Matricos daugyba | Rekursyvus
Duotos dvi matricos A ir B. Užduotis – rekursyviai padauginti matricą A ir matricą B. Jei matrica A ir matrica B nesuderinamos su dauginimu, generuokite išvestį „Neįmanoma“.
Pavyzdžiai:
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
Pirmiausia rekomenduojama kreiptis Iteratyvus matricos dauginimas .
Pirmiausia patikrinkite, ar galima dauginti tarp matricų, ar ne. Norėdami tai padaryti, patikrinkite, ar pirmosios matricos stulpelių skaičius yra lygus antrosios matricos eilučių skaičiui, ar ne. Jei abu yra lygūs, tęskite toliau, kitaip generuokite išvestį „Neįmanoma“.
Rekursyvinėje matricos daugyboje mes įgyvendiname tris iteracijos kilpas per rekursinius skambučius. Vidinis labiausiai rekursyvus skambutis multiplyMatrix () yra kartoti k (col1 arba row2). Antrasis rekursinis skambutis multiplyMatrix () yra pakeisti stulpelius, o atokiausias rekursinis kvietimas yra pakeisti eilutes.
Žemiau yra rekursinės matricos daugybos kodas.
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
Išvestis30 36 42 66 81 96 102 126 150Laiko sudėtingumas: O(1 eilutė * stulpelis 2 * stulpelis1)
Pagalbinė erdvė: O(log (maks.(1 eilė2)) Kaip implicit stack naudojamas dėl rekursijosSukurti viktoriną
