Given a square matrix and the task is to check the matrix is in upper triangular form or not. A square matrix is called upper triangular if all the entries below the main diagonal are zero.
Examples:
Input : mat[4][4] = {{1, 3, 5, 3}, {0, 4, 6, 2}, {0, 0, 2, 5}, {0, 0, 0, 6}}; Output : Matrix is in Upper Triangular form. Input : mat[4][4] = {{5, 6, 3, 6}, {0, 4, 6, 6}, {1, 0, 8, 5}, {0, 1, 0, 6}}; Output : Matrix is not in Upper Triangular form.
PHP
<?php // PHP Program to check upper // triangular matrix. $N = 4;
// Function to check matrix is // in upper triangular form or // not. function isUpperTriangularMatrix( $mat )
{ global $N ;
for ( $i = 1; $i < $N ; $i ++)
for ( $j = 0; $j < $i ; $j ++)
if ( $mat [ $i ][ $j ] != 0)
return false;
return true;
} // Driver Code
$mat = array ( array (1, 3, 5, 3),
array (0, 4, 6, 2) ,
array (0, 0, 2, 5),
array (0, 0, 0, 6));
if (isUpperTriangularMatrix( $mat ))
echo "Yes" ;
else
echo "No" ;
// This code is contributed by anuj_67. ?> |
Output:
Yes
Time Complexity: O(n2), where n represents the number of rows and columns of the matrix.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
Please refer complete article on Program to check if matrix is upper triangular for more details!
Recommended Articles