Given a square matrix and the task is to check the matrix is in lower triangular form or not. A square matrix is called lower triangular if all the entries above the main diagonal are zero.
Examples:
Input : mat[4][4] = {{1, 0, 0, 0},
{1, 4, 0, 0},
{4, 6, 2, 0},
{0, 4, 7, 6}};
Output : Matrix is in lower triangular form.
Input : mat[4][4] = {{1, 0, 0, 0},
{4, 3, 0, 1},
{7, 9, 2, 0},
{8, 5, 3, 6}};
Output : Matrix is not in lower triangular form.
PHP
<?php// PHP Program to check lower// triangular matrix.$N = 4;// Function to check matrix is in // lower triangular form or not.function isLowerTriangularMatrix($mat){ global $N; for ($i = 0; $i < $N; $i++) for ($j = $i + 1; $j < $N; $j++) if ($mat[$i][$j] != 0) return false; return true;}// Driver Code$mat = array(array( 1, 0, 0, 0 ), array( 1, 4, 0, 0 ), array( 4, 6, 2, 0 ), array( 0, 4, 7, 6 )); // Function callif (isLowerTriangularMatrix($mat)) echo("Yes");else echo("No");// This code is contributed by Ajit.?> |
Output:
Yes
Time Complexity: O(n2), where n represents the number of rows and columns of the given 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 lower triangular for more details!
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