Celkové pokrytie všetkých núl v binárnej matici
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Výstup
#practiceLinkDiv { display: none !important; } Vzhľadom na binárnu maticu, ktorá obsahuje iba 0 a 1, potrebujeme nájsť súčet pokrytia všetkých núl matice, kde pokrytie pre konkrétnu 0 je definované ako celkový počet jednotiek okolo nuly v smere zľava doprava nahor a nadol. Tie môžu byť kdekoľvek až po rohový bod v smere.
Príklady:
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 Pokrytie všetkých núl v binárnej matici Skúste to! A jednoduché riešenie na vyriešenie tohto problému je počítanie jednotiek okolo núl nezávisle, t. j. spustíme slučku štyrikrát v každom smere pre každú bunku pre danú maticu. Kedykoľvek nájdeme 1 v ľubovoľnej slučke, prerušíme slučku a zvýšime výsledok o 1.
An efektívne riešenie je urobiť nasledovné.
- Prejdite všetky riadky zľava doprava a výsledok prírastku, ak je už vidieť 1 (v aktuálnom prechode) a aktuálny prvok je 0.
- Prejdite všetky riadky sprava doľava a výsledok prírastku, ak je už videná 1 (v aktuálnom prechode) a aktuálny prvok je 0.
- Prejdite všetky stĺpce zhora nadol ako výsledok prírastku, ak už je viditeľná 1 (v aktuálnom prechode) a aktuálny prvok je 0.
- Prejdite všetky stĺpce od spodného po horný výsledok prírastku, ak je už vidieť 1 (v aktuálnom prechode) a aktuálny prvok je 0.
V nižšie uvedenom kóde sa berie booleovská premenná isOne, ktorá sa stane pravdivou, akonáhle sa v aktuálnom prechode vyskytne jednotka pre všetky nuly po tom, čo sa výsledok iterácie zvýši jedným rovnakým postupom, ktorý sa použije vo všetkých štyroch smeroch, aby sa získala konečná odpoveď. Po každom prechode resetujeme isOne na hodnotu false.
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>
Výstup
20
Časová zložitosť: O(n 2 )
Pomocný priestor: O(1)
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