#practiceLinkDiv { mostrar: cap !important; }Donada una matriu binària que només conté 0 i 1, hem de trobar la suma de la cobertura de tots els zeros de la matriu on la cobertura d'un 0 particular es defineix com el nombre total d'uns al voltant d'un zero en les direccions esquerra, dreta, amunt i avall. Els poden estar a qualsevol lloc fins a la cantonada en una direcció.
cadena a int
Exemples:
Input : mat[][] = {0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0} Output : 20 First four zeros are surrounded by only one 1. So coverage for zeros in first row is 1 + 1 + 1 + 1 Zeros in second row are surrounded by three 1's. Note that there is no 1 above. There are 1's in all other three directions. Coverage of zeros in second row = 3 + 3. Similarly counting for others also we get overall count as below. 1 + 1 + 1 + 1 + 3 + 3 + 2 + 2 + 2 + 2 + 2 = 20 Input : mat[][] = {1 1 1 0 1 0 0 1} Output : 8 Coverage of first zero is 2 Coverages of other two zeros is 3 Total coverage = 2 + 3 + 3 = 8Recommended Practice Cobertura de tots els zeros en una matriu binària Prova-ho! A solució senzilla per resoldre aquest problema és comptant uns al voltant de zeros de manera independent, és a dir, fem un bucle quatre vegades en cada direcció per a cada cel·la per a la matriu donada. Sempre que trobem un 1 en qualsevol bucle, trenquem el bucle i augmentem el resultat en 1.
An solució eficient és fer el següent.
- Travessa totes les files d'esquerra a dreta increment del resultat si ja es veu un 1 (en el recorregut actual) i l'element actual és 0.
- Travessa totes les files de dreta a esquerra increment del resultat si ja es veu un 1 (en el recorregut actual) i l'element actual és 0.
- Recorre totes les columnes de dalt a baix del resultat de l'increment si ja es veu un 1 (en el recorregut actual) i l'element actual és 0.
- Travessa totes les columnes de baix a dalt increment del resultat si ja es veu un 1 (en el recorregut actual) i l'element actual és 0.
Al codi següent es pren una variable booleana isOne que es fa vertadera tan bon punt es troba una en el recorregut actual per a tots els zeros després que el resultat de la iteració s'incrementi mitjançant un mateix procediment que s'aplica en les quatre direccions per obtenir la resposta final. Reiniciem isOne a false després de cada recorregut.
C++// C++ program to get total coverage of all zeros in // a binary matrix #include
// Java program to get total // coverage of all zeros in // a binary matrix import java .io.*; class GFG { static int R = 4; static int C = 4; // Returns total coverage // of all zeros in mat[][] static int getTotalCoverageOfMatrix(int [][]mat) { int res = 0; // looping for all // rows of matrix for (int i = 0; i < R; i++) { // 1 is not seen yet boolean isOne = false; // looping in columns from // left to right direction // to get left ones for (int j = 0; j < C; j++) { // If one is found // from left if (mat[i][j] == 1) isOne = true; // If 0 is found and we // have found a 1 before. else if (isOne) res++; } // Repeat the above // process for right // to left direction. isOne = false; for (int j = C - 1; j >= 0; j--) { if (mat[i][j] == 1) isOne = true; else if (isOne) res++; } } // Traversing across columns // for up and down directions. for (int j = 0; j < C; j++) { // 1 is not seen yet boolean isOne = false; for (int i = 0; i < R; i++) { if (mat[i][j] == 1) isOne = true; else if (isOne) res++; } isOne = false; for (int i = R - 1; i >= 0; i--) { if (mat[i][j] == 1) isOne = true; else if (isOne) res++; } } return res; } // Driver code static public void main (String[] args) { int [][]mat = {{0 0 0 0} {1 0 0 1} {0 1 1 0} {0 1 0 0}}; System.out.println( getTotalCoverageOfMatrix(mat)); } } // This code is contributed by anuj_67.
# Python3 program to get total coverage of all zeros in # a binary matrix R = 4 C = 4 # Returns total coverage of all zeros in mat[][] def getTotalCoverageOfMatrix(mat): res = 0 # looping for all rows of matrix for i in range(R): isOne = False # 1 is not seen yet # looping in columns from left to right # direction to get left ones for j in range(C): # If one is found from left if (mat[i][j] == 1): isOne = True # If 0 is found and we have found # a 1 before. else if (isOne): res += 1 # Repeat the above process for right to # left direction. isOne = False for j in range(C - 1 -1 -1): if (mat[i][j] == 1): isOne = True else if (isOne): res += 1 # Traversing across columns for up and down # directions. for j in range(C): isOne = False # 1 is not seen yet for i in range(R): if (mat[i][j] == 1): isOne = True else if (isOne): res += 1 isOne = False for i in range(R - 1 -1 -1): if (mat[i][j] == 1): isOne = True else if (isOne): res += 1 return res # Driver code mat = [[0 0 0 0][1 0 0 1][0 1 1 0][0 1 0 0]] print(getTotalCoverageOfMatrix(mat)) # This code is contributed by shubhamsingh10
// C# program to get total coverage // of all zeros in a binary matrix using System; class GFG { static int R = 4; static int C = 4; // Returns total coverage of all zeros in mat[][] static int getTotalCoverageOfMatrix(int []mat) { int res = 0; // looping for all rows of matrix for (int i = 0; i < R; i++) { // 1 is not seen yet bool isOne = false; // looping in columns from left to // right direction to get left ones for (int j = 0; j < C; j++) { // If one is found from left if (mat[ij] == 1) isOne = true; // If 0 is found and we // have found a 1 before. else if (isOne) res++; } // Repeat the above process for // right to left direction. isOne = false; for (int j = C-1; j >= 0; j--) { if (mat[ij] == 1) isOne = true; else if (isOne) res++; } } // Traversing across columns // for up and down directions. for (int j = 0; j < C; j++) { // 1 is not seen yet bool isOne = false; for (int i = 0; i < R; i++) { if (mat[ij] == 1) isOne = true; else if (isOne) res++; } isOne = false; for (int i = R-1; i >= 0; i--) { if (mat[ij] == 1) isOne = true; else if (isOne) res++; } } return res; } // Driver code to test above methods static public void Main () { int []mat = {{0 0 0 0} {1 0 0 1} {0 1 1 0} {0 1 0 0}}; Console.WriteLine(getTotalCoverageOfMatrix(mat)); } } // This code is contributed by vt_m.
<script> // Javascript program to get total // coverage of all zeros in // a binary matrix let R = 4; let C = 4; // Returns total coverage // of all zeros in mat[][] function getTotalCoverageOfMatrix(mat) { let res = 0; // looping for all // rows of matrix for (let i = 0; i < R; i++) { // 1 is not seen yet let isOne = false; // looping in columns from // left to right direction // to get left ones for (let j = 0; j < C; j++) { // If one is found // from left if (mat[i][j] == 1) isOne = true; // If 0 is found and we // have found a 1 before. else if (isOne) res++; } // Repeat the above // process for right // to left direction. isOne = false; for (let j = C - 1; j >= 0; j--) { if (mat[i][j] == 1) isOne = true; else if (isOne) res++; } } // Traversing across columns // for up and down directions. for (let j = 0; j < C; j++) { // 1 is not seen yet let isOne = false; for (let i = 0; i < R; i++) { if (mat[i][j] == 1) isOne = true; else if (isOne) res++; } isOne = false; for (let i = R - 1; i >= 0; i--) { if (mat[i][j] == 1) isOne = true; else if (isOne) res++; } } return res; } let mat = [[0 0 0 0] [1 0 0 1] [0 1 1 0] [0 1 0 0]]; document.write(getTotalCoverageOfMatrix(mat)); </script>
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Complexitat temporal: O(n2)
Espai auxiliar: O(1)
pila java
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