Find the number of cells in the table contains X

Given two integer N and X. N represents the number of rows and columns of a table. And the element at the ith row and the jth column in the table is i*j. The task is to find the number of cells in the table that contains X.

Examples:

Input : N = 6, X = 12
Output : 4
Cells {2, 6}, {3, 4}, {4, 3}, {6, 2} contains the number 12

Input : N = 5, X = 11
Output : 0

Approach:
It’s easy to see that number x can appear only once in a row. If x contains in the ith row then the column number will be x/i. x contains in the ith row if x is divisible by i. let’s check that x divides i and x/i <= n. If these conditions met then update the answer.

Below is the implementation of the above approach :

C++

// CPP program to find number of 
// cells in the table contains X
#include <bits/stdc++.h>

using namespace std;
 
// Function to find number of 
// cells in the table contains X

int Cells(int n, int x)
{

    int ans = 0;

    for (int i = 1; i <= n; i++)

        if (x % i == 0 && x / i <= n)

            ans++;
 
    return ans;
}
 
// Driver code

int main()
{

    int n = 6, x = 12;
 
    // Function call

    cout << Cells(n, x);
 
    return 0;
}

Java

// Java program to find number of 
// cells in the table contains X 

class GFG 
{
 
    // Function to find number of

    // cells in the table contains X

    public static int Cells(int n, int x) 

    {

        int ans = 0;

        for (int i = 1; i <= n; i++)

            if (x % i == 0 && x / i <= n)

                ans++;
 
        return ans;

    }
 
    // Driver code

    public static void main(String[] args) 

    {

        int n = 6, x = 12;
 
        // Function call

        System.out.println(Cells(n, x));

    }
}
 
// This code is contributed by sanjeev2552

Python3

# Python3 program to find number of 
# cells in the table contains X
 
# Function to find number of 
# cells in the table contains X

def Cells(n, x):
 
    ans = 0;

    for i in range(1, n + 1):

        if (x % i == 0 and x / i <= n):

            ans += 1;
 
    return ans;
 
# Driver code

if __name__ == '__main__':
 
    n = 6; x = 12;
 
    # Function call

    print(Cells(n, x));
 
# This code is contributed by 29AjayKumar

// C# program to find number of 
// cells in the table contains X 

using System;
 
class GFG 
{

    // Function to find number of

    // cells in the table contains X

    static int Cells(int n, int x) 

    {

        int ans = 0;

        for (int i = 1; i <= n; i++)

            if (x % i == 0 && x / i <= n)

                ans++;
 
        return ans;

    }
 
    // Driver code

    public static void Main()

    {

        int n = 6, x = 12;

        // Function call

        Console.WriteLine(Cells(n,x)); 

    }
}
 
// This code is contributed by nidhiva

Javascript

<script>
 
// JavaScript program to find number of 
// cells in the table contains X
 
// Function to find number of 
// cells in the table contains X

function Cells(n, x)
{

    let ans = 0;

    for (let i = 1; i <= n; i++)

        if (x % i == 0 && parseInt(x / i) <= n)

            ans++;
 
    return ans;
}
 
// Driver code

    let n = 6, x = 12;
 
    // Function call

    document.write(Cells(n, x));
 
</script>

Output

Time Complexity: O(n), since there runs a loop for once from 1 to n.

Auxiliary Space: O(1), since no extra space has been taken.

Approach:

Ignore the cases with negative squares. If n is 0, there won’t be any numbers in the square and if x is 0 it won’t appear in a square, so return 0 in both cases. If x is greater than n^2, it won’t be in the square, so return 0 in that case as well.
Next, loop through all numbers i from 1 to the square root of x, If i is a factor of x and x/i <= n, there are at least two additional places x is on the n-squared chart, due to the associative property: i*(x/i) and (x/i)*i, e.g., if x is 12 and i is 3: 3*4 and 4*3.
Lastly, find out if the square root of x is whole. If it is, it appears one additional time on the diagonal of the n-square table, which is the list of all squares.
| 1 | 2 | 3 | 4 | 5 | 6 |

| 2 | 4 | 6 | 8 | 10 | 12 |

| 3 | 6 | 9 | 12 | 15 | 18 |

| 4 | 8 | 12 | 16 | 20 | 24 |

| 5 | 10 | 15 | 20 | 25 | 30 |

| 6 | 12 | 18 | 24 | 30 | 36 |

Below is the implementation of the above approach :

C++

// C++ program to find number of
// cells in the table contains X
#include <bits/stdc++.h>

using namespace std;
 
// Function to find number of
// cells in the table contains X

int Cells(int n, int x)
{

    if (n <= 0 || x <= 0 || x > n * n)

        return 0;

    int i = 0, count = 0;

    while (++i * i < x)

        if (x % i == 0 && x <= n * i)

            count += 2;

    return i * i == x ? count + 1 : count;
}
 
// Driver code

int main()
{

    int n = 6, x = 12;
 
    // Function call

    cout << (Cells(n, x));

    return 0;
}
 
// This code is contributed by subhammahato348

Java

// Java program to find number of
// cells in the table contains X

class GFG {
 
    // Function to find number of

    // cells in the table contains X

    public static int Cells(int n, int x)

    {

        if (n <= 0 || x <= 0 || x > n * n)

            return 0;

        int i = 0, count = 0;

        while (++i * i < x)

            if (x % i == 0 && x <= n * i)

                count += 2;

        return i * i == x ? count + 1 : count;

    }
 
    // Driver code

    public static void main(String[] args)

    {

        int n = 6, x = 12;
 
        // Function call

        System.out.println(Cells(n, x));

    }
}
 
// This code is contributed by stephenbrasel

Python3

# Python program to find number of
# cells in the table contains X

# Function to find number of
# cells in the table contains X

def Cells(n, x):

    if (n <= 0 or x <= 0 or x > n * n):

        return 0;

    i = 1

    count = 0

    while (i * i < x):

        if (x % i == 0 and x <= n * i):

            count += 2;

        i+=1

    if(i * i == x):

        return count + 1

    else:

        return count
 
# Driver Code

n = 6
 
x = 12
 
print(Cells(n, x))
 
# This code is contributed by rag2127.

// C# program to find number of
// cells in the table contains X

using System;
 
class GFG{
 
// Function to find number of
// cells in the table contains X

public static int Cells(int n, int x)
{

    if (n <= 0 || x <= 0 || x > n * n)

        return 0;

    int i = 0, count = 0;

    while (++i * i < x)

        if (x % i == 0 && x <= n * i)

            count += 2;

    return i * i == x ? count + 1 : count;
}
 
// Driver code

static public void Main ()
{

    int n = 6, x = 12;
 
    // Function call

    Console.WriteLine(Cells(n, x));
}
}
 
// This code is contributed by kirti

Javascript

<script>
 
// JavaScript program to find number of
// cells in the table contains X
 
// Function to find number of
// cells in the table contains X

function Cells(n, x)
{

    if (n <= 0 || x <= 0 || x > n * n)

        return 0;

    var i = 0, count = 0;

    while (++i * i < x)

        if (x % i == 0 && x <= n * i)

            count += 2;

    return i * i == x ? count + 1 : count;
}
 
// Driver Code

var n = 6, x = 12;
 
// Function call
document.write(Cells(n, x));
 
// This code is contributed by Khushboogoyal499
 
</script>

Output

Time Complexity: O(sqrt(x)), since there runs a loop for once from 1 to n^1/2.

Auxiliary Space: O(1), since no extra space has been taken.

Article Tags :

DSA

Mathematical

Matrix

Constructive Algorithms