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Skontrolujte horizontálnu a vertikálnu symetriu v binárnej matici

Daná 2D binárna matica N riadky a M stĺpci. Úlohou je skontrolovať, či je matica horizontálne symetrická vertikálne symetrická alebo oboje. Matica sa považuje za horizontálnu symetrickú, ak je prvý riadok rovnaký ako posledný riadok, druhý riadok je rovnaký ako predposledný riadok atď. A o matici sa hovorí, že je vertikálne symetrická, ak je prvý stĺpec rovnaký ako posledný stĺpec, druhý stĺpec je rovnaký ako predposledný stĺpec atď.

Tlačiť VERTIKÁLNY " ak je matica vertikálne symetrická " HORIZONTÁLNY " ak je matica vertikálne symetrická " OBOJE " ak je matica vertikálna a horizontálna symetrická a " NIE “ ak nie sú symetrické.

Príklady:   



Vstup: N = 3 M = 3
0 1 0
0 0 0
0 1 0
výstup: Obaja
Vysvetlenie: Prvý a tretí rad sú rovnaké a aj druhý rad je v strede. Takže horizontálne symetrické. Podobne prvý a tretí stĺpec sú rovnaké a aj druhý stĺpec je v strede, takže vertikálne symetrický.

java na prestávku

Vstup: N = 3 M = 3
0 0 1
1 1 0
0 0 1
výstup: Obaja 

Prístup: Myšlienkou je použiť ukazovatele označujúce dva riadky (alebo stĺpce) a porovnať každú bunku oboch označených riadkov (alebo stĺpcov). 

  • Pre horizontálnu symetriu inicializujte jeden ukazovateľ i = 0 a ďalší ukazovateľ j = N - 1. 
  • Teraz porovnajte každý prvok i-tého a j-tého riadku. Zvýšte i o 1 a znížte j o 1 v každom cykle slučky. 
    • Ak sa nájde aspoň jeden neidentický prvok, označte maticu ako nie horizontálne symetrickú.
  • Podobne pre vertikálnu symetriu inicializujte jeden ukazovateľ i = 0 a ďalší ukazovateľ j = M - 1. 
  • Teraz porovnajte každý prvok i-tého stĺpca a j-tého stĺpca. Zvýšte i o 1 a znížte j o 1 v každom cykle slučky. 
    • Ak sa nájde aspoň jeden neidentický prvok, označte maticu ako nie vertikálne symetrickú.

Nižšie je uvedená implementácia vyššie uvedenej myšlienky: 

konečné kľúčové slovo v jazyku Java
C++
// C++ program to find if a matrix is symmetric. #include    #define MAX 1000 using namespace std; void checkHV(int arr[][MAX] int N int M) {  // Initializing as both horizontal and vertical  // symmetric.  bool 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 (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]) {  vertical = false;  break;  }  }  }  if (!horizontal && !vertical)  cout << 'NOn';  else if (horizontal && !vertical)  cout << 'HORIZONTALn';  else if (vertical && !horizontal)  cout << 'VERTICALn';  else  cout << 'BOTHn'; } // Driven Program int main() {  int mat[MAX][MAX]  = { { 0 1 0 } { 0 0 0 } { 0 1 0 } };  checkHV(mat 3 3);  return 0; } 
Java
// 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
# 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#
// 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
 // 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.  ?> 
JavaScript
<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> 

Výstup
BOTH

Časová zložitosť: O(N*M).
Pomocný priestor: O(1)


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