Question

Suppose an algorithm consists of two loops, where one loop executes and finishes, and then the other loop executes and finishes. we can easily determine the time complexities of the individual loops. to determine the time complexity of the entire algorithm, we should:

O We would not be able to determine the time complexity of the algorithm with the information given
O take the fastest time complexity of the two
O multiply the time complexities together
O add the time complexities together

Answer 1

To determine the time complexity of an algorithm consisting of two loops, we need to add the time complexities of the individual loops together.

Step-by-step explanation:

To determine the time complexity of the entire algorithm consisting of two loops, we need to consider the time complexities of both loops and find the overall time complexity. One way to approach this is to analyze the loops separately and then combine their time complexities using the rules of algorithmic analysis.

If the first loop has a time complexity of O(n) and the second loop has a time complexity of O(m), where 'n' and 'm' represent the sizes of the input in each loop, we would want to know how these two loops interact with each other.

If these loops execute sequentially, one after the other, then we can add their time complexities together to determine the overall time complexity. Therefore, the correct answer would be to add the time complexities together.

To calculate the overall time complexity of an algorithm consisting of two loops that are executed sequentially, we simply add the time complexities of the individual loops together. If one loop has a time complexity of O(n) and the other has O(m), where 'n' and 'm' are sized differently, the overall time complexity would be O(n + m).

This is because each loop runs independently and finishes before the next loop starts, which means their execution times are additive, not multiplicative. Hence, the correct option is to add the time complexities together.