In the previous article, we have discussed Python Program to Calculate Sum of all Maximum Occurring Elements in Matrix

Given a number n (which is the size of the matrix)and another number k, the task is to find the frequency of k of the matrix with size n and matrix (i,j)=i+j.

**What is a matrix:**

A matrix is a rectangular sequence of numbers divided into columns and rows. A matrix element or entry is a number that appears in a matrix.

**Example:**

Above is the matrix which contains 5 rows and 4 columns and having elements from 1 to 20.

In this order, the dimensions of a matrix indicate the number of rows and columns.

Here as there are 5 rows and 4 columns it is called a 5*4 matrix.

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**Examples:**

**Example1:**

**Input:**

Given size of matrix = 3 Given k value = 6

**Output:**

The given k value{ 6 } frequency in the matix = 1

**Example2:**

**Input:**

Given size of matrix = 4 Given k value = 3

**Output:**

The given k value{ 3 } frequency in the matix = 2

## Program to Count Frequency of k in a Matrix of Size n Where Matrix(i, j) = i+j in Python

Below are the ways to find the frequency of k of the matrix with size n and matrix (i,j)=i+j in python:

### Method #1: Using Mathematical Formula (Static Input)

**Approach:**

- Import math module using the import keyword.
- Give the number(size of matrix) as static input and store it in a variable.
- Give another number k as static input and store it in another variable.
- Create a function to say
**findfreqencyof_k()**which takes the given number(size of matrix) and the given k value as the arguments and returns the frequency of k of the matrix with size n and matrix (i,j)=i+j. - Inside the function, check if the given number+1 is greater than or equal to the given k value using the if conditional statement.
- If it is true, then return given k value -1.
- Else return (2 * gvn_numb + 1 – gvn_k_val).
- Pass the given number(size of matrix) and the given k value as the arguments to the
**findfreqencyof_k****()**function and store it in another variable. - Check if the above result is less than 0 using the if conditional statement.
- If it is true, then print “The given element k does not exist in the matrix”.
- Else print the frequency of the given k value.
- The Exit of the Program.

**Below is the implementation:**

# Import math module using the import keyword. import math # Create a function to say findfreqencyof_k() which takes the given number(size of matrix) # and the given k value as the arguments and returns the frequency of k of the matrix # with size n and matrix (i,j)=i+j. def findfreqencyof_k(gvn_numb, gvn_k_val): # Inside the function, check if the given number+1 is greater than or equal to the given # k value using the if conditional statement. if (gvn_numb + 1 >= gvn_k_val): # If it is true, then return given k value -1. return (gvn_k_val - 1) else: # Else return (2 * gvn_numb + 1 - gvn_k_val). return (2 * gvn_numb + 1 - gvn_k_val) # Give the number(size of matrix) as static input and store it in a variable. gvn_numb = 3 # Give another number k as static input and store it in another variable. gvn_k_val = 6 # Pass the given number(size of matrix) and the given k value as the arguments to the # findfreqencyof_k() function and store it in another variable. rslt = findfreqencyof_k(gvn_numb, gvn_k_val) # Check if the above result is less than 0 using the if conditional statement. if (rslt < 0): # If it is true, then print "The given element k does not exist in the matrix". print("The given element{", gvn_k_val, "} does not exist in the matrix") else: # Else print the frequency of the given k value. print(" The given k value{", gvn_k_val, "} frequency in the matix = ", rslt)

**Output:**

The given k value{ 6 } frequency in the matix = 1

### Method #2: Using Mathematical Formula (User Input)

**Approach:**

- Import math module using the import keyword.
- Give the number(size of matrix) as user input using the int(input()) function and store it in a variable.
- Give another number k as user input using the int(input()) function and store it in another variable.
- Create a function to say
**findfreqencyof_k()**which takes the given number(size of matrix) and the given k value as the arguments and returns the frequency of k of the matrix with size n and matrix (i,j)=i+j. - Inside the function, check if the given number+1 is greater than or equal to the given k value using the if conditional statement.
- If it is true, then return given k value -1.
- Else return (2 * gvn_numb + 1 – gvn_k_val).
- Pass the given number(size of matrix) and the given k value as the arguments to the
**findfreqencyof_k****()**function and store it in another variable. - Check if the above result is less than 0 using the if conditional statement.
- If it is true, then print “The given element k does not exist in the matrix”.
- Else print the frequency of the given k value.
- The Exit of the Program.

**Below is the implementation:**

# Import math module using the import keyword. import math # Create a function to say findfreqencyof_k() which takes the given number(size of matrix) # and the given k value as the arguments and returns the frequency of k of the matrix # with size n and matrix (i,j)=i+j. def findfreqencyof_k(gvn_numb, gvn_k_val): # Inside the function, check if the given number+1 is greater than or equal to the given # k value using the if conditional statement. if (gvn_numb + 1 >= gvn_k_val): # If it is true, then return given k value -1. return (gvn_k_val - 1) else: # Else return (2 * gvn_numb + 1 - gvn_k_val). return (2 * gvn_numb + 1 - gvn_k_val) # Give the number(size of matrix) as user input using the int(input()) function # and store it in a variable. gvn_numb = int(input("Enter some random number = ")) # Give another number k as user input using the int(input()) function and # store it in another variable. gvn_k_val = int(input("Enter some random number = ")) # Pass the given number(size of matrix) and the given k value as the arguments to the # findfreqencyof_k() function and store it in another variable. rslt = findfreqencyof_k(gvn_numb, gvn_k_val) # Check if the above result is less than 0 using the if conditional statement. if (rslt < 0): # If it is true, then print "The given element k does not exist in the matrix". print("The given element{", gvn_k_val, "} does not exist in the matrix") else: # Else print the frequency of the given k value. print(" The given k value{", gvn_k_val, "} frequency in the matix = ", rslt)

**Output:**

Enter some random number = 4 Enter some random number = 3 The given k value{ 3 } frequency in the matix = 2

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