Kopējais visu nulles pārklājums binārā matricā
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#practiceLinkDiv { display: none !important; } Ņemot vērā bināro matricu, kas satur tikai 0 un 1, mums ir jāatrod visu matricas nulles pārklājuma summa, kur pārklājums konkrētai 0 ir definēts kā kopējais vieninieku skaits ap nulli virzienā pa kreisi, pa labi un uz leju. Tie var atrasties jebkurā vietā, līdz stūris norāda virzienā.
Piemēri:
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 = 8 Recommended Practice Visu nulles pārklājums binārajā matricā Izmēģiniet to! A vienkāršs risinājums Lai atrisinātu šo problēmu, neatkarīgi skaitot vieniniekus ap nullēm, t.i., mēs veicam cilpu četras reizes katrā virzienā katrai šūnai dotajai matricai. Ikreiz, kad jebkurā cilpā atrodam 1, mēs pārtraucam cilpu un palielinām rezultātu par 1.
An efektīvs risinājums ir rīkoties šādi.
- Pārvietojiet visas rindas no kreisās uz labo pusi, ja jau ir redzams 1 (pašreizējā pārvietošanā) un pašreizējais elements ir 0.
- Pārvietojiet visas rindas no labās puses uz kreiso, palielinot rezultātu, ja jau ir redzams 1 (pašreizējā šķērsošanā) un pašreizējais elements ir 0.
- Pārvietojiet visas kolonnas no augšas uz leju, palielinot rezultātu, ja jau ir redzams 1 (pašreizējā pārvietošanā) un pašreizējais elements ir 0.
- Pārvietojiet visas kolonnas no apakšas uz augšu, palielinot rezultātu, ja jau ir redzams 1 (pašreizējā šķērsošanā) un pašreizējais elements ir 0.
Zemāk esošajā kodā tiek ņemts Būla mainīgais isOne, kas tiek padarīts patiess, tiklīdz tiek sastapts viens pašreizējā šķērsošanas laikā visām nullēm pēc tam, kad iterācijas rezultāts tiek palielināts ar vienu un to pašu procedūru piemēro visos četros virzienos, lai iegūtu galīgo atbildi. Mēs atiestatām isOne uz false pēc katras šķērsošanas.
C++ // C++ program to get total coverage of all zeros in // a binary matrix #include using namespace std ; #define R 4 #define C 4 // Returns total coverage of all zeros in mat[][] int getTotalCoverageOfMatrix ( int mat [ R ][ C ]) { int res = 0 ; // looping for all rows of matrix for ( int i = 0 ; i < R ; i ++ ) { bool isOne = false ; // 1 is not seen yet // 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 ++ ) { bool isOne = false ; // 1 is not seen yet 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 to test above methods int main () { int mat [ R ][ C ] = {{ 0 0 0 0 } { 1 0 0 1 } { 0 1 1 0 } { 0 1 0 0 } }; cout < < getTotalCoverageOfMatrix ( mat ); return 0 ; }
Java // 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 # 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# // 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 [ 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 bool 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 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.
JavaScript < 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>
Izvade
20
Laika sarežģītība: O(n 2 )
Palīgtelpa: O(1)
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