يتم إعطاء مصفوفة مربعة تمثل فيها كل خلية إما فراغًا أو عائقًا. يمكننا وضع المرايا في وضع فارغ. سيتم وضع جميع المرايا بزاوية 45 درجة، أي يمكنها نقل الضوء من الأسفل إلى اليمين في حالة عدم وجود أي عائق في طريقها.
في هذا السؤال، علينا حساب عدد المرايا التي يمكن وضعها في مصفوفة مربعة يمكنها نقل الضوء من الأسفل إلى اليمين.
قراءة ملف CSV في جافا
أمثلة:
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.
يمكننا حل هذه المشكلة عن طريق التحقق من موضع هذه المرايا في المصفوفة، فالمرآة التي يمكنها نقل الضوء من الأسفل إلى اليمين لن يكون لها أي عائق في طريقها، أي.
إذا كانت هناك مرآة في الفهرس (i j) إذن
لن يكون هناك أي عائق عند الفهرس (k j) لجميع k i< k <= N
لن يكون هناك عائق عند الفهرس (i k) لجميع k j< k <= N
مع الأخذ في الاعتبار المعادلتين أعلاه، يمكننا العثور على العائق الموجود في أقصى اليمين في كل صف في تكرار واحد لمصفوفة معينة ويمكننا العثور على العائق السفلي في كل عمود في تكرار آخر لمصفوفة معينة. بعد تخزين هذه المؤشرات في مصفوفة منفصلة يمكننا التحقق من كل مؤشر فيما إذا كان لا يفي بأي شرط من العوائق أم لا ثم نزيد العدد وفقًا لذلك.
يوجد أدناه حل مطبق على المفهوم أعلاه والذي يتطلب وقت O(N^2) ومساحة إضافية O(N).
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>
الإخراج
2
تعقيد الوقت: O(n2).
المساحة المساعدة: O(n)