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.
C++
// Program to check lower // triangular matrix. #include <bits/stdc++.h> #define N 4 using namespace std; // Function to check matrix is in // lower triangular form or not. bool isLowerTriangularMatrix(int mat[N][N]) { for (int i = 0; i < N; i++) for (int j = i + 1; j < N; j++) if (mat[i][j] != 0) return false; return true; } // Driver function. int main() { int mat[N][N] = { { 1, 0, 0, 0 }, { 1, 4, 0, 0 }, { 4, 6, 2, 0 }, { 0, 4, 7, 6 } }; // Function call if (isLowerTriangularMatrix(mat)) cout << "Yes"; else cout << "No"; return 0; } |
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Java
// Java Program to check for // a lower triangular matrix. import java.io.*; class Lower_triangular { int N = 4; // Function to check matrix is // in lower triangular form or not. boolean isLowerTriangularMatrix(int mat[][]) { for (int i = 0; i < N; i++) for (int j = i + 1; j < N; j++) if (mat[i][j] != 0) return false; return true; } // Driver function. public static void main(String args[]) { Lower_triangular ob = new Lower_triangular(); int mat[][] = { { 1, 0, 0, 0 }, { 1, 4, 0, 0 }, { 4, 6, 2, 0 }, { 0, 4, 7, 6 } }; // Function call if (ob.isLowerTriangularMatrix(mat)) System.out.println("Yes"); else System.out.println("No"); } } // This code is contributed by Anshika Goyal. |
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Python3
# Python3 Program to check # lower triangular matrix. # Function to check matrix # is in lower triangular def islowertriangular(M): for i in range(0, len(M)): for j in range(i + 1, len(M)): if(M[i][j] != 0): return False return True # Driver function. M = [[1,0,0,0], [1,4,0,0], [4,6,2,0], [0,4,7,6]] if islowertriangular(M): print ("Yes") else: print ("No") # This code is contributed by Anurag Rawat |
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C#
// C# program to check for // a lower triangular matrix. using System; class Lower_triangular { int N = 4; // Function to check matrix is // in lower triangular form or not. bool isLowerTriangularMatrix(int[, ] mat) { for (int i = 0; i < N; i++) for (int j = i + 1; j < N; j++) if (mat[i, j] != 0) return false; return true; } // Driver function. public static void Main() { Lower_triangular ob = new Lower_triangular(); int[, ] mat = { { 1, 0, 0, 0 }, { 1, 4, 0, 0 }, { 4, 6, 2, 0 }, { 0, 4, 7, 6 } }; // Function call if (ob.isLowerTriangularMatrix(mat)) Console.WriteLine("Yes"); else Console.WriteLine("No"); } } // This code is contributed by vt_m. |
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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 $mat = array(array( 1, 0, 0, 0 ), array( 1, 4, 0, 0 ), array( 4, 6, 2, 0 ), array( 0, 4, 7, 6 )); // Function call if (isLowerTriangularMatrix($mat)) echo("Yes"); else echo("No"); // This code is contributed by Ajit. ?> |
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Output:
Yes
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