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Code Matrix

# Check if matrix is upper triangular

The problem is about the checking whether a given matrix is upper triangular or not. An upper triangular matrix is a special type of square matrix where all the elements below the main diagonal (elements with row index greater than column index) are zero.

## Problem Statement and Example

Given a matrix, we want to determine if it's an upper triangular matrix. For example, consider the following matrix:

``````1  2  3  4
0  1  2  3
0  0  1  2
0  0  0  5``````

In this example, the matrix is indeed upper triangular because all the elements below the main diagonal are zeros.

## Idea to Solve

To solve this problem, we need to iterate through each element of the matrix and check if it satisfies the conditions of being an upper triangular matrix. Specifically, for each element at position `(i, j)`, we need to ensure that all elements with row indices greater than `i` (i.e., the elements below the current row) and column indices less than `j` (i.e., the elements to the left of the current column) are zero.

## Pseudocode

``````function isUpperTriangular(matrix)
for i = 0 to number_of_rows(matrix) - 1
for j = 0 to i
if matrix[i][j] != 0
return false
return true``````

## Algorithm Explanation

1. Loop through each row of the matrix using the variable `i`.
2. For each row, loop through the columns from `0` to `i` using the variable `j`.
3. Check if the element at position `(i, j)` is non-zero. If it's not zero, the matrix can't be upper triangular, so return `false`.
4. If all elements below the main diagonal are zero, the matrix is upper triangular, so return `true`.

## Code Solution

``````/*
C Program
+ Check if matrix is upper triangular
*/
#include<stdio.h>
//Size of matrix
#define ROW 4
#define COL 4

//Display the element of given 2d matrix
void show_data(int matrix[][COL]) {

for (int i = 0; i < ROW; ++i) {

for (int j = 0; j < COL; ++j) {

printf("%4d", matrix[i][j]);
}

printf("\n");
}

printf("\n");
}
//Check if given matrix is upper triangular or not
void upper_triangular(int matrix[ROW][COL])
{
int status=1;

for (int i = 0; i < COL && status==1; ++i)
{
for (int j = 0; j < i && status==1; ++j)
{
if(matrix[i][j] != 0)
{
//When matrix is not upper triangular
status=0;
}
}

}
if(status==1)
{
printf("  Yes\n");
}
else
{
printf("  NO\n");
}

}
int main(){

int matrix[ROW][COL]=  {
{ 1, 2, 3, 4 },
{ 0, 1, 2, 3 },
{ 0, 0, 1, 2 },
{ 0, 0, 0, 5 }  };
show_data(matrix);
upper_triangular(matrix);

return 0;
}```
```

#### Output

``````   1   2   3   4
0   1   2   3
0   0   1   2
0   0   0   5

Yes``````
``````/*
C++ Program
Check if matrix is upper triangular
*/
#include<iostream>
#define ROW 4
#define COL 4
using namespace std;

class MyMatrix {
public:

//Display the element of given 2d matrix
void show_data(int matrix[][COL], int row, int col) {
for (int i = 0; i < row; ++i) {
for (int j = 0; j < col; ++j) {
cout << " " << matrix[i][j];
}
cout << "\n";
}
cout << "\n";
}
//Check if given matrix is upper triangular or not
void upper_triangular(int matrix[][COL], int row, int col) {
int status = 1;
for (int i = 0; i < col && status == 1; ++i) {
for (int j = 0; j < i && status == 1; ++j) {
if (matrix[i][j] != 0) {
//When matrix is not upper triangular
status = 0;
}
}
}
if (status == 1) {
cout << " Yes\n";
} else {
cout << " NO\n";
}
}
};
int main() {
MyMatrix obj ;
int matrix[][COL] = {
{
1,
2,
3,
4
},
{
0,
1,
2,
3
},
{
0,
0,
1,
2
},
{
0,
0,
0,
5
}
};

obj.show_data(matrix, ROW, COL);
obj.upper_triangular(matrix, ROW, COL);
return 0;
}```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes``````
``````/*
Java Program
Check if matrix is upper triangular
*/
public class MyMatrix {

//Display the element of given 2d matrix
public void show_data(int [][]matrix, int row,int col) {

for (int i = 0; i < row; ++i) {

for (int j = 0; j < col; ++j) {

System.out.print("  "+ matrix[i][j]);
}

System.out.print("\n");
}

System.out.print("\n");
}
//Check if given matrix is upper triangular or not
public void upper_triangular(int [][]matrix, int row,int col)
{
int status=1;

for (int i = 0; i < col && status==1; ++i)
{
for (int j = 0; j < i && status==1; ++j)
{
if(matrix[i][j] != 0)
{
//When matrix is not upper triangular
status=0;
}
}

}
if(status==1)
{
System.out.print("  Yes\n");
}
else
{
System.out.print("  NO\n");
}

}

public static void main(String[] args)
{

MyMatrix obj = new MyMatrix();
int [][]matrix =  {
{ 1, 2, 3, 4 },
{ 0, 1, 2, 3 },
{ 0, 0, 1, 2 },
{ 0, 0, 0, 5 }
};
//This is size of matrix
int row = matrix.length;
int col = matrix[0].length;

obj.show_data(matrix,row,col);
obj.upper_triangular(matrix,row,col);

}
}```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes``````
``````/*
C# Program
Check if matrix is upper triangular
*/
using System;
public class MyMatrix {
//Display the element of given 2d matrix
public void show_data(int[,] matrix, int row, int col) {
for (int i = 0; i < row; ++i) {
for (int j = 0; j < col; ++j) {
Console.Write(" " + matrix[i,j]);
}
Console.Write("\n");
}
Console.Write("\n");
}
//Check if given matrix is upper triangular or not
public void upper_triangular(int[,] matrix, int row, int col) {
int status = 1;
for (int i = 0; i < col && status == 1; ++i) {
for (int j = 0; j < i && status == 1; ++j) {
if (matrix[i,j] != 0) {
//When matrix is not upper triangular
status = 0;
}
}
}
if (status == 1) {
Console.Write(" Yes\n");
} else {
Console.Write(" NO\n");
}
}
public static void Main(String[] args) {
MyMatrix obj = new MyMatrix();
int[,] matrix = {
{
1,
2,
3,
4
},
{
0,
1,
2,
3
},
{
0,
0,
1,
2
},
{
0,
0,
0,
5
}
};
//This is size of matrix
int row = matrix.GetLength(0);
int col = matrix.GetLength(1);
obj.show_data(matrix, row, col);
obj.upper_triangular(matrix, row, col);
}
}```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes``````
``````<?php
/*
Php Program
Check if matrix is upper triangular
*/
class MyMatrix {
//Display the element of given 2d matrix

public 	function show_data(\$matrix, \$row, \$col) {
for (\$i = 0; \$i < \$row; ++\$i) {
for (\$j = 0; \$j < \$col; ++\$j) {
echo(" ". \$matrix[\$i][\$j]);
}
echo("\n");
}
echo("\n");
}
//Check if given matrix is upper triangular or not

public 	function upper_triangular(\$matrix, \$row, \$col) {
\$status = 1;
for (\$i = 0; \$i < \$col && \$status == 1; ++\$i) {
for (\$j = 0; \$j < \$i && \$status == 1; ++\$j) {
if (\$matrix[\$i][\$j] != 0) {
//When matrix is not upper triangular
\$status = 0;
}
}
}
if (\$status == 1) {
echo(" Yes\n");
} else {
echo(" NO\n");
}
}
};

function main() {
\$obj = new MyMatrix();
\$matrix = array(
array(1, 2, 3, 4),
array(0, 1, 2, 3),
array(0, 0, 1, 2),
array(0, 0, 0, 5)
);
//This is size of matrix
\$row = count(\$matrix);
\$col = count(\$matrix[0]);
\$obj->show_data(\$matrix, \$row, \$col);
\$obj->upper_triangular(\$matrix, \$row, \$col);

}
main();```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes``````
``````/*
Node Js Program
Check if matrix is upper triangular
*/
class MyMatrix {
//Display the element of given 2d matrix
show_data(matrix, row, col) {
for (var i = 0; i < row; ++i) {
for (var j = 0; j < col; ++j) {
process.stdout.write(" " + matrix[i][j]);
}

process.stdout.write("\n");
}

process.stdout.write("\n");
}

//Check if given matrix is upper triangular or not
upper_triangular(matrix, row, col) {
var status = 1;
for (var i = 0; i < col && status == 1; ++i) {
for (var j = 0; j < i && status == 1; ++j) {
if (matrix[i][j] != 0) {
//When matrix is not upper triangular
status = 0;
}
}
}

if (status == 1) {
process.stdout.write(" Yes\n");
} else {
process.stdout.write(" NO\n");
}
}
}

function main(args) {
var obj = new MyMatrix();
var matrix = [
[1, 2, 3, 4],
[0, 1, 2, 3],
[0, 0, 1, 2],
[0, 0, 0, 5]
];
//This is size of matrix
var row = matrix.length;
var col = matrix[0].length;
obj.show_data(matrix, row, col);
obj.upper_triangular(matrix, row, col);
}

main();```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes``````
``````#  Python 3 Program
#  Check if matrix is upper triangular
class MyMatrix :
# Display the element of given 2d matrix
def show_data(self, matrix, row, col) :
i = 0
while (i < row) :
j = 0
while (j < col) :
print(" ", matrix[i][j], end = "")
j += 1

print("\n", end = "")
i += 1

print("\n", end = "")

# Check if given matrix is upper triangular or not
def upper_triangular(self, matrix, row, col) :
status = 1
i = 0
while (i < col and status == 1) :
j = 0
while (j < i and status == 1) :
if (matrix[i][j] != 0) :
# When matrix is not upper triangular
status = 0

j += 1

i += 1

if (status == 1) :
print(" Yes\n", end = "")
else :
print(" NO\n", end = "")

def main() :
obj = MyMatrix()
matrix = [
[1, 2, 3, 4],
[0, 1, 2, 3],
[0, 0, 1, 2],
[0, 0, 0, 5]
]
row = len(matrix)
col = len(matrix[0])
obj.show_data(matrix, row, col)
obj.upper_triangular(matrix, row, col)

if __name__ == "__main__":
main()```
```

#### Output

``````  1  2  3  4
0  1  2  3
0  0  1  2
0  0  0  5

Yes``````
``````# Ruby Program
# Check if matrix is upper triangular
class MyMatrix
# Display the element of given 2d matrix
def show_data(matrix, row, col)
i = 0
while (i < row)
j = 0
while (j < col)
print(" ", matrix[i][j])
j += 1
end
print("\n")
i += 1
end
print("\n")
end
# Check if given matrix is upper triangular or not
def upper_triangular(matrix, row, col)
status = 1
i = 0
while (i < col && status == 1)
j = 0
while (j < i && status == 1)
if (matrix[i][j] != 0)
# When matrix is not upper triangular
status = 0
end
j += 1
end
i += 1
end
if (status == 1)
print(" Yes\n")
else
print(" NO\n")
end
end
end
def main()
obj = MyMatrix.new()
matrix = [
[1, 2, 3, 4],
[0, 1, 2, 3],
[0, 0, 1, 2],
[0, 0, 0, 5]
]
row = matrix.length
col = matrix[0].length
obj.show_data(matrix, row, col)
obj.upper_triangular(matrix, row, col)
end
main()```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes
``````
``````/*
Scala Program
Check if matrix is upper triangular
*/
class MyMatrix {
//Display the element of given 2d matrix
def show_data(matrix: Array[Array[Int]], row: Int, col: Int): Unit = {
var i: Int = 0;
while (i < row) {
var j: Int = 0;
while (j < col) {
print(" " + matrix(i)(j));
j += 1;
}
print("\n");
i += 1;
}
print("\n");
}
//Check if given matrix is upper triangular or not
def upper_triangular(matrix: Array[Array[Int]], row: Int, col: Int): Unit = {
var status: Int = 1;
var i: Int = 0;
while (i < col && status == 1) {
var j: Int = 0;
while (j < i && status == 1) {
if (matrix(i)(j) != 0) {
//When matrix is not upper triangular
status = 0;
}
j += 1;
}
i += 1;
}
if (status == 1) {
print(" Yes\n");
} else {
print(" NO\n");
}
}
}
object Main {
def main(args: Array[String]): Unit = {
val obj: MyMatrix = new MyMatrix();
val matrix: Array[Array[Int]] = Array(
Array(1, 2, 3, 4),
Array(0, 1, 2, 3),
Array(0, 0, 1, 2),
Array(0, 0, 0, 5));
val row: Int = matrix.length;
val col: Int = matrix(0).length;
obj.show_data(matrix, row, col);
obj.upper_triangular(matrix, row, col);
}
}```
```

#### Output

`````` 1 2 3 4
0 1 2 3
0 0 1 2
0 0 0 5

Yes``````
``````/*
Swift Program
Check if matrix is upper triangular
*/
class MyMatrix {
//Display the element of given 2d matrix
func show_data(_ matrix: [
[Int]
], _ row: Int, _ col: Int) {
var i: Int = 0;
while (i < row) {
var j: Int = 0;
while (j < col) {
print(" ", matrix[i][j], terminator: "");
j += 1;
}
print("\n", terminator: "");
i += 1;
}
print("\n", terminator: "");
}
//Check if given matrix is upper triangular or not
func upper_triangular(_ matrix: [
[Int]
], _ row: Int, _ col: Int) {
var status: Int = 1;
var i: Int = 0;
while (i < col && status == 1) {
var j: Int = 0;
while (j < i && status == 1) {
if (matrix[i][j] != 0) {
//When matrix is not upper triangular
status = 0;
}
j += 1;
}
i += 1;
}
if (status == 1) {
print(" Yes\n", terminator: "");
} else {
print(" NO\n", terminator: "");
}
}
}
func main() {
let obj: MyMatrix = MyMatrix();
let matrix: [
[Int]
] = [
[1, 2, 3, 4],
[0, 1, 2, 3],
[0, 0, 1, 2],
[0, 0, 0, 5]
];
let row: Int = matrix.count;
let col: Int = matrix[0].count;
obj.show_data(matrix, row, col);
obj.upper_triangular(matrix, row, col);
}
main();```
```

#### Output

``````  1  2  3  4
0  1  2  3
0  0  1  2
0  0  0  5

Yes``````

## Time Complexity

The time complexity of this algorithm is O(n^2), where 'n' is the number of rows (or columns) in the matrix. This is because we need to iterate through each element of the matrix once and perform a constant amount of work for each element.

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