Egy négyzetes mátrixot adunk meg, amelyben minden cella üres vagy akadályt jelöl. A tükröket üres pozícióba helyezhetjük. Minden tükör 45 fokos szögben helyezkedik el, azaz alulról jobbra továbbítják a fényt, ha nincs akadály az útjukban.
Ebben a kérdésben meg kell számolnunk, hogy hány olyan tükör helyezhető el négyzetmátrixban, amely alulról jobbra képes fényt továbbítani.
Példák:
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.
Ezt a problémát úgy tudjuk megoldani, hogy ellenőrizzük az ilyen tükrök helyzetét a mátrixban, a fényt alulról jobbra továbbító tükörnek nem lesz akadálya, pl.
ha egy tükör ott van az (i j) indexnél, akkor
a (k j) indexnél nem lesz akadály minden k i-re< k <= N
nem lesz akadály az (i k) indexnél minden k j esetén< k <= N
A fenti két egyenletet szem előtt tartva az adott mátrix egyik iterációjában minden sorában megtalálhatjuk a jobb szélső akadályt, és az adott mátrix egy másik iterációjában minden oszlopban a legalsó akadályt. Miután ezeket az indexeket külön tömbben tároltuk, minden indexnél ellenőrizhetjük, hogy nem teljesíti-e az akadályfeltételt vagy sem, majd ennek megfelelően növeljük a számot.
Az alábbiakban a fenti koncepcióra implementált megoldást mutatjuk be, amely O(N^2) időt és O(N) extra helyet igényel.
C++// C++ program to find how many mirror can transfer // light from bottom to right #include
// 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 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# 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
<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>
Kimenet
2
Időbonyolultság: O(n2).
Segédtér: O(n)