Espejos máximos que pueden transferir luz de abajo a derecha.
Se proporciona una matriz cuadrada en la que cada celda representa un espacio en blanco o un obstáculo. Podemos colocar espejos en posición en blanco. Todos los espejos estarán situados a 45 grados, es decir, pueden transferir luz de abajo a derecha si no hay ningún obstáculo en su camino.
En esta pregunta necesitamos contar cuántos espejos de este tipo se pueden colocar en una matriz cuadrada que pueda transferir luz de abajo a derecha.
Ejemplos:
Output for above example is 2. In above diagram mirror at (3 1) and (5 5) are able to send light from bottom to right so total possible mirror count is 2.
Podemos resolver este problema verificando la posición de dichos espejos en la matriz; el espejo que puede transferir luz de abajo a la derecha no tendrá ningún obstáculo en su camino, es decir,
si hay un espejo en el índice (i j), entonces
no habrá ningún obstáculo en el índice (k j) para todos los k i < k <= N
no habrá ningún obstáculo en el índice (i k) para todo k j < k <= N
Teniendo en cuenta las dos ecuaciones anteriores, podemos encontrar el obstáculo más a la derecha en cada fila en una iteración de la matriz dada y podemos encontrar el obstáculo más abajo en cada columna en otra iteración de la matriz dada. Después de almacenar estos índices en una matriz separada, podemos verificar en cada índice si no satisface la condición de obstáculo o no y luego aumentar el recuento en consecuencia.
A continuación se implementa la solución según el concepto anterior que requiere O(N^2) tiempo y O(N) espacio adicional.
C++ // C++ program to find how many mirror can transfer // light from bottom to right #include using namespace std ; // method returns number of mirror which can transfer // light from bottom to right int maximumMirrorInMatrix ( string mat [] int N ) { // To store first obstacles horizontally (from right) // and vertically (from bottom) int horizontal [ N ] vertical [ N ]; // initialize both array as -1 signifying no obstacle memset ( horizontal -1 sizeof ( horizontal )); memset ( vertical -1 sizeof ( vertical )); // looping matrix to mark column for obstacles for ( int i = 0 ; i < N ; i ++ ) { for ( int j = N -1 ; j >= 0 ; j -- ) { if ( mat [ i ][ j ] == 'B' ) continue ; // mark rightmost column with obstacle horizontal [ i ] = j ; break ; } } // looping matrix to mark rows for obstacles for ( int j = 0 ; j < N ; j ++ ) { for ( int i = N -1 ; i >= 0 ; i -- ) { if ( mat [ i ][ j ] == 'B' ) continue ; // mark leftmost row with obstacle vertical [ j ] = i ; break ; } } int res = 0 ; // Initialize result // if there is not obstacle on right or below // then mirror can be placed to transfer light for ( int i = 0 ; i < N ; i ++ ) { for ( int j = 0 ; j < N ; j ++ ) { /* if i > vertical[j] then light can from bottom if j > horizontal[i] then light can go to right */ if ( i > vertical [ j ] && j > horizontal [ i ]) { /* uncomment this code to print actual mirror position also cout < < i < < ' ' < < j < < endl; */ res ++ ; } } } return res ; } // Driver code to test above method int main () { int N = 5 ; // B - Blank O - Obstacle string mat [ N ] = { 'BBOBB' 'BBBBO' 'BBBBB' 'BOOBO' 'BBBOB' }; cout < < maximumMirrorInMatrix ( mat N ) < < endl ; return 0 ; }
Java // Java program to find how many mirror can transfer // light from bottom to right import java.util.* ; class GFG { // method returns number of mirror which can transfer // light from bottom to right static int maximumMirrorInMatrix ( String mat [] int N ) { // To store first obstacles horizontally (from right) // and vertically (from bottom) int [] horizontal = new int [ N ] ; int [] vertical = new int [ N ] ; // initialize both array as -1 signifying no obstacle Arrays . fill ( horizontal - 1 ); Arrays . fill ( vertical - 1 ); // looping matrix to mark column for obstacles for ( int i = 0 ; i < N ; i ++ ) { for ( int j = N - 1 ; j >= 0 ; j -- ) { if ( mat [ i ] . charAt ( j ) == 'B' ) { continue ; } // mark rightmost column with obstacle horizontal [ i ] = j ; break ; } } // looping matrix to mark rows for obstacles for ( int j = 0 ; j < N ; j ++ ) { for ( int i = N - 1 ; i >= 0 ; i -- ) { if ( mat [ i ] . charAt ( j ) == 'B' ) { continue ; } // mark leftmost row with obstacle vertical [ j ] = i ; break ; } } int res = 0 ; // Initialize result // if there is not obstacle on right or below // then mirror can be placed to transfer light for ( int i = 0 ; i < N ; i ++ ) { for ( int j = 0 ; j < N ; j ++ ) { /* if i > vertical[j] then light can from bottom if j > horizontal[i] then light can go to right */ if ( i > vertical [ j ] && j > horizontal [ i ] ) { /* uncomment this code to print actual mirror position also cout < < i < < ' ' < < j < < endl; */ res ++ ; } } } return res ; } // Driver code public static void main ( String [] args ) { int N = 5 ; // B - Blank O - Obstacle String mat [] = { 'BBOBB' 'BBBBO' 'BBBBB' 'BOOBO' 'BBBOB' }; System . out . println ( maximumMirrorInMatrix ( mat N )); } } /* This code is contributed by PrinciRaj1992 */
Python3 # Python3 program to find how many mirror can transfer # light from bottom to right # method returns number of mirror which can transfer # light from bottom to right def maximumMirrorInMatrix ( mat N ): # To store first obstacles horizontally (from right) # and vertically (from bottom) horizontal = [ - 1 for i in range ( N )] vertical = [ - 1 for i in range ( N )]; # looping matrix to mark column for obstacles for i in range ( N ): for j in range ( N - 1 - 1 - 1 ): if ( mat [ i ][ j ] == 'B' ): continue ; # mark rightmost column with obstacle horizontal [ i ] = j ; break ; # looping matrix to mark rows for obstacles for j in range ( N ): for i in range ( N - 1 - 1 - 1 ): if ( mat [ i ][ j ] == 'B' ): continue ; # mark leftmost row with obstacle vertical [ j ] = i ; break ; res = 0 ; # Initialize result # if there is not obstacle on right or below # then mirror can be placed to transfer light for i in range ( N ): for j in range ( N ): ''' if i > vertical[j] then light can from bottom if j > horizontal[i] then light can go to right ''' if ( i > vertical [ j ] and j > horizontal [ i ]): ''' uncomment this code to print actual mirror position also''' res += 1 ; return res ; # Driver code to test above method N = 5 ; # B - Blank O - Obstacle mat = [ 'BBOBB' 'BBBBO' 'BBBBB' 'BOOBO' 'BBBOB' ]; print ( maximumMirrorInMatrix ( mat N )); # This code is contributed by rutvik_56.
C# // C# program to find how many mirror can transfer // light from bottom to right using System ; class GFG { // method returns number of mirror which can transfer // light from bottom to right static int maximumMirrorInMatrix ( String [] mat int N ) { // To store first obstacles horizontally (from right) // and vertically (from bottom) int [] horizontal = new int [ N ]; int [] vertical = new int [ N ]; // initialize both array as -1 signifying no obstacle for ( int i = 0 ; i < N ; i ++ ) { horizontal [ i ] =- 1 ; vertical [ i ] =- 1 ; } // looping matrix to mark column for obstacles for ( int i = 0 ; i < N ; i ++ ) { for ( int j = N - 1 ; j >= 0 ; j -- ) { if ( mat [ i ][ j ] == 'B' ) { continue ; } // mark rightmost column with obstacle horizontal [ i ] = j ; break ; } } // looping matrix to mark rows for obstacles for ( int j = 0 ; j < N ; j ++ ) { for ( int i = N - 1 ; i >= 0 ; i -- ) { if ( mat [ i ][ j ] == 'B' ) { continue ; } // mark leftmost row with obstacle vertical [ j ] = i ; break ; } } int res = 0 ; // Initialize result // if there is not obstacle on right or below // then mirror can be placed to transfer light for ( int i = 0 ; i < N ; i ++ ) { for ( int j = 0 ; j < N ; j ++ ) { /* if i > vertical[j] then light can from bottom if j > horizontal[i] then light can go to right */ if ( i > vertical [ j ] && j > horizontal [ i ]) { /* uncomment this code to print actual mirror position also cout < < i < < ' ' < < j < < endl; */ res ++ ; } } } return res ; } // Driver code public static void Main ( String [] args ) { int N = 5 ; // B - Blank O - Obstacle String [] mat = { 'BBOBB' 'BBBBO' 'BBBBB' 'BOOBO' 'BBBOB' }; Console . WriteLine ( maximumMirrorInMatrix ( mat N )); } } // This code is contributed by Princi Singh
JavaScript < script > // JavaScript program to find how many mirror can transfer // light from bottom to right // method returns number of mirror which can transfer // light from bottom to right function maximumMirrorInMatrix ( mat N ) { // To store first obstacles horizontally (from right) // and vertically (from bottom) var horizontal = Array ( N ). fill ( - 1 ); var vertical = Array ( N ). fill ( - 1 ); // looping matrix to mark column for obstacles for ( var i = 0 ; i < N ; i ++ ) { for ( var j = N - 1 ; j >= 0 ; j -- ) { if ( mat [ i ][ j ] == 'B' ) { continue ; } // mark rightmost column with obstacle horizontal [ i ] = j ; break ; } } // looping matrix to mark rows for obstacles for ( var j = 0 ; j < N ; j ++ ) { for ( var i = N - 1 ; i >= 0 ; i -- ) { if ( mat [ i ][ j ] == 'B' ) { continue ; } // mark leftmost row with obstacle vertical [ j ] = i ; break ; } } var res = 0 ; // Initialize result // if there is not obstacle on right or below // then mirror can be placed to transfer light for ( var i = 0 ; i < N ; i ++ ) { for ( var j = 0 ; j < N ; j ++ ) { /* if i > vertical[j] then light can from bottom if j > horizontal[i] then light can go to right */ if ( i > vertical [ j ] && j > horizontal [ i ]) { /* uncomment this code to print actual mirror position also cout < < i < < ' ' < < j < < endl; */ res ++ ; } } } return res ; } // Driver code var N = 5 ; // B - Blank O - Obstacle var mat = [ 'BBOBB' 'BBBBO' 'BBBBB' 'BOOBO' 'BBBOB' ]; document . write ( maximumMirrorInMatrix ( mat N )); < /script>
Producción
2
Complejidad del tiempo: O (n 2 ).
Espacio auxiliar: O(n)
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