M, vector<int>(N,0));
    for(auto&r:v) for(auto&c:r) cin >> c;
    int nlayer = min(N,M)/2;
    for (int i=0; i < nlayer; ++i) {
       // cerr << "layer#"<<i<<endl;        
        vector<int*> layer;
        int nrows = M-2*i;
        int ncols = N-2*i;
       // cerr << "nrows="<<nrows << endl << "ncols="<<ncols<<endl;
        
        for (int c=i; c < N-i-1; ++c) layer.push_back(&v[i][c]); // top
       // for (auto i:layer) cerr << *i <<" ";cerr<<endl;
       for (int r=i; r < M-1-i; ++r) layer.push_back(&v[r][N-1-i]); // right
        //for (auto i:layer) cerr <<*i <<" ";cerr<<endl;
       for (int c=i; c < N-i-1; ++c) layer.push_back(&v[M-1-i][N-1-c]); // bottom
       // for (auto i:layer) cerr <<*i <<" ";cerr<<endl;
       for (int r=i; r < M-1-i; ++r) layer.push_back(&v[M-1-r][i]); // left
        //for (auto i:layer) cerr <<*i <<" ";cerr<<endl;
        
        vector<int> l(layer.size());
        transform(layer.begin(),layer.end(),l.begin(),[](auto p){return*p;});
        int r = R % (l.size());
        rotate(l.begin(), l.begin()+r, l.end());
        //for (int i:l) cerr << i << " "; cerr << endl;
        for (size_t i=0; i < l.size(); ++i) {
            *layer[i] = l[i];
        }
        
     //   cerr<<endl;
    }
    
    for(auto&r:v) {
        for(auto&c:r) cout << c << " ";
        cout << endl;
    }
    
    return 0;
}

Matrix Layer Rotation C Sharp Solution

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication1
{
	public class MatrixRotation
	{
		
		public Int32 RowNumber { get; set; }
		public Int32 ColumnNumber { get; set;}
		public Int32 RotationNumer { get; set; }

	    public Int32[,] Matrix;
	    public Int32[,] Matrix_Rotation;
        /// <summary>
        /// cross line position, [0,0],[1,1]...[n,n]
        /// </summary>
	    public List<Tuple<Int32,Int32>> DiagonalNumber { get; set; }

        public void PrintMatrix(Int32[,] matrix)
        {
            Int32 lengthX = matrix.GetLength(1);
            Int32 lengthY = matrix.GetLength(0);
            for (Int32 y = 0; y < lengthY; y++)
            {
                for (Int32 x = 0; x < lengthX; x++)
                {
                    if(x==lengthX-1)
                        Console.Write(matrix[y, x]);
                    else
                    {
                        Console.Write(matrix[y, x] + " ");
                    }
                    
                }
                Console.WriteLine();
            }
        }

        public Int32[,] RotateRight(Int32[,] matrix)
        {
            Int32 lengthY = matrix.GetLength(0);
            Int32 lengthX = matrix.GetLength(1);
            Int32[,] result = new Int32[lengthX, lengthY];
            for (Int32 y = 0; y < lengthY; y++)
                for (Int32 x = 0; x < lengthX; x++)
                    result[x, y] = matrix[lengthY - 1 - y, x];
            return result;
        }

	    public void Test()
	    {
            TestRotation(new Int32[4, 4] { { 1, 2,3,4 }, { 5,6,7,8 }, { 9,10,11,12 },{13,14,15,16} });
            Console.WriteLine();
            TestRotation(new Int32[2, 3] { { 0, 1, 2 }, { 3, 4, 5 } });
	    }

        public void TestRotation(Int32[,] matrix)
        {
            Console.WriteLine("the original matrix:");
            PrintMatrix(matrix);
            Console.WriteLine();
            Console.WriteLine("the right rotated matrix:");
            PrintMatrix(RotateRight(matrix));
            Console.WriteLine();
            //Console.WriteLine("the left rotated matrix:");
            //PrInt32Matrix(RotateLeft(matrix));
        }

	    public void CreateEmptyMatrix()
	    {	       
            Matrix=new Int32[RowNumber,ColumnNumber];
            Matrix_Rotation=new Int32[RowNumber,ColumnNumber];
	    }
	    public void CreateMatrix(Int32 rowIdx, string s)
	    {
	        string[] rowStringList = s.Split(' ');
	        for (Int32 i = 0; i < ColumnNumber; i++)
	        {
	            Matrix[rowIdx, i] = Convert.ToInt32(rowStringList[i]);
	            Matrix_Rotation[rowIdx, i] = Convert.ToInt32(rowStringList[i]);
	        } 
	    }

        public void PrintMatrixRotation()
		{
			if (Matrix.Length > 0 && RowNumber > 0 && ColumnNumber > 0)
			{
				DiagonalNumber = new List<Tuple<Int32, Int32>>();
				// calculate the each rotation index
				// for example
				// row =10, colunn =10
				// first round is (row=0, column=9)
				// second round is (row =1, column=8)
				// .... etc (row = 4, column =5)
				for (Int32 rowIdx = 0, colIdx = 0; rowIdx < RowNumber && colIdx < ColumnNumber; rowIdx++, colIdx++)
				{
					if (DiagonalNumber.Count(x => x.Item1 == rowIdx && x.Item2 == colIdx) == 0)
					{
						DiagonalNumber.Add(new Tuple<int,int>(rowIdx,colIdx));
						List<Tuple<Int32, Int32>> currentRotation = new List<Tuple<Int32, Int32>>();
						int ColNumberInCurrentRoation = ColumnNumber - 2*colIdx;
						int RowNumberInCurrentRotation = RowNumber - 2*rowIdx;
						//Move Right
						for (Int32 col = colIdx; col <= ColumnNumber - colIdx - 1; col++)
						{
							if (col == rowIdx && DiagonalNumber.Count(x => x.Item1 == rowIdx && x.Item2 == colIdx) == 0)
								DiagonalNumber.Add(new Tuple<Int32, Int32>(rowIdx, col));
							currentRotation.Add(new Tuple<Int32, Int32>(rowIdx, col));
						}

						//Move Down
						for (Int32 row = rowIdx + 1; row <= RowNumber - rowIdx - 1; row++)
						{
							if (!currentRotation.Any(x => x.Item1 == row &&
									x.Item2 == ColumnNumber - colIdx - 1))
							{
								currentRotation.Add(new Tuple<Int32, Int32>(row, ColumnNumber - colIdx - 1));
								if (ColumnNumber - colIdx - 1 == row &&
									DiagonalNumber.Count(x => x.Item1 == rowIdx && x.Item2 == ColumnNumber - colIdx - 1) == 0)
									DiagonalNumber.Add(new Tuple<Int32, Int32>(row, ColumnNumber - colIdx - 1));

							}
						}

						//Move Left
						for (Int32 col = ColumnNumber - colIdx - 1 - 1; col >= colIdx; col--)
						{
							if (!currentRotation.Any(x => x.Item1 == RowNumber - rowIdx - 1 &&
														  x.Item2 == col))
							{
								currentRotation.Add(new Tuple<Int32, Int32>(RowNumber - rowIdx - 1, col));
								if (RowNumber - rowIdx - 1 == col &&
									DiagonalNumber.Count(x => x.Item1 == RowNumber - rowIdx - 1 && x.Item2 == col) == 0)
									DiagonalNumber.Add(new Tuple<Int32, Int32>(RowNumber - rowIdx - 1, col));
							}
						}

						//Move Up
						for (Int32 row = RowNumber - rowIdx - 1 - 1; row >= rowIdx; row--)
						{
							if (!currentRotation.Any(x => x.Item1 == row &&
														  x.Item2 == colIdx))
							{
								if (row == colIdx &&
									DiagonalNumber.Count(x => x.Item1 == row && x.Item2 == colIdx)==0)
								{
									DiagonalNumber.Add(new Tuple<Int32, Int32>(row, colIdx));
								}
								currentRotation.Add(new Tuple<Int32, Int32>(row, colIdx));
							}
						}

						// shift matrix based on current rotation position list
						for (int shiftIdx = 0; shiftIdx < RotationNumer % ((ColNumberInCurrentRoation+RowNumberInCurrentRotation - 2) * 2); shiftIdx++)
								ShiftMatrix(currentRotation);
					}
					else
					{
						break;
					}
				}
			}


			//PrInt32Matrix(Matrix);
			//PrInt32Matrix(Matrix_Rotation);
		}
        //private void PrInt32Matrix(Int32[,] Matrix_Rotation)
        //{
        //    if (Matrix_Rotation.Length > 0)
        //    {
        //        for (Int32 i = 0; i < Matrix_Rotation.Length; i++)
        //        {
        //            for (Int32 j = 0; j < Matrix_Rotation.Rank; j++)
        //            {
        //                Console.Write("{0} ", Matrix_Rotation[i, j]);
        //            }

        //            Console.WriteLine();
        //        }
        //    }
        //}

	    private void ShiftMatrix(List<Tuple<Int32, Int32>> rotationList)
	    {
            if (rotationList.Count > 0)
            {
                Int32 firstNumber = 0;
                for (Int32 i = 0; i <= rotationList.Count; i++)
	            {
	                if (i == 0)
	                {
                        Int32 item1 = rotationList[i].Item1;
                        Int32 item2 = rotationList[i].Item2;

                        Int32 v = Matrix_Rotation[item1, item2];

                        firstNumber = Matrix_Rotation[rotationList[i].Item1, rotationList[i].Item2];
	                }
                    else if (i == rotationList.Count)
	                {
                        Int32 item1 = rotationList[i-1].Item1;
                        Int32 item2 = rotationList[i-1].Item2;

                        Int32 v = Matrix_Rotation[item1, item2];

                        Matrix_Rotation[rotationList[i-1].Item1, rotationList[i-1].Item2] = firstNumber;
	                }
	                else
                    {
                        Int32 item1 = rotationList[i].Item1;
                        Int32 item2 = rotationList[i].Item2;

                        Int32 v_pre = Matrix_Rotation[rotationList[i - 1].Item1, rotationList[i - 1].Item2];
                        Int32 v = Matrix_Rotation[rotationList[i].Item1, rotationList[i].Item2];

                        Matrix_Rotation[rotationList[i - 1].Item1, rotationList[i - 1].Item2] =
                            Matrix_Rotation[rotationList[i].Item1, rotationList[i].Item2];
	                }
	            }
	        }            
	    }
        
        static void Main(string[] args)
    {
        MatrixRotation mrObjRotation = new MatrixRotation();
            string input = Console.ReadLine();
            string[] rowcols= input.Split(' ');
            int rowIdx = 0;
            mrObjRotation.RowNumber = Convert.ToInt32(rowcols[0]);
            mrObjRotation.ColumnNumber = Convert.ToInt32(rowcols[1]);
            mrObjRotation.RotationNumer = Convert.ToInt32(rowcols[2]);

            mrObjRotation.CreateEmptyMatrix();
            string inputRow = Console.ReadLine();
            while (!string.IsNullOrEmpty(inputRow))
            {
                mrObjRotation.CreateMatrix(rowIdx, inputRow);

                inputRow = Console.ReadLine();   
                rowIdx++;
            }

        mrObjRotation.PrintMatrixRotation();
           
            mrObjRotation.PrintMatrix(mrObjRotation.Matrix_Rotation);
    }
	}
    
    
}

Matrix Layer Rotation Java Solution


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

class Result {

    /*
     * Complete the 'matrixRotation' function below.
     *
     * The function accepts following parameters:
     *  1. 2D_INTEGER_ARRAY matrix
     *  2. INTEGER r
     *
     *
     *
     */

    public static void matrixRotation(List<List<Integer>> matrix, int rotate) {

        List<Integer> layerone=null;

        int cols = matrix.get(0).size();
        int rows = matrix.size();

        int rows_start =0;
        int rows_end=rows-1;

        int cols_start=0;
        int cols_end=cols-1;

        // the number of layer is the min(M,N)/2
        int numboflayer = matrix.size()<matrix.get(0).size()?matrix.size()/2:matrix.get(0).size()/2;

        List<Integer> layerone_order = null;
        Map<Integer,List<Integer>> mapLayers = new HashMap<>();

        // create  matrix layer
        for(int layer=0;layer<numboflayer;layer++)
        {
            layerone_order = new ArrayList<>();
            layerone=new ArrayList<>();
            rows_start=layer;
            rows_end=rows-1-layer;
            cols_start=layer;
            cols_end=cols-1-layer;

            layerone.addAll(matrix.get(rows_start).subList(cols_start,cols_end));

            for(int r=rows_start;r<=rows_end;r++)
            {
                layerone.add(matrix.get(r).get(cols_end));
            }

            List<Integer> tempList = new ArrayList<>();
            tempList.addAll(matrix.get(rows_end).subList(cols_start,cols_end));
            Collections.reverse(tempList);
            layerone.addAll(tempList);

            for(int i=rows_end-1;i>rows_start;i--)
            {
                layerone.add(matrix.get(i).get(rows_start));
            }



            layerone_order.addAll(layerone.subList(rotate%layerone.size(),layerone.size()));

            layerone_order.addAll(layerone.subList(0,rotate%layerone.size()));

            mapLayers.put(layer,layerone_order);

        }
        // print layer matrix rotation
        //aprintLayers(mapLayers);

        int index=0;
        for(int layer=0;layer<numboflayer;layer++)
        {
            index=0;
            rows_start=layer;
            rows_end=rows-1-layer;
            cols_start=layer;
            cols_end=cols-1-layer;



            for(int col_layer=0;col_layer<=cols_end-cols_start;col_layer++)
            {
                matrix.get(rows_start).set(cols_start+col_layer,mapLayers.get(layer).get(col_layer));

            }

            index=0;
            for(int row=rows_start+1;row<rows_end;row++)
            {
                index++;
                matrix.get(row).set(cols_start,mapLayers.get(layer).get(mapLayers.get(layer).size()-index));
                matrix.get(row).set(cols_end,mapLayers.get(layer).get(cols_end-cols_start+index));

            }

            for(int col_layer=0;col_layer<=cols_end-cols_start;col_layer++) {
                matrix.get(rows_end).set(cols_start+col_layer,mapLayers.get(layer).get(mapLayers.get(layer).size()-index-col_layer-1));
            }


        }

        printMatrix(matrix);

    }

    private static void printLayers(Map<Integer,List<Integer>> mapLayers)
    {
        mapLayers.forEach((key,value)->{
            System.out.print(" - " + key + " - ");
            value.stream().forEach(el->{
                System.out.print(el+" ");
            });
        });
        System.out.println("");

    }

    private static void printMatrix(List<List<Integer>> matrix)
    {
        matrix.stream().forEach(row->{
            row.stream().forEach(col->{
                System.out.print(col + " ");
            });
            System.out.println("");
        });
    }


}


public class Solution {

    public static void main(String[] args) throws IOException {
        try(BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in)))
        {

            String line = bufferedReader.readLine();
            //System.out.println(line);
            //System.out.println(line.replaceAll("\\s+$", "").split(" "));
            String[] firstMultipleInput = line.replaceAll("\\s+$", "").split(" ");

            int m = Integer.parseInt(firstMultipleInput[0]);

            int n = Integer.parseInt(firstMultipleInput[1]);

            int r = Integer.parseInt(firstMultipleInput[2]);

            List<List<Integer>> matrix = new ArrayList<>();

            IntStream.range(0, m).forEach(i -> {
                try {
                    matrix.add(
                            Stream.of(bufferedReader.readLine().replaceAll("\\s+$", "").split(" "))
                                    .map(Integer::parseInt)
                                    .collect(Collectors.toList())
                    );
                } catch (IOException ex) {
                    throw new RuntimeException(ex);
                }
            });

            Result.matrixRotation(matrix, r);
        }
        catch(IOException io)
        {
            throw new RuntimeException(io);
        }



    }


}

Matrix Layer Rotation JavaScript Solution

function processData(input) {
    var lines = input.split('\n');
    var params = lines[0].split(' ').map(Number);
    var numRows = params[0];
    var numCols = params[1];
    var numRotations = params[2];
    var a = [];
    for(var i=0; i<numRows; i++){
        var row = lines[i+1].split(' ').map(Number);
        a.push(row);
    }
    
    var sequences = readArray(a, numRows, numCols);
    
    sequences.forEach(function(sequence){
        rotateSequence(sequence, numRotations);
    });
    
    var result = writeArray(sequences, numRows, numCols);
    
    printResult(result);
}

function readArray(a, numRows, numCols){
    var sequences = [];
    var numSequences = Math.ceil(Math.min(numRows/2, numCols/2));
    for(var i=0; i<numSequences; i++){
        var sequence = [];
        var p = { x:i, y:i };
        var d = { x:0, y:1 };
        var hasCompleted = false;
        sequence.push(a[p.y][p.x]);
        
        while(!hasCompleted){
            p.x += d.x;
            p.y += d.y;
            if(p.y >= numRows-i){
                d.x = 1;
                d.y = 0;
                p.x += 1;
                p.y -= 1;
            } else if(p.x >= numCols-i){
                d.x = 0;
                d.y = -1;
                p.x -= 1;
                p.y -= 1;
            } else if(p.y < i){
                d.x = -1;
                d.y = 0;
                p.x -= 1;
                p.y += 1;
            }
            
            if(p.x == i && p.y == i){
                hasCompleted = true;
            } else {
                sequence.push(a[p.y][p.x]);
            }
        }
        sequences.push(sequence);
    }
    return sequences;
}

function rotateSequence(sequence, numRotations){
    numRotations = numRotations % sequence.length;
    var temp = sequence.splice(sequence.length-numRotations, numRotations);
    sequence.unshift.apply(sequence, temp);
}

function writeArray(sequences, numRows, numCols){
    var a = [];
    for(var i=0; i<numRows; i++){
        a[i] = [];
    }
    
    sequences.forEach(function(sequence, i){
        var j = 0;
        var p = { x:i, y:i };
        var d = { x:0, y:1 };
        var hasCompleted = false;
        a[p.y][p.x] = sequence[j];
        
        while(!hasCompleted){
            p.x += d.x;
            p.y += d.y;
            if(p.y >= numRows-i){
                d.x = 1;
                d.y = 0;
                p.x += 1;
                p.y -= 1;
            } else if(p.x >= numCols-i){
                d.x = 0;
                d.y = -1;
                p.x -= 1;
                p.y -= 1;
            } else if(p.y < i){
                d.x = -1;
                d.y = 0;
                p.x -= 1;
                p.y += 1;
            }
            
            if(p.x == i && p.y == i){
                hasCompleted = true;
            } else {
                j += 1;
                a[p.y][p.x] = sequence[j];
            }
        }
    });
    return a;
}

function printResult(a){
    a.forEach(function(row){
        console.log(row.join(' '));
    });
}

process.stdin.resume();
process.stdin.setEncoding("ascii");
_input = "";
process.stdin.on("data", function (input) {
    _input += input;
});

process.stdin.on("end", function () {
   processData(_input);
});

Matrix Layer Rotation Python Solution

m,n,r = list( map( int, input().split() ) )
loops = int( min( m,n ) / 2 )

def roundtrip( i, m, n ):

    for r in range( i, m-i-1 ):
        yield ( r, i )

    for r in range( i, n-i-1 ):
        yield ( m-i-1, r )

    for r in range( m-i-1, i, -1 ):
        yield ( r, n-i-1 )

    for r in range( n-i-1, i, -1 ):
        yield ( i, r )

posToLoop = {}
loopToPos = {}
loopMax = {}
for l in range(loops):
    idx = 0
    for i in roundtrip( l, m, n ):
        posToLoop[ i ] = ( l, idx )
        loopToPos[ ( l, idx ) ] = i
        idx += 1
    loopMax[ l ] = idx

matrix = [[0 for x in range(n)] for x in range(m)]
y = 0
for i in range( m ):
    line = input().split()
    x = 0
    for num in line:
        l,p = posToLoop[ (y,x) ]
        p = ( p + r ) % loopMax[ l ]
        p = loopToPos[ (l,p) ]
        matrix[ p[0] ][ p[1] ] = num
        x += 1

    y += 1

for l in matrix:
    print( ' '.join( l ) )

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