Write a Program to Print the Diagonal Elements of the Given 2D Matrix
In this tutorial, we will write the Python program to print the diagonal elements of the given matrix. It is a common program that can be asked in technical interviews.
A 2D matrix is given; we need to print the primary and secondary diagonals.
Input:
Output:
Primary Diagonal: 1, 3, 9, 3 Secondary Diagonal: 4, 2, 8, 6
Input:
Output:
Primary Diagonal: 2, 2, 2 Secondary Diagonal: 2, 2, 2
Let’s understand the row-column pattern of the matrix in Python.
- To get the primary diagonal element, we need to find the Mat00, Mat11, Mat22, and Mat33; it is formed by using the same row and column name.
- To get the primary diagonal element, we need to find the Mat03, Mat12, Mat21, Mat30; The condition for secondary diagonal is –
What is Matrix?
A matrix is a 2-dimensional structure storing data in rows and columns. It can store an integer, strings, expressions, special symbols and more.
A matrix is a collection of rows and columns, and its structure is denoted by RXC, where R is denoted by the number of rows and C denotes the number of matrix columns, respectively.
In Python, we can create matrix using the two methods – using list and Numpy library.
The following code represents 3×3 matrices of numbers.
Example –
Output:
[['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']]
Matrix Representation in Python
Remember that we always put the row number first and then the column number. The correct format of an element X inside a matrix becomes X (R, C), where R and C represent the row and column where the element is present.
Let’s see the following 3×3 and 2×2 matrixes of numbers, and Z represents a 2X3 matrix of string.
Example –
Output:
[['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']] [[27, 34], [61, 18]] [['one', 'two', 'three'], ['four', 'five', 'six']]
Now we have the basic idea of the matrix presentation in Python. Now let’s jump to the solution part.
Solution
Let’s understand the first method.
Method – 1:
In this method, we will use the two for loops for columns and a loop for rows, and in the inner loop, we check for the condition.
Example –
Output:
Primary Diagonal is: 1,3,9,3,
Explanation –
In the above code, we get the rows and col of and matrix and we have used the two for loops. In the inner loop, we checked the conditions if the i and j are equal than print the corresponding element.
Now we will write Program to get the secondary diagonal
Example – 2:
Output:
Secondary Diagonal: 4, 2, 8, 6,
Time Complexity – O(n2)
As there is a nested loop involved so the time complexity is squared.
Auxiliary Space: O(1).
As no extra space is occupied
Method – 2:
We can solve this problem using the single for loop. Let’s understand the following example.
Example –
Output:
Principal Diagonal: 1, 6, 3, 8,
Explanation –
In the above code, we run a for loop until length of matrix n, and print the mat[i][i] where i is the index variable.
For Secondary Diagonal Elements
Example – 2:
Output:
Secondary Diagonal: 4, 7, 2, 1,
Explanation –
We have used the same approach as above and print mat[i][k] where i is the index variable and k = matrix_length – 1 and decrease k until i < n.
Complexity Analysis:
- Time Complexity: O (n).
As a nested loop is involved, the time complexity is squared. - Auxiliary Space:O (1).
As no extra space is occupied.