# Count entries equal to x in a special matrix

You are given a square matrix (matrix[][]) of order n, where matrix[i][j] = i*j. Find the number of cells which have entry equal to a given number x.
NOte : Indexing of matrix starts from 1, i.e. 1<= i,j <= n.

Examples :

```Input : matrix[][] = {1, 2, 3, 4,
2, 4, 6, 8,
3, 6, 9, 12,
4, 8, 12, 16}
x = 4
Output : 3

Input : matrix[][] = {1, 2, 3, 4,
2, 4, 6, 8,
3, 6, 9, 12,
4, 8, 12, 16}
x = 12
Output : 2

```

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

A simple Approach is to traverse the whole of matrix and check whether cell value is equal to given x and then increase count value accordingly. Time complexity in this approach is quite high and is equal to O(n^2).

```// traverse and check whole matrix
for (int i=1; i<=n ; i++)
{
for (int j=1; j<=n; j++)
if (i * j == x)
count++;
}
// return count
return count;
```

An efficient approach is to only find the number of factors of given x in the range 0 to x and also those factors (including divisor and quotient ) must be less than or equal to n (order of matrix). In this case time complexity will be O(n).

```// traverse and find the factors
for (int i=1; i<=n && i<=x ; i++)
{
// x%i == 0 means i is factor of x
// x/i <= n means i and j are <= n (for i*j=x)
if ( x/i <= n && x%i ==0)
count++;
}
// return count
return count;
```

## C++

 `// CPP program for counting number of cell  ` `// equals to given x ` `#include ` `using` `namespace` `std; ` ` `  `// function to count factors as number of cell ` `int` `count (``int` `n, ``int` `x) ` `{ ` `    ``int` `count == 0; ` `    ``// traverse and find the factors ` `    ``for` `(``int` `i=1; i<=n && i<=x ; i++) ` `    ``{ ` `        ``// x%i == 0 means i is factor of x ` `        ``// x/i <= n means i and j are <= n (for i*j=x) ` `        ``if` `( x/i <= n && x%i ==0) ` `            ``count++; ` `    ``} ` `    ``// return count  ` `    ``return` `count; ` `} ` ` `  `// driver program ` `int` `main() ` `{ ` `    ``int` `n = 8; ` `    ``// we can manually assume matrix of order 8*8 ` `    ``// where mat[i][j] = i*j , 0

## Java

 `// Java program for counting number of ` `// cell equals to given x ` `class` `GFG ` `{ ` `    ``// function to count factors as  ` `    ``// number of cell ` `    ``static` `int` `count (``int` `n, ``int` `x) ` `    ``{ ` `        ``int` `count = ``0``; ` `     `  `        ``// traverse and find the factors ` `        ``for` `(``int` `i = ``1``; i <= n && i <= x ; ` `                                    ``i++) ` `        ``{ ` `            ``// x%i == 0 means i is factor ` `            ``// of x. x/i <= n means i and ` `            ``// j are <= n (for i*j=x) ` `            ``if` `( x / i <= n && x % i == ``0``) ` `                ``count++; ` `        ``} ` `         `  `        ``// return count  ` `        ``return` `count; ` `    ``} ` ` `  `    ``// driver program ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``8``; ` `         `  `        ``// we can manually assume matrix  ` `        ``// of order 8*8 where  ` `        ``// mat[i][j] = i*j , 0

## Python3

 `# Python 3 program for counting  ` `# number of cell equals to given x  ` ` `  `# function to count factors  ` `# as number of cell  ` `def` `count(n, x): ` `    ``cnt ``=` `0` ` `  `    ``# traverse and find the factors  ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` ` `  `        ``# // x%i == 0 means i is factor of x  ` `        ``# x/i <= n means i and j are <= n (for i*j=x)  ` `        ``if` `i <``=` `x: ` `            ``if` `x ``/``/` `i <``=` `n ``and` `x ``%` `i ``=``=` `0``: ` `                ``cnt ``+``=` `1` `    ``return` `cnt ` ` `  `# Driver code ` `n ``=` `8` `x ``=` `24` `print``(count(n, x)) ` ` `  `# This code is contributed by Shrikant13 `

## C#

 `// C# program for counting number ` `// of cell equals to given x ` `using` `System;  ` ` `  `class` `GFG { ` `     `  `    ``// function to count factors as  ` `    ``// number of cell ` `    ``static` `int` `count (``int` `n, ``int` `x) { ` `         `  `        ``int` `count = 0; ` `     `  `        ``// traverse and find the factors ` `        ``for` `(``int` `i = 1; i <= n &&  ` `             ``i <= x ; i++) ` `        ``{ ` `             `  `            ``// x%i == 0 means i is factor ` `            ``// of x. x/i <= n means i and ` `            ``// j are <= n (for i*j=x) ` `            ``if` `( x / i <= n && x % i == 0) ` `                ``count++; ` `        ``} ` `         `  `        ``// return count  ` `        ``return` `count; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 8; ` `         `  `        ``// we can manually assume matrix  ` `        ``// of order 8*8 where  ` `        ``// mat[i][j] = i*j , 0

## PHP

 ` `

Output :

```4
```

Matrix Matrix