Donada una matriu binària 2D de N files i M columnes. La tasca és comprovar si la matriu és horitzontal simètrica vertical simètrica o ambdues coses. Es diu que la matriu és simètrica horitzontal si la primera fila és la mateixa que l'última fila, la segona fila és la mateixa que l'última fila i així successivament. I es diu que la matriu és simètrica vertical si la primera columna és la mateixa que l'última columna, la segona columna és la mateixa que la segona darrera columna i així successivament.
Imprimeix ' VERTICAL 'si la matriu és simètrica verticalment' HORIZONTAL 'si la matriu és simètrica verticalment' Tots dos 'si la matriu és simètrica vertical i horitzontal i' NO si no és simètric.
alfabet en nombres
Exemples:
Entrada: N = 3 M = 3
0 1 0
0 0 0
0 1 0
Sortida: Tots dos
Explicació: La primera i la tercera fila són iguals i també la segona fila està al mig. Així, simètric horitzontal. De la mateixa manera, la primera i la tercera columna són iguals i la segona columna es troba al mig, de manera que simètrica vertical.Entrada: N = 3 M = 3
0 0 1
1 1 0
0 0 1
Sortida: Tots dos
Enfocament: La idea és utilitzar punters que indiquin dues files (o columnes) i comparar cada cel·la de les dues files (o columnes).
- Per a la simetria horitzontal, inicialitzeu un punter i = 0 i un altre punter j = N - 1.
- Ara compareu cada element de la fila i i la fila j. Augmenta i en 1 i disminueix j en 1 en cada cicle de bucle.
- Si es troba almenys un element no idèntic, marqueu la matriu com a no simètrica horitzontal.
- De la mateixa manera, per a la simetria vertical, inicialitzeu un punter i = 0 i un altre punter j = M - 1.
- Ara compareu cada element de la columna i i la columna j. Augmenta i en 1 i disminueix j en 1 en cada cicle de bucle.
- Si es troba almenys un element no idèntic, marqueu la matriu com a no simètrica vertical.
A continuació es mostra la implementació de la idea anterior:
C++// C++ program to find if a matrix is symmetric. #include
// Java program to find if // a matrix is symmetric. import java.io.*; public class GFG { static void checkHV(int[][] arr int N int M) { // Initializing as both horizontal // and vertical symmetric. boolean horizontal = true; boolean vertical = true; // Checking for Horizontal Symmetry. // We compare first row with last // row second row with second // last row and so on. for (int i = 0 k = N - 1; i < N / 2; i++ k--) { // Checking each cell of a column. for (int j = 0; j < M; j++) { // check if every cell is identical if (arr[i][j] != arr[k][j]) { horizontal = false; break; } } } // Checking for Vertical Symmetry. We compare // first column with last column second column // with second last column and so on. for (int j = 0 k = M - 1; j < M / 2; j++ k--) { // Checking each cell of a row. for (int i = 0; i < N; i++) { // check if every cell is identical if (arr[i][j] != arr[i][k]) { horizontal = false; break; } } } if (!horizontal && !vertical) System.out.println('NO'); else if (horizontal && !vertical) System.out.println('HORIZONTAL'); else if (vertical && !horizontal) System.out.println('VERTICAL'); else System.out.println('BOTH'); } // Driver Code static public void main(String[] args) { int[][] mat = { { 1 0 1 } { 0 0 0 } { 1 0 1 } }; checkHV(mat 3 3); } } // This code is contributed by vt_m.
# Python3 program to find if a matrix is symmetric. MAX = 1000 def checkHV(arr N M): # Initializing as both horizontal and vertical # symmetric. horizontal = True vertical = True # Checking for Horizontal Symmetry. We compare # first row with last row second row with second # last row and so on. i = 0 k = N - 1 while(i < N // 2): # Checking each cell of a column. for j in range(M): # check if every cell is identical if (arr[i][j] != arr[k][j]): horizontal = False break i += 1 k -= 1 # Checking for Vertical Symmetry. We compare # first column with last column second column # with second last column and so on. i = 0 k = M - 1 while(j < M // 2): # Checking each cell of a row. for i in range(N): # check if every cell is identical if (arr[i][j] != arr[i][k]): vertical = False break j += 1 k -= 1 if (not horizontal and not vertical): print('NO') elif (horizontal and not vertical): print('HORIZONTAL') elif (vertical and not horizontal): print('VERTICAL') else: print('BOTH') # Driver code mat = [[1 0 1] [0 0 0] [1 0 1]] checkHV(mat 3 3) # This code is contributed by shubhamsingh10
// C# program to find if // a matrix is symmetric. using System; public class GFG { static void checkHV(int[ ] arr int N int M) { // Initializing as both horizontal // and vertical symmetric. bool horizontal = true; bool vertical = true; // Checking for Horizontal Symmetry. // We compare first row with last // row second row with second // last row and so on. for (int j = 0 k = N - 1; j < N / 2; j++ k--) { // Checking each cell of a column. for (int i = 0; i < M; i++) { // check if every cell is identical if (arr[i j] != arr[i k]) { horizontal = false; break; } } } // Checking for Vertical Symmetry. We compare // first column with last column second column // with second last column and so on. for (int i = 0 k = M - 1; i < M / 2; i++ k--) { // Checking each cell of a row. for (int j = 0; j < N; j++) { // check if every cell is identical if (arr[i j] != arr[k j]) { horizontal = false; break; } } } if (!horizontal && !vertical) Console.WriteLine('NO'); else if (horizontal && !vertical) Console.WriteLine('HORIZONTAL'); else if (vertical && !horizontal) Console.WriteLine('VERTICAL'); else Console.WriteLine('BOTH'); } // Driver Code static public void Main() { int[ ] mat = { { 1 0 1 } { 0 0 0 } { 1 0 1 } }; checkHV(mat 3 3); } } // This code is contributed by vt_m.
// PHP program to find if // a matrix is symmetric. function checkHV($arr $N $M) { // Initializing as both horizontal // and vertical symmetric. $horizontal = true; $vertical = true; // Checking for Horizontal Symmetry. // We compare first row with last row // second row with second last row // and so on. for ($i = 0 $k = $N - 1; $i < $N / 2; $i++ $k--) { // Checking each cell of a column. for ($j = 0; $j < $M; $j++) { // check if every cell is identical if ($arr[$i][$j] != $arr[$k][$j]) { $horizontal = false; break; } } } // Checking for Vertical Symmetry. // We compare first column with // last column second column with // second last column and so on. for ($j = 0 $k = $M - 1; $j < $M / 2; $j++ $k--) { // Checking each cell of a row. for ($i = 0; $i < $N; $i++) { // check if every cell is identical if ($arr[$i][$j] != $arr[$i][$k]) { $horizontal = false; break; } } } if (!$horizontal && !$vertical) echo 'NOn'; else if ($horizontal && !$vertical) cout << 'HORIZONTALn'; else if ($vertical && !$horizontal) echo 'VERTICALn'; else echo 'BOTHn'; } // Driver Code $mat = array(array (1 0 1) array (0 0 0) array (1 0 1)); checkHV($mat 3 3); // This code is contributed by nitin mittal. ?> <script> // Javascript program to find if // a matrix is symmetric. function checkHV(arr N M) { // Initializing as both horizontal // and vertical symmetric. let horizontal = true; let vertical = true; // Checking for Horizontal Symmetry. // We compare first row with last // row second row with second // last row and so on. for (let i = 0 k = N - 1; i < parseInt(N / 2 10); i++ k--) { // Checking each cell of a column. for (let j = 0; j < M; j++) { // check if every cell is identical if (arr[i][j] != arr[k][j]) { horizontal = false; break; } } } // Checking for Vertical Symmetry. We compare // first column with last column second column // with second last column and so on. for (let j = 0 k = M - 1; j < parseInt(M / 2 10); j++ k--) { // Checking each cell of a row. for (let i = 0; i < N; i++) { // check if every cell is identical if (arr[i][j] != arr[i][k]) { horizontal = false; break; } } } if (!horizontal && !vertical) document.write('NO'); else if (horizontal && !vertical) document.write('HORIZONTAL'); else if (vertical && !horizontal) document.write('VERTICAL'); else document.write('BOTH'); } let mat = [ [ 1 0 1 ] [ 0 0 0 ] [ 1 0 1 ] ]; checkHV(mat 3 3); </script>
Sortida
BOTH
Complexitat temporal: O(N*M).
Espai auxiliar: O(1)