Program to print Lower triangular and Upper triangular matrix of an array

Difficulty Level : Easy
Last Updated : 14 Jan, 2019

Prerequisite – Multidimensional Arrays in C / C++

Given a two dimensional array, Write a program to print lower triangular matrix and upper triangular matrix.

Lower triangular matrix is a matrix which contain elements below principle diagonal including principle diagonal elements and rest of the elements are 0.
Upper triangular matrix is a matrix which contain elements above principle diagonal including principle diagonal elements and rest of the elements are 0.

LOWER TRIANGULAR :
$\begin{bmatrix} A_{00} & 0 & 0 & ... & 0\\ A_{10} & A_{11} & 0 & ... & 0\\ A_{20} & A_{21} & A_{22} & ... & 0\\ . & . & . & . & .\\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ A_{row0} & A_{row1} & A_{row2} & ... & A_{rowcol} \end{bmatrix}$

UPPER TIRANGULAR :
$\begin{bmatrix} A_{00} & A_{01} & A_{02} & ... & A_{0col}\\ 0 & A_{11} & A_{22} & ... & A_{1col}\\ 0 & 0 & A_{22} & ... & A_{2col}\\ . & . & . & . & .\\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ 0 & 0 & 0 & ... & A_{rowcol} \end{bmatrix}$

Examples :

Input : matrix[3][3] = {1 2 3
                       4 5 6
                       7 8 9}
Output :
Lower : 1 0 0        Upper : 1 2 3
        4 5 0                0 5 6
        7 8 9                0 0 9

Input : matrix[3][3] = {7 8 9
                        3 2 1
                        6 5 4}
Output :
Lower : 7 0 0       Upper : 7 8 9
        3 2 0               0 2 1
        6 5 4               0 0 4

Steps:

For lower triangular matrix, we check the index position i and j i.e row and column respectively. If column position is greater than row position we simply make that position 0.
For upper triangular matrix, we check the index position i and j i.e row and column respectively. If column position is smaller than row position we simply make that position 0.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

// C++ program to print Lower  
// triangular and Upper triangular 
// matrix of an array 
#include<iostream> 
  
using namespace std; 
  
// Function to form  
// lower triangular matrix 
void lower(int matrix[3][3], int row, int col) 
{ 
    int i, j; 
    for (i = 0; i < row; i++) 
    { 
        for (j = 0; j < col; j++) 
        { 
            if (i < j) 
            { 
                cout << "0" << " "; 
            } 
            else
            cout << matrix[i][j] << " "; 
        } 
        cout << endl; 
    } 
} 
  
// Function to form upper triangular marix 
void upper(int matrix[3][3], int row, int col) 
{ 
    int i, j; 
      
    for (i = 0; i < row; i++) 
    { 
        for (j = 0; j < col; j++) 
        { 
            if (i > j) 
            { 
                cout << "0" << " "; 
            } 
            else
            cout << matrix[i][j] << " "; 
        } 
        cout << endl; 
    } 
} 
  
// Driver Code 
int main() 
{ 
    int matrix[3][3] = {{1, 2, 3},  
                        {4, 5, 6},  
                        {7, 8, 9}}; 
    int row = 3, col = 3; 
      
    cout << "Lower triangular matrix: \n"; 
    lower(matrix, row, col); 
      
    cout << "Upper triangular matrix: \n"; 
    upper(matrix, row, col); 
          
    return 0; 
} 

Java

// Java program to print Lower  
// triangular and Upper triangular 
// matrix of an array 
class GFG 
{ 
    // method to form lower  
    // triangular matrix 
    static void lower(int matrix[][],  
                      int row, int col) 
    { 
        int i, j; 
        for (i = 0; i < row; i++) 
        { 
            for (j = 0; j < col; j++) 
            { 
                if (i < j) 
                { 
                    System.out.print("0" + " "); 
                } 
                else
                System.out.print(matrix[i][j] + " "); 
            } 
            System.out.println(); 
        } 
    } 
      
    // Method to form upper 
    // triangular matrix 
    static void upper(int matrix[][],  
                      int row, int col) 
    { 
        int i, j; 
        for (i = 0; i < row; i++) 
        { 
            for (j = 0; j < col; j++) 
            { 
                if (i > j) 
                { 
                    System.out.print("0" + " "); 
                } 
                else
                System.out.print(matrix[i][j] + " "); 
            } 
            System.out.println(); 
        } 
    } 
       
    // Driver Code 
    public static void main(String args[]) 
    { 
        int matrix[][] = {{1, 2, 3},  
                          {4, 5, 6},  
                          {7, 8, 9}}; 
        int row = 3, col = 3; 
          
        System.out.println("Lower triangular matrix: "); 
        lower(matrix, row, col); 
          
        System.out.println("Upper triangular matrix: "); 
        upper(matrix, row, col); 
    } 
} 

Python3

# Python3 program to print Lower  
# triangular and Upper triangular 
# matrix of an array 
  
# Function to form lower triangular  
# matrix 
def lower(matrix, row, col): 
  
      
    for i in range(0, row): 
      
        for j in range(0, col): 
          
            if (i < j): 
              
                print("0", end = " "); 
              
            else: 
                print(matrix[i][j],  
                       end = " " ); 
          
        print(" "); 
      
# Function to form upper triangular marix 
def upper(matrix, row, col): 
  
    for i in range(0, row): 
      
        for j in range(0, col): 
          
            if (i > j): 
                print("0", end = " "); 
              
            else: 
                print(matrix[i][j],  
                       end = " " ); 
          
        print(" "); 
  
# Driver Code 
matrix = [[1, 2, 3],  
          [4, 5, 6],  
          [7, 8, 9]]; 
row = 3; 
col = 3; 
      
print("Lower triangular matrix: "); 
lower(matrix, row, col); 
      
print("Upper triangular matrix: "); 
upper(matrix, row, col); 
          
# This code is contributed by 
# Shivi_Aggarwal  

C#

// C# program to print   
// Lower triangular and 
// Upper triangular 
// matrix of an array 
using System; 
  
class GFG 
{ 
    // method to form lower  
    // triangular matrix 
    static void lower(int [,]matrix,  
                      int row, int col) 
    { 
        int i, j; 
        for (i = 0; i < row; i++) 
        { 
            for (j = 0; j < col; j++) 
            { 
                if (i < j) 
                { 
                    Console.Write("0" + " "); 
                } 
                else
                Console.Write(matrix[i, j] + " "); 
            } 
            Console.WriteLine(); 
        } 
    } 
      
    // Method to form upper 
    // triangular matrix 
    static void upper(int [,]matrix,  
                      int row, int col) 
    { 
        int i, j; 
        for (i = 0; i < row; i++) 
        { 
            for (j = 0; j < col; j++) 
            { 
                if (i > j) 
                { 
                    Console.Write("0" + " "); 
                } 
                else
                Console.Write(matrix[i, j] + " "); 
            } 
        Console.WriteLine(); 
        } 
    } 
      
    // Driver Code 
    static public void Main () 
    { 
        int [,]matrix = {{1, 2, 3},  
                        {4, 5, 6},  
                        {7, 8, 9}}; 
        int row = 3, col = 3; 
          
        Console.WriteLine("Lower triangular matrix: "); 
        lower(matrix, row, col); 
          
        Console.WriteLine("Upper triangular matrix: "); 
        upper(matrix, row, col); 
    } 
} 
  
// This code is contributed by ajit  

PHP

<?php 
// PHP program to print Lower  
// triangular and Upper triangular 
// matrix of an array 
  
// Function to form  
// lower triangular matrix 
function lower($matrix, $row, $col) 
{ 
    $i; $j; 
    for ($i = 0; $i < $row; $i++) 
    { 
        for ($j = 0; $j < $col; $j++) 
        { 
            if ($i < $j) 
            { 
                echo "0" , " "; 
            } 
            else
            echo $matrix[$i][$j] , " "; 
        } 
        echo "\n"; 
    } 
} 
  
// Function to form 
// upper triangular marix 
function upper($matrix, $row, $col) 
{ 
    $i; $j; 
      
    for ($i = 0; $i < $row; $i++) 
    { 
        for ($j = 0; $j < $col; $j++) 
        { 
            if ($i > $j) 
            { 
                echo "0" , " "; 
            } 
            else
            echo $matrix[$i][$j] ," "; 
        } 
    echo "\n"; 
    } 
} 
  
// Driver Code 
$matrix = array (array (1, 2, 3), 
                  array (4, 5, 6), 
                 array (7, 8, 9)); 
$row = 3; $col = 3; 
  
echo "Lower triangular matrix: \n"; 
lower($matrix, $row, $col); 
  
echo "Upper triangular matrix: \n"; 
upper($matrix, $row, $col); 
      
// This code is contributed by jit_t 
?> 

Output :

Lower triangular matrix: 
1 0 0 
4 5 0 
7 8 9 
Upper triangular matrix: 
1 2 3 
0 5 6 
0 0 9

This article is contributed by Rishabh Jain. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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Related Articles

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP