JavaScript program to check horizontal and vertical symmetry in binary matrices

A binary matrix is ​​a two-dimensional array containing only 1 and 0 elements in each cell. The horizontal symmetry of a binary matrix means that if the first row is the same as the last row, the second row is the same as the second-to-last row, and so on. Similarly, vertical symmetry means whether the first and last columns, the second to last column and the second to last column, etc. are the same. In this problem, we are given a matrix and we will detect whether there is horizontal and vertical symmetry in it.

Enter

1 0 1
0 0 0 
1 0 1 

Output

Both, horizontal and vertical symmetry is present. 

Explanation - The first and last rows are the same, which means there is horizontal symmetry. Likewise, the first and last columns are identical, resulting in vertical symmetry.

Enter

1 0 1
0 0 0 
1 1 0 

Output

None of the symmetry is present.

Explanation- The first row is not equal to the last row, and the first column is not equal to the last column.

method

We have seen examples to understand the given problem, now let us see the steps to implement the code -

• First, we will define a function to check the horizontal symmetry of a given matrix. This function will take a single argument of the given matrix and return whether the current matrix is ​​horizontally symmetric.

• We will iterate over the matrix and for each row we will compare to the row on the other side of an imaginary line that goes through the middle of the matrix and is the same distance from the current row. p>

• We will define a function to check the vertical symmetry of a given matrix. This function will take one argument, the given matrix.

• We will iterate through the matrix and for each column we will compare to the column on the other side of an imaginary line that goes through the middle of the matrix and is the same distance from the current column. p>

• We will call these two functions and print the results based on the return value.

Example

// function to check horizontal symmetry 
function horizontalSymm(mat){
   var rows = mat.length;
   var cols = mat[0].length; 
   for(var i = 0; i< rows/2; i++){
      for(var j = 0;j<cols; j++){
         if(mat[i][j] != mat[rows-i-1][j]){
            return false;
         }
      }
   }
   return true;
}

// function to check vertical symmetry 
function verticalSymm(mat){
   var rows = mat.length;
   var cols = mat[0].length; 
   for(var i = 0; i< cols/2; i++){
      for(var j = 0;j<rows; j++){
         if(mat[j][i] != mat[j][cols-i-1]){
            return false;
         }
      }
   }
   return true;
}

// function to check the symmetry of the given matrix 
function check(mat){
   var horSymm = horizontalSymm(mat);
   var varSymm = verticalSymm(mat);
   if(horSymm && varSymm){
      console.log("Both, horizontal and vertical symmetries are present in the given matrix");
   }
   else if(horSymm){
      console.log("The given binary matrix is only horizontally symmetric");
   }
   else if(varSymm){
      console.log("The given binary matrix is only vertically symmetric");
   }
   else{
      console.log("The given binary matrix is neither horizontally symmetric nor vertically symmetric");
   }
}

// defining the given matrix 
var mat = [[1, 0, 1], [0, 0, 0], [1, 0, 1]];
console.log("The given matrix is: ")
console.log(mat);
check(mat);

// defining the given matrix 
var mat = [[1, 0, 1], [0, 0, 0], [1, 1, 0]];
console.log("The given matrix is: ")
console.log(mat);
check(mat);

Output

The given matrix is: 
[ [ 1, 0, 1 ], [ 0, 0, 0 ], [ 1, 0, 1 ] ]
Both, horizontal and vertical symmetries are present in the given matrix
The given matrix is: 
[ [ 1, 0, 1 ], [ 0, 0, 0 ], [ 1, 1, 0 ] ]
The given binary matrix is neither horizontally symmetric nor vertically symmetric

Time and space complexity

The time complexity of the above code is O(N*M), where N is the number of rows of the given matrix and M is the number of columns of the given matrix. We will traverse the entire matrix twice, once for horizontal symmetry and once for vertical symmetry.

The space complexity of the above code is O(1) because we are not using any extra space.

in conclusion

In this tutorial, we implemented a JavaScript program to find, given a matrix, whether the current matrix is ​​horizontally or vertically symmetrical. The horizontal symmetry of a binary matrix means that if the first row is identical to the last row, then the second row is identical to the second-to-last row, and so on. Similarly, vertical symmetry means whether the first and last columns, the second to last column and the second to last column, etc. are the same. We implemented a program with time complexity O(N*M) and space complexity O(1).

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