Chapter7MultidimensionalArrays1MotivationsThusfar,youhaveusedone-dimensionalarraystomodellinearcollectionsofelements.Youcanuseatwo-dimensionalarraytorepresentamatrixoratable.Forexample,thefollowingtablethatdescribesthedistancesbetweenthecitiescanberepresentedusingatwo-dimensionalarray.2ObjectivesTogiveexamplesofrepresentingdatausingtwo-dimensionalarrays(§7.1).Todeclarevariablesfortwo-dimensionalarrays,createarrays,andaccessarrayelementsinatwo-dimensionalarrayusingrowandcolumnindexes(§7.2).Toprogramcommonoperationsfortwo-dimensionalarrays(displayingarrays,summingallelements,findingminandmaxelements,andrandomshuffling)(§7.3).Topasstwo-dimensionalarraystomethods(§7.4).Towriteaprogramforgradingmultiple-choicequestionsusingtwo-dimensionalarrays(§7.5).Tosolvetheclosest-pairproblemusingtwo-dimensionalarrays(§7.6).TocheckaSudokusolutionusingtwo-dimensionalarrays(§7.7).Tousemultidimensionalarrays(§7.8).3Declare/CreateTwo-dimensionalArrays//DeclarearrayrefvardataType[][]refVar;//CreatearrayandassignitsreferencetovariablerefVar=newdataType[10][10];//CombinedeclarationandcreationinonestatementdataType[][]refVar=newdataType[10][10];//AlternativesyntaxdataTyperefVar[][]=newdataType[10][10];4DeclaringVariablesofTwo-dimensionalArraysandCreatingTwo-dimensionalArraysint[][]matrix=newint[10][10];orintmatrix[][]=newint[10][10];matrix[0][0]=3;for(inti=0;i<matrix.length;i++)for(intj=0;j<matrix[i].length;j++)matrix[i][j]=(int)(Math.random()*1000);double[][]x;5Two-dimensionalArrayIllustration6array.length?4array[0].length?3matrix.length?5matrix[0].length?5Declaring,Creating,andInitializingUsingShorthandNotationsYoucanalsouseanarrayinitializertodeclare,createandinitializeatwo-dimensionalarray.Forexample,7int[][]array=newint[4][3];array[0][0]=1;array[0][1]=2;array[0][2]=3;array[1][0]=4;array[1][1]=5;array[1][2]=6;array[2][0]=7;array[2][1]=8;array[2][2]=9;array[3][0]=10;array[3][1]=11;array[3][2]=12;

int[][]array={{1,2,3},{4,5,6},{7,8,9},{10,11,12}};SameasLengthsofTwo-dimensionalArraysint[][]x=newint[3][4];8LengthsofTwo-dimensionalArrays,[][]array={{1,2,3},{4,5,6},{7,8,9},{10,11,12}};9array.lengtharray[0].lengtharray[1].lengtharray[2].lengtharray[3].lengtharray[4].lengthArrayIndexOutOfBoundsExceptionRaggedArraysEachrowinatwo-dimensionalarrayisitselfanarray.So,therowscanhavedifferentlengths.Suchanarrayisknownasaraggedarray.Forexample,int[][]matrix={{1,2,3,4,5},{2,3,4,5},{3,4,5},{4,5},{5}};10matrix.lengthis5matrix[0].lengthis5matrix[1].lengthis4matrix[2].lengthis3matrix[3].lengthis2matrix[4].lengthis1RaggedArrays,cont.11ProcessingTwo-DimensionalArraysSeetheexamplesinthetext.(Initializingarrayswithinputvalues)(Printingarrays)(Summingallelements)(Summingallelementsbycolumn)(Whichrowhasthelargestsum)(Findingthesmallestindexofthelargestelement)(Randomshuffling)12Initializingarrayswithinputvaluesjava.util.Scannerinput=newScanner(System.in);System.out.println("Enter"+matrix.length+"rowsand"+matrix[0].length+"columns:");for(introw=0;row<matrix.length;row++){

for(intcolumn=0;column<matrix[row].length;column++){matrix[row][column]=input.nextInt();}}13Initializingarrayswithrandomvaluesfor(introw=0;row<matrix.length;row++){

for(intcolumn=0;column<matrix[row].length;column++){matrix[row][column]=(int)(Math.random()*100);}}14Printingarraysfor(introw=0;row<matrix.length;row++){

for(intcolumn=0;column<matrix[row].length;column++){System.out.print(matrix[row][column]+"");}System.out.println();}15Summingallelementsinttotal=0;for(introw=0;row<matrix.length;row++){

for(intcolumn=0;column<matrix[row].length;column++){total+=matrix[row][column];}}16Summingelementsbycolumnfor(intcolumn=0;column<matrix[0].length;column++){inttotal=0;for(introw=0;row<matrix.length;row++)total+=matrix[row][column];System.out.println("Sumforcolumn"+column+"is"+total);}17Randomshufflingfor(inti=0;i<matrix.length;i++){

for(intj=0;j<matrix[i].length;j++){

inti1=(int)(Math.random()*matrix.length);

intj1=(int)(Math.random()*matrix[i].length);//Swapmatrix[i][j]withmatrix[i1][j1]inttemp=matrix[i][j];matrix[i][j]=matrix[i1][j1];matrix[i1][j1]=temp;}}18PassingTow-DimensionalArraystoMethods19PassTwoDimensionalArrayRunProblem:GradingMultiple-ChoiceTestObjective:writeaprogramthatgradesmultiple-choicetest.20GradeExamRunProblem:FindingTwoPointsNearesttoEachOther21FindNearestPointsRunWhatisSudoku?22Everyrowcontainsthenumbers1to923Everycolumncontainsthenumbers1to924

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CheckingWhetheraSolutionIsCorrect26RunCheckSudokuSolutionMultidimensionalArraysOccasionally,youwillneedtorepresentn-dimensionaldatastructures.InJava,youcancreaten-dimensionalarraysforanyintegern.

Thewaytodeclaretwo-dimensionalarrayvariablesandcreatetwo-dimensionalarrayscanbegeneralizedtodeclaren-dimensionalarrayvariablesandcreaten-dimensionalarraysforn>=3.Forexample,thefollowingsyntaxdeclares