Count of matrices (of different orders) with given number of elements
Last Updated :
13 May, 2021
Given a number N denotes the total number of elements in a matrix, the task is to print all possible order of matrix. An order is a pair (m, n) of integers where m is number of rows and n is number of columns. For example, if the number of elements is 8 then all possible orders are:
(1, 8), (2, 4), (4, 2), (8, 1).
Examples:
Input: N = 8
Output: (1, 2) (2, 4) (4, 2) (8, 1)
Input: N = 100
Output:
(1, 100) (2, 50) (4, 25) (5, 20) (10, 10) (20, 5) (25, 4) (50, 2) (100, 1)
Approach:
A matrix is said to be of order m x n if it has m rows and n columns. The total number of elements in a matrix is equal to (m*n). So we start from 1 and check one by one if it divides N(the total number of elements). If it divides, it will be one possible order.
Below is the implementation of the above approach:
C++
#include <iostream>
using namespace std;
void printAllOrder( int n)
{
for ( int i = 1; i <= n; i++) {
if (n % i == 0) {
cout << i << " " << n / i << endl;
}
}
}
int main()
{
int n = 10;
printAllOrder(n);
return 0;
}
|
Java
class GFG
{
static void printAllOrder( int n)
{
for ( int i = 1 ; i <= n; i++) {
if (n % i == 0 ) {
System.out.println( i + " " + n / i );
}
}
}
public static void main(String []args)
{
int n = 10 ;
printAllOrder(n);
}
}
|
Python
def printAllOrder(n):
for i in range ( 1 ,n + 1 ):
if (n % i = = 0 ) :
print ( i ,n / / i )
n = 10
printAllOrder(n)
|
C#
using System;
class GFG
{
static void printAllOrder( int n)
{
for ( int i = 1; i <= n; i++) {
if (n % i == 0) {
Console.WriteLine( i + " " + n / i );
}
}
}
public static void Main()
{
int n = 10;
printAllOrder(n);
}
}
|
PHP
<?php
function printAllOrder( $n )
{
for ( $i = 1; $i <= $n ; $i ++)
{
if ( $n % $i == 0)
{
echo $i , " " , ( $n / $i ), "\n" ;
}
}
}
$n = 10;
printAllOrder( $n );
?>
|
Javascript
<script>
function printAllOrder( n)
{
for (let i = 1; i <= n; i++) {
if (n % i == 0) {
document.write( i + " " + n / i+ "<br>" );
}
}
}
let n = 10;
printAllOrder(n);
</script>
|
Output:
1 10
2 5
5 2
10 1
Time Complexity: O(n)
Auxiliary Space: O(1)
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