# Program to check if matrix is upper triangular

Last Updated : 01 Oct, 2023

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.`

Implementation:

## C++

 `// Program to check upper triangular matrix.` `#include ` `#define N 4` `using` `namespace` `std;`   `// Function to check matrix is in upper triangular` `// form or not.` `bool` `isUpperTriangularMatrix(``int` `mat[N][N])` `{` `    ``for` `(``int` `i = 1; i < N; i++)` `        ``for` `(``int` `j = 0; j < i; j++)` `            ``if` `(mat[i][j] != 0)` `                ``return` `false``;` `    ``return` `true``;` `}`   `// Driver function.` `int` `main()` `{` `    ``int` `mat[N][N] = { { 1, 3, 5, 3 },` `                      ``{ 0, 4, 6, 2 },` `                      ``{ 0, 0, 2, 5 },` `                      ``{ 0, 0, 0, 6 } };` `    ``if` `(isUpperTriangularMatrix(mat))` `        ``cout << ``"Yes"``;` `    ``else` `        ``cout << ``"No"``;` `    ``return` `0;` `}`

## Java

 `// Java Program to check upper ` `// triangular matrix.` `import` `java.util.*;` `import` `java.lang.*;`   `public` `class` `GfG` `{` `    ``private` `static` `final` `int` `N = ``4``;`   `    ``// Function to check matrix is in` `    ``// upper triangular form or not.` `    ``public` `static` `Boolean isUpperTriangularMatrix(``int` `mat[][])` `    ``{` `        ``for` `(``int` `i = ``1``; i < N ; i++)` `            ``for` `(``int` `j = ``0``; j < i; j++)` `                ``if` `(mat[i][j] != ``0``)` `                    ``return` `false``;` `        ``return` `true``;` `    ``} ` `    `  `    ``// driver function` `    ``public` `static` `void` `main(String argc[]){` `        ``int``[][] mat= { { ``1``, ``3``, ``5``, ``3` `},` `                       ``{ ``0``, ``4``, ``6``, ``2` `},` `                       ``{ ``0``, ``0``, ``2``, ``5` `},` `                       ``{ ``0``, ``0``, ``0``, ``6` `} };` `                    `  `        ``if` `(isUpperTriangularMatrix(mat))` `            ``System.out.println(``"Yes"``);` `        ``else` `            ``System.out.println(``"No"``);` `    ``}` `}`   `/* This code is contributed by Sagar Shukla */`

## Python3

 `# Python3 Program to check upper ` `# triangular matrix.`   `# Function to check matrix ` `# is in upper triangular` `def` `isuppertriangular(M):` `    ``for` `i ``in` `range``(``1``, ``len``(M)):` `        ``for` `j ``in` `range``(``0``, i):` `            ``if``(M[i][j] !``=` `0``): ` `                    ``return` `False` `    ``return` `True` `    `  `# Driver function.` `M ``=` `[[``1``,``3``,``5``,``3``],` `    ``[``0``,``4``,``6``,``2``],` `    ``[``0``,``0``,``2``,``5``],` `    ``[``0``,``0``,``0``,``6``]]`   `if` `isuppertriangular(M):` `    ``print` `(``"Yes"``)` `else``:` `    ``print` `(``"No"``)`   `# This code is contributed by Anurag Rawat`

## C#

 `// C# Program to check upper ` `// triangular matrix.` `using` `System;`   `public` `class` `GfG` `{` `    ``private` `static` `int` `N = 4;`   `    ``// Function to check matrix is in` `    ``// upper triangular form or not.` `    ``public` `static` `bool` `isUpperTriangularMatrix(``int` `[,]mat)` `    ``{` `        ``for` `(``int` `i = 1; i < N ; i++)` `            ``for` `(``int` `j = 0; j < i; j++)` `                ``if` `(mat[i, j] != 0)` `                    ``return` `false``;` `        ``return` `true``;` `    ``} ` `    `  `    ``// Driver function` `    ``public` `static` `void` `Main(){` `        ``int` `[,]mat= { { 1, 3, 5, 3 },` `                    ``{ 0, 4, 6, 2 },` `                    ``{ 0, 0, 2, 5 },` `                    ``{ 0, 0, 0, 6 } };` `                    `  `        ``if` `(isUpperTriangularMatrix(mat))` `            ``Console.WriteLine(``"Yes"``);` `        ``else` `            ``Console.WriteLine(``"No"``);` `    ``}` `}`   `/* This code is contributed by vt_m */`

## Javascript

 ``

## PHP

 ``

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.

Approach 2:

The approach used in the program is to check whether all the elements of the matrix below the diagonal are zero or not. If all the elements below the diagonal are zero, then the matrix is considered to be an upper triangular matrix. This is achieved by looping through all the elements of the matrix below the diagonal and checking if each element is zero or not. If any non-zero element is found, the matrix is not upper triangular. If all the elements below the diagonal are zero, the matrix is upper triangular.

## C++

 `#include ` `#define N 4` `using` `namespace` `std;`   `// Function to check matrix is in upper triangular` `// form or not.` `bool` `isUpperTriangularMatrix(``int` `mat[N][N])` `{` `    ``for` `(``int` `i = 1; i < N; i++)` `        ``for` `(``int` `j = 0; j < i; j++)` `            ``if` `(mat[i][j] != 0)` `                ``return` `false``;` `    ``return` `true``;` `}`   `// Driver function.` `int` `main()` `{` `    ``int` `mat[N][N] = { { 1, 3, 5, 3 },` `                      ``{ 0, 4, 6, 2 },` `                      ``{ 0, 0, 2, 5 },` `                      ``{ 0, 0, 0, 6 } };` `    ``if` `(isUpperTriangularMatrix(mat))` `        ``cout << ``"Yes"``;` `    ``else` `        ``cout << ``"No"``;` `    ``return` `0;` `}`

## Java

 `public` `class` `GFG {`   `    ``// Function to check if a matrix is in upper triangular form or not` `    ``public` `static` `boolean` `isUpperTriangularMatrix(``int``[][] mat) {` `        ``int` `n = mat.length; ``// Size of the matrix`   `        ``// Iterate over each row starting from the second row` `        ``for` `(``int` `i = ``1``; i < n; i++) {` `            ``// Iterate over each column up to the diagonal of the current row` `            ``for` `(``int` `j = ``0``; j < i; j++) {` `                ``// If any element below the diagonal is non-zero, it's not an ` `              ``// upper triangular matrix` `                ``if` `(mat[i][j] != ``0``) {` `                    ``return` `false``;` `                ``}` `            ``}` `        ``}`   `        ``// If all elements below the diagonal are zero, ` `      ``// it's an upper triangular matrix` `        ``return` `true``;` `    ``}`   `    ``public` `static` `void` `main(String[] args) {` `        ``int``[][] mat = { { ``1``, ``3``, ``5``, ``3` `},` `                        ``{ ``0``, ``4``, ``6``, ``2` `},` `                        ``{ ``0``, ``0``, ``2``, ``5` `},` `                        ``{ ``0``, ``0``, ``0``, ``6` `} };`   `        ``if` `(isUpperTriangularMatrix(mat)) {` `            ``System.out.println(``"Yes"``);` `        ``} ``else` `{` `            ``System.out.println(``"No"``);` `        ``}` `    ``}` `}`

## Python

 `def` `is_upper_triangular_matrix(mat):` `    ``n ``=` `len``(mat)` `    ``for` `i ``in` `range``(``1``, n):` `        ``for` `j ``in` `range``(i):` `            ``if` `mat[i][j] !``=` `0``:` `                ``return` `False` `    ``return` `True`   `# Driver function.` `if` `__name__ ``=``=` `"__main__"``:` `    ``mat ``=` `[[``1``, ``3``, ``5``, ``3``],` `           ``[``0``, ``4``, ``6``, ``2``],` `           ``[``0``, ``0``, ``2``, ``5``],` `           ``[``0``, ``0``, ``0``, ``6``]]` `    `  `    ``if` `is_upper_triangular_matrix(mat):` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)`

## C#

 `using` `System;`   `class` `GFG` `{` `    ``const` `int` `N = 4;`   `    ``// Function to check if the matrix is in upper triangular form or not.` `    ``static` `bool` `IsUpperTriangularMatrix(``int``[,] mat)` `    ``{` `        ``for` `(``int` `i = 1; i < N; i++)` `        ``{` `            ``for` `(``int` `j = 0; j < i; j++)` `            ``{` `                ``// If any element below the main diagonal is non-zero, the matrix is not upper triangular.` `                ``if` `(mat[i, j] != 0)` `                    ``return` `false``;` `            ``}` `        ``}` `        ``return` `true``;` `    ``}`   `    ``// Driver function.` `    ``static` `void` `Main()` `    ``{` `        ``int``[,] mat = { { 1, 3, 5, 3 },` `                       ``{ 0, 4, 6, 2 },` `                       ``{ 0, 0, 2, 5 },` `                       ``{ 0, 0, 0, 6 } };`   `        ``if` `(IsUpperTriangularMatrix(mat))` `            ``Console.WriteLine(``"Yes"``);` `        ``else` `            ``Console.WriteLine(``"No"``);` `    ``}` `}`

## Javascript

 `function` `isUpperTriangularMatrix(mat) {` `    ``let n = mat.length; ``// Size of the matrix`   `    ``// Iterate over each row starting from the second row` `    ``for` `(let i = 1; i < n; i++) {` `        ``// Iterate over each column up to the diagonal of the current row` `        ``for` `(let j = 0; j < i; j++) {` `            ``// If any element below the diagonal is non-zero, it's not an ` `            ``// upper triangular matrix` `            ``if` `(mat[i][j] !== 0) {` `                ``return` `false``;` `            ``}` `        ``}` `    ``}`   `    ``// If all elements below the diagonal are zero, ` `    ``// it's an upper triangular matrix` `    ``return` `true``;` `}`   `let mat = [` `    ``[1, 3, 5, 3],` `    ``[0, 4, 6, 2],` `    ``[0, 0, 2, 5],` `    ``[0, 0, 0, 6]` `];`   `if` `(isUpperTriangularMatrix(mat)) {` `    ``console.log(``"Yes"``);` `} ``else` `{` `    ``console.log(``"No"``);` `}`

Output

```Yes

```

Time Complexity: O(n^2)

Auxiliary Space: O(n^2)

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