Course Content
Algorithms and Data Structures Overview
Algorithms and Data Structures Overview
Challenge: How to Determine Algorithm Complexity
Here is a simplified guideline how to determine time complexity of the algorithm:
- Identify the Key Operations: Start by identifying your algorithm's key operations or steps. These operations could be loops, recursive calls, or other significant actions contributing to the algorithm's runtime;
- Count the Dominant Operation: Determine which operation dominates the overall runtime of the algorithm. Focus on the operation that contributes the most to the overall runtime, especially as the input size grows larger;
- Express Complexity in Terms of Input Size: Express the algorithm's runtime as a function of the input size (usually denoted as "n"). Consider how the number of operations scales with the size of the input;
- Remove Constants and Lower-Order Terms: Simplify the expression by removing constants and lower-order terms. Big O notation focuses on the dominant term that has the most significant impact on the runtime as the input size grows towards infinity;
- Determine the Big O Complexity: Once you have the expression representing the algorithm's runtime in terms of "n," determine the Big O complexity by identifying the fastest-growing term. This term represents the upper bound of the algorithm's runtime.
Task
Let's delve into the time complexity of a straightforward algorithm: Linear Search.
Linear Search is a fundamental searching method that examines each element in a list one by one until it locates a match or exhausts the list.
Your objective is to determine the number of comparisons the algorithm needs to locate the last element of the list. This count will establish the upper limit of the algorithm's time complexity.
Note
In this task, we aim to determine the worst-case time complexity of Linear Search. We need to find the last element in the list to estimate it. This requires traversing through all
nelements of the list. Consequently, the time complexity of Linear Search isO(n), as we must examine each element linearly until we find the target.
- Initialize the
comparisonsvariable. - Calculate the number of comparisons during algorithm execution.
- Print the number of comparisons at the end of the program code.
Once you've completed this task, click the button below the code to check your solution.
Everything was clear?
Course Content
Algorithms and Data Structures Overview
Algorithms and Data Structures Overview
Challenge: How to Determine Algorithm Complexity
Here is a simplified guideline how to determine time complexity of the algorithm:
- Identify the Key Operations: Start by identifying your algorithm's key operations or steps. These operations could be loops, recursive calls, or other significant actions contributing to the algorithm's runtime;
- Count the Dominant Operation: Determine which operation dominates the overall runtime of the algorithm. Focus on the operation that contributes the most to the overall runtime, especially as the input size grows larger;
- Express Complexity in Terms of Input Size: Express the algorithm's runtime as a function of the input size (usually denoted as "n"). Consider how the number of operations scales with the size of the input;
- Remove Constants and Lower-Order Terms: Simplify the expression by removing constants and lower-order terms. Big O notation focuses on the dominant term that has the most significant impact on the runtime as the input size grows towards infinity;
- Determine the Big O Complexity: Once you have the expression representing the algorithm's runtime in terms of "n," determine the Big O complexity by identifying the fastest-growing term. This term represents the upper bound of the algorithm's runtime.
Task
Let's delve into the time complexity of a straightforward algorithm: Linear Search.
Linear Search is a fundamental searching method that examines each element in a list one by one until it locates a match or exhausts the list.
Your objective is to determine the number of comparisons the algorithm needs to locate the last element of the list. This count will establish the upper limit of the algorithm's time complexity.
Note
In this task, we aim to determine the worst-case time complexity of Linear Search. We need to find the last element in the list to estimate it. This requires traversing through all
nelements of the list. Consequently, the time complexity of Linear Search isO(n), as we must examine each element linearly until we find the target.
- Initialize the
comparisonsvariable. - Calculate the number of comparisons during algorithm execution.
- Print the number of comparisons at the end of the program code.
Once you've completed this task, click the button below the code to check your solution.
Everything was clear?
