Time Complexity Examples 2

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In this class, we will try to understand Time Complexity Examples 2.

The have already discussed an example to find the time complexity in our previous class.

Time Complexity Examples 2

To understand how to find an algorithm’s time complexity, consider the image below.

Time Complexity Examples 2 - 1
Time Complexity Examples 2 – 1

The above image shows the algorithm for matrix addition.

First, we will understand the algorithm and then find an algorithm’s time complexity.

The outer for loop iterates for m + 1 times.

Each time we come into the loop the inner loop will iterate for m(n + 1) times.

For each iteration of the inner for loop a row values will be added.

The values of m and n represents the number of rows and columns.

The expression c[i, j] = a[i, j] + b[i, j] will add the values in the matrix A nd B and will will stored in C.

The expression c[i, j] = a[i, j] + b[i, j] will be executed for mn times.

The number of times each step of the algorithm is executed is shown below.

Time Complexity Examples 2 - 2
Time Complexity Examples 2 – 2

The time complexity of the algorithm is m + 1 + mn + m + mn = 2mn + 2m + 1.