Màxim miralls que poden transferir la llum de baix a dreta
Es dóna una matriu quadrada en la qual cada cel·la representa un espai en blanc o un obstacle. Podem col·locar miralls en posició en blanc. Tots els miralls estaran situats a 45 graus, és a dir, poden transferir la llum de baix a dreta si no hi ha cap obstacle al seu camí.
En aquesta pregunta hem de comptar quants miralls es poden col·locar en una matriu quadrada que pot transferir la llum de baix a dreta.
Exemples:
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.
Podem resoldre aquest problema comprovant la posició d'aquests miralls a la matriu, el mirall que pot transferir la llum de baix a dreta no tindrà cap obstacle al seu pas, és a dir.
si hi ha un mirall a l'índex (i j), aleshores
no hi haurà cap obstacle a l'índex (k j) per a tots els k i < k <= N
no hi haurà cap obstacle a l'índex (i k) per a tots els k j < k <= N
Tenint en compte dues equacions per sobre, podem trobar l'obstacle més a la dreta a cada fila d'una iteració de la matriu donada i podem trobar l'obstacle més baix a cada columna en una altra iteració de la matriu donada. Després d'emmagatzemar aquests índexs en una matriu separada, podem comprovar a cada índex si no compleix cap condició d'obstacle o no i després augmentar el recompte en conseqüència.
A continuació s'implementa la solució del concepte anterior que requereix O (N ^ 2) temps i O (N) espai addicional.
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>
Sortida
2
Complexitat temporal: O(n 2 ).
Espai auxiliar: O(n)
Crea un qüestionari
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