Matrixvermenigvuldiging | Recursief
Gegeven twee matrices A en B. De taak is om matrix A en matrix B recursief te vermenigvuldigen. Als matrix A en matrix B niet multiplicatief compatibel zijn, genereer dan uitvoer 'Niet mogelijk'.
Voorbeelden:
Input: A = 12 56
45 78
B = 2 6
5 8
Output: 304 520
480 894
Input: A = 1 2 3
4 5 6
7 8 9
B = 1 2 3
4 5 6
7 8 9
Output: 30 36 42
66 81 96
102 126 150
Het is raadzaam om eerst te verwijzen Iteratieve matrixvermenigvuldiging .
Controleer eerst of vermenigvuldiging tussen matrices mogelijk is of niet. Controleer hiervoor of het aantal kolommen van de eerste matrix gelijk is aan het aantal rijen van de tweede matrix of niet. Als beide gelijk zijn, ga dan verder en genereer anders uitvoer 'Niet mogelijk'.
Bij recursieve matrixvermenigvuldiging implementeren we drie iteratielussen via recursieve aanroepen. De innerlijke meest recursieve oproep van vermenigvuldigMatrix() is het herhalen van k (col1 of rij2). De tweede recursieve aanroep van vermenigvuldigMatrix() is om de kolommen te veranderen en de buitenste recursieve oproep is om rijen te veranderen.
Hieronder vindt u de recursieve matrixvermenigvuldigingscode.
C++Java// Recursive code for Matrix Multiplication #includeconst int MAX = 100 ; void multiplyMatrixRec ( int row1 int col1 int A [][ MAX ] int row2 int col2 int B [][ MAX ] int C [][ MAX ]) { // Note that below variables are static // i and j are used to know current cell of // result matrix C[][]. k is used to know // current column number of A[][] and row // number of B[][] to be multiplied static int i = 0 j = 0 k = 0 ; // If all rows traversed. if ( i >= row1 ) return ; // If i < row1 if ( j < col2 ) { if ( k < col1 ) { C [ i ][ j ] += A [ i ][ k ] * B [ k ][ j ]; k ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } k = 0 ; j ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } j = 0 ; i ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } // Function to multiply two matrices A[][] and B[][] void multiplyMatrix ( int row1 int col1 int A [][ MAX ] int row2 int col2 int B [][ MAX ]) { if ( row2 != col1 ) { printf ( 'Not Possible n ' ); return ; } int C [ MAX ][ MAX ] = { 0 }; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); // Print the result for ( int i = 0 ; i < row1 ; i ++ ) { for ( int j = 0 ; j < col2 ; j ++ ) printf ( '%d ' C [ i ][ j ]); printf ( ' n ' ); } } // Driven Program int main () { int A [][ MAX ] = { { 1 2 3 } { 4 5 6 } { 7 8 9 } }; int B [][ MAX ] = { { 1 2 3 } { 4 5 6 } { 7 8 9 } }; int row1 = 3 col1 = 3 row2 = 3 col2 = 3 ; multiplyMatrix ( row1 col1 A row2 col2 B ); return 0 ; } // This code is contributed by Aarti_Rathi Python3// Java recursive code for Matrix Multiplication class GFG { public static int MAX = 100 ; // Note that below variables are static // i and j are used to know current cell of // result matrix C[][]. k is used to know // current column number of A[][] and row // number of B[][] to be multiplied public static int i = 0 j = 0 k = 0 ; static void multiplyMatrixRec ( int row1 int col1 int A [][] int row2 int col2 int B [][] int C [][] ) { // If all rows traversed if ( i >= row1 ) return ; // If i < row1 if ( j < col2 ) { if ( k < col1 ) { C [ i ][ j ] += A [ i ][ k ] * B [ k ][ j ] ; k ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } k = 0 ; j ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } j = 0 ; i ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } // Function to multiply two matrices A[][] and B[][] static void multiplyMatrix ( int row1 int col1 int A [][] int row2 int col2 int B [][] ) { if ( row2 != col1 ) { System . out . println ( 'Not Possiblen' ); return ; } int [][] C = new int [ MAX ][ MAX ] ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); // Print the result for ( int i = 0 ; i < row1 ; i ++ ) { for ( int j = 0 ; j < col2 ; j ++ ) System . out . print ( C [ i ][ j ]+ ' ' ); System . out . println (); } } // driver program public static void main ( String [] args ) { int row1 = 3 col1 = 3 row2 = 3 col2 = 3 ; int A [][] = { { 1 2 3 } { 4 5 6 } { 7 8 9 }}; int B [][] = { { 1 2 3 } { 4 5 6 } { 7 8 9 } }; multiplyMatrix ( row1 col1 A row2 col2 B ); } } // Contributed by Pramod KumarC## Recursive code for Matrix Multiplication MAX = 100 i = 0 j = 0 k = 0 def multiplyMatrixRec ( row1 col1 A row2 col2 B C ): # Note that below variables are static # i and j are used to know current cell of # result matrix C[][]. k is used to know # current column number of A[][] and row # number of B[][] to be multiplied global i global j global k # If all rows traversed. if ( i >= row1 ): return # If i < row1 if ( j < col2 ): if ( k < col1 ): C [ i ][ j ] += A [ i ][ k ] * B [ k ][ j ] k += 1 multiplyMatrixRec ( row1 col1 A row2 col2 B C ) k = 0 j += 1 multiplyMatrixRec ( row1 col1 A row2 col2 B C ) j = 0 i += 1 multiplyMatrixRec ( row1 col1 A row2 col2 B C ) # Function to multiply two matrices # A[][] and B[][] def multiplyMatrix ( row1 col1 A row2 col2 B ): if ( row2 != col1 ): print ( 'Not Possible' ) return C = [[ 0 for i in range ( MAX )] for i in range ( MAX )] multiplyMatrixRec ( row1 col1 A row2 col2 B C ) # Print the result for i in range ( row1 ): for j in range ( col2 ): print ( C [ i ][ j ] end = ' ' ) print () # Driver Code A = [[ 1 2 3 ] [ 4 5 6 ] [ 7 8 9 ]] B = [[ 1 2 3 ] [ 4 5 6 ] [ 7 8 9 ]] row1 = 3 col1 = 3 row2 = 3 col2 = 3 multiplyMatrix ( row1 col1 A row2 col2 B ) # This code is contributed by sahilshelangiaJavaScript// C# recursive code for // Matrix Multiplication using System ; class GFG { public static int MAX = 100 ; // Note that below variables // are static i and j are used // to know current cell of result // matrix C[][]. k is used to // know current column number of // A[][] and row number of B[][] // to be multiplied public static int i = 0 j = 0 k = 0 ; static void multiplyMatrixRec ( int row1 int col1 int [] A int row2 int col2 int [] B int [] C ) { // If all rows traversed if ( i >= row1 ) return ; // If i < row1 if ( j < col2 ) { if ( k < col1 ) { C [ i j ] += A [ i k ] * B [ k j ]; k ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } k = 0 ; j ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } j = 0 ; i ++ ; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); } // Function to multiply two // matrices A[][] and B[][] static void multiplyMatrix ( int row1 int col1 int [] A int row2 int col2 int [] B ) { if ( row2 != col1 ) { Console . WriteLine ( 'Not Possiblen' ); return ; } int [] C = new int [ MAX MAX ]; multiplyMatrixRec ( row1 col1 A row2 col2 B C ); // Print the result for ( int i = 0 ; i < row1 ; i ++ ) { for ( int j = 0 ; j < col2 ; j ++ ) Console . Write ( C [ i j ] + ' ' ); Console . WriteLine (); } } // Driver Code static public void Main () { int row1 = 3 col1 = 3 row2 = 3 col2 = 3 ; int [] A = {{ 1 2 3 } { 4 5 6 } { 7 8 9 }}; int [] B = {{ 1 2 3 } { 4 5 6 } { 7 8 9 }}; multiplyMatrix ( row1 col1 A row2 col2 B ); } } // This code is contributed by m_kit
Uitvoer30 36 42 66 81 96 102 126 150Tijdcomplexiteit: O(rij1 * col2* col1)
Hulpruimte: O(log (max(rij1col2)) Omdat impliciete stapel wordt gebruikt vanwege recursieQuiz maken
