Difference between revisions of "2D array problem"
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{{1010PrAD|ProblemName=Editing 2D matrix problem | {{1010PrAD|ProblemName=Editing 2D matrix problem | ||
− | |Problem= This problem is a simplified version of problem 11 | + | |Problem= This problem is a simplified version of problem 11 at Project Euler[http://www.projecteuler.net/]. |
+ | |||
+ | Using the provided array find 4 adjacent numbers along any row, column or diagonal with the greatest product. To keep things simple we will only worry about diagonals going down to the right. I have included some skeleton code to make problem a little easier. | ||
For example at row 0, column 0 there are three lines to check.<br> | For example at row 0, column 0 there are three lines to check.<br> | ||
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|SideSectionTitle=More with Arrays | |SideSectionTitle=More with Arrays | ||
|SideSection= | |SideSection= | ||
− | [[Image:Wiki_method01.jpg|center]] | + | [[Image:Wiki_method01.jpg|center]]<BR> |
− | <BR> | + | |
|Solution= | |Solution= | ||
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} | } | ||
</pre> | </pre> | ||
+ | |||
With printing out of the way the next method to write is checkLine. This method checks if a set of numbers is the new highest. The current highest set of number and their product is stored in bestNumbers and bestNumber. Manually check a few lines to make sure you are getting the right results. | With printing out of the way the next method to write is checkLine. This method checks if a set of numbers is the new highest. The current highest set of number and their product is stored in bestNumbers and bestNumber. Manually check a few lines to make sure you are getting the right results. | ||
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</pre> | </pre> | ||
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+ | You're almost there, fill in checkCol, checkDiagonal, and verify that you are getting the right answer.<br><br> | ||
− | + | <b>BONUS</b><br> | |
+ | <ol> | ||
+ | <li> Can you find the line with the highest average?</li> | ||
+ | <li> Whats the best line of length 5?</li> | ||
+ | <li> How about with diagonals going lines down to the left?</li> | ||
+ | </ol> | ||
− | + | ||
+ | |SolutionCode= | ||
public class matrix { | public class matrix { | ||
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====== | ====== | ||
66 x 91 x 88 x 97 = 51267216 | 66 x 91 x 88 x 97 = 51267216 | ||
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}} | }} |
Latest revision as of 14:28, 9 April 2010
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ProblemThis problem is a simplified version of problem 11 at Project Euler[1]. Using the provided array find 4 adjacent numbers along any row, column or diagonal with the greatest product. To keep things simple we will only worry about diagonals going down to the right. I have included some skeleton code to make problem a little easier. For example at row 0, column 0 there are three lines to check.
public class matrix { static final int lineLength = 4; //length of line to check static int[] bestNumbers = new int[lineLength]; //best line found so far static int bestNumber = 0; //product of the best line static final int array[][] ={ { 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8}, {49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0}, {81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65}, {52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91}, {22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80}, {24,47,32,60,99, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50}, {32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70}, {67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21}, {24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72}, {21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95}, {78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92}, {16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57}, {86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58}, {19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40}, {04,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66}, {88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69}, {04,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36}, {20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16}, {20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54}, {01,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48} }; public static void main(String[] args) { for( int row = 0; row < array[0].length; row++ ) { for( int col = 0; col < array.length; col++ ) { checkRow( row, col ); checkCol( row, col ); checkDiagonal( row, col ); } } printLine( bestNumbers, bestNumber ); } //prints a nice output for a provided line public static void printLine( int[] toPrintArray, int toPrintProd ) { } //calculate the product for the line passed //if it the product is better than bestNumber update it public static void checkLine( int[] toCheck ) { } //from (row,col) check product of the row public static void checkRow( int row, int col ) { int[] tempRow = new int[ 4 ]; ... checkLine( tempRow ); } //from (row,col) check product of the column public static void checkCol( int row, int col ) { int[] tempRow = new int[ 4 ]; ... checkLine( tempRow ); } //from (row,col) check product of the diagonal public static void checkDiagonal( int row, int col ) { int[] tempRow = new int[ 4 ]; ... checkLine( tempRow ); } } |
More with Arrays | |
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SolutionFirst a quick overview of how we are going to solve the problem. The main body is a good place to start. The body reads a lot like the description of the problem. The two for loops scan the array, and at each cell we check the row, column and diagonal. public static void main(String[] args) { //for each row for( int row = 0; row < array[0].length; row++ ) { //and each column for( int col = 0; col < array.length; col++ ) { checkRow( row, col ); //check the row starting here checkCol( row, col ); //check the column starting here checkDiagonal( row, col ); //check the diagonal starting here } } //print the best numbers we found printLine( bestNumbers, bestNumber ); }
//prints a nice output for a provided line //8 x 2 x 22 x 97 = 34144 public static void printLine( int[] toPrintArray, int toPrintProd ) { System.out.print( toPrintArray[ 0 ] ); for( int i = 1; i < toPrintArray.length; i++ ) { System.out.print( " x " + toPrintArray[ i ] ); } System.out.println( " = " + toPrintProd ); }
static int[] bestNumbers = new int[lineLength]; static int bestNumber = 0; public static void checkLine( int[] toCheck ) { int tempProduct = 1; for( int i = 0; i < toCheck.length; i++ ) { tempProduct = tempProduct * toCheck[i]; } if( tempProduct > bestNumber ) { bestNumber = tempProduct; bestNumbers = toCheck; } }
//from (row,col) check product of the row public static void checkRow( int row, int col ) { //make sure the row we are checking does not exceed the array row length if( col + lineLength <= array[0].length ) { int[] tempRow = new int[ 4 ]; for( int i = 0; i < lineLength; i++ ) { tempRow[ i ] = array[ row ][ col + i ]; } checkLine( tempRow ); } }//checkRow
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