Given a positive integer N, the task is to print the Upper Hessenberg matrix of order N which includes any one-digit random positive integer as its non-zero elements.
Upper Hessenberg matrix is a square matrix in which all of its elements below the sub-diagonal are zero. In mathematical term mat[i][j] = 0 for all i > j + 1.
Examples:
Input: N = 3
Output:
1 2 8
1 3 4
0 3 4
Input: N = 4
Output:
1 2 2 3
1 3 4 2
0 3 4 2
0 0 1 4
Approach: For printing an upper Hessenberg matrix with one-digit positive elements print zero for all the cells of the matrix where i > j + 1 and any single-digit random number with help of rand() function.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to print the Upper Hessenberg// matrix of order nvoid UpperHessenbergMatrix(int n){ for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { // If element is below sub-diagonal // then print 0 if (i > j + 1) cout << '0' << " "; // Print a random digit for // every non-zero element else cout << rand() % 10 << " "; } cout << "\n"; }}// Driver codeint main(){ int n = 4; UpperHessenbergMatrix(n); return 0;} |
Java
// Java implementation of the approachclass GFG {// Function to print the Lower Hessenberg // matrix of order n static void UpperHessenbergMatrix(int n) { for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { // If element is above super-diagonal // then print 0 if (i > j + 1) { System.out.print(0 + " "); } // Print a random digit for // every non-zero element else { System.out.print((int)(Math.random() * 10) + " "); } } System.out.println(); }}// Driver code public static void main(String[] args) { int n = 4; UpperHessenbergMatrix(n);}}// This code is contributed by 29AjayKumar |
Python3
# Python3 implementation of the approachimport random# Function to print the Upper Hessenberg# matrix of order ndef UpperHessenbergMatrix(n): for i in range(1, n + 1): for j in range(1, n + 1): # If element is below sub-diagonal # then pr0 if (i > j + 1): print('0', end = " ") # Pra random digit for # every non-zero element else: print(random.randint(1, 10), end = " ") print()# Driver coden = 4;UpperHessenbergMatrix(n)# This code is contributed # by Mohit Kumar |
C#
// C# implementation of the approach using System;class GFG{ // Function to print the Lower Hessenberg // matrix of order n static void UpperHessenbergMatrix(int n) { Random rand = new Random(); for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { // If element is above super-diagonal // then print 0 if (i > j + 1) Console.Write(0 + " "); // Print a random digit for // every non-zero element else Console.Write(rand.Next(1, 10) + " "); } Console.WriteLine(); } } // Driver code static public void Main () { int n = 4; UpperHessenbergMatrix(n); }} // This code is contributed by AnkitRai01 |
Javascript
<script>// Javascript implementation of the approach// Function to print the Upper Hessenberg// matrix of order nfunction UpperHessenbergMatrix( n){ for (var i = 1; i <= n; i++) { for (var j = 1; j <= n; j++) { // If element is below sub-diagonal // then print 0 if (i > j + 1) document.write( '0' + " "); // Print a random digit for // every non-zero element else document.write( Math.floor(Math.random() * 10) + " "); } document.write("<br>"); }}// Driver codevar n = 4;UpperHessenbergMatrix(n);</script> |
Output:
3 6 7 5 3 5 6 2 0 9 1 2 0 0 7 0
Time Complexity: O(n2)
Auxiliary Space: O(1)
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