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What is an important factor to consider when planning a journey from point A to point B?
When choosing the best route from A to B, which type of cost should be considered?
Which situation may lead to a higher tolerance for cost when planning travel?
What is the primary goal when studying algorithms?
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What issue arises when an airline does not have enough aircraft?
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What might be a reason for an airline to have too many aircraft in operation?
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What is asymptotic complexity used for in algorithm analysis?
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Which notation is typically used to express the efficiency of algorithms?
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In addition to direct costs, what other type of constraints should be considered in route planning?
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What role do data structures play in algorithms?
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What can happen if an airline does not plan for maintenance adequately?
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What type of scenario may require an urgent travel decision that could override cost considerations?
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What technique involves breaking a problem down into non-overlapping components?
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In algorithm design, what is essential to create a suitable mathematical model?
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Why is it important to prove the correctness of algorithms?
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Which of the following best describes the overall focus of this course?
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What is a primary factor that influences the complexity of a connectivity problem in a graph representation of cities?
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How does the number of direct flights (F) affect the algorithm designed for computing paths?
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If the number of cities (N) increases significantly, how might the algorithm's performance be affected?
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What would be a reasonable expectation for an online booking system's response time regarding flight queries?
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Which assessment relates to the feasibility of scaling algorithms for larger airline networks?
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What critical aspect must be evaluated to determine the running time of the connectivity algorithm?
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What might happen if the number of cities in a network doubles, in terms of algorithm performance?
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What is an important question to address before determining if an algorithm is efficient?
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If the input size of a problem is always at least 1, what would happen if n equals 0?
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For n greater than 5, which inequality holds true for the function 100n + 5?
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Which of the following statements is true about the upper bound of the function 100n + 5?
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If n0 is chosen to be 1 and c is 105, which inequality can be established?
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What does it mean that n0 and c are not unique in establishing big O notation?
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Why can we consider 100n + 5 as big O of n in a tighter sense?
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If we consider 100n squared + 20n + 5, which assumption is important for analysis?
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What is the implication of establishing that 101n is smaller than 100n squared?
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What is the time complexity of the loop that finds the maximum value in an array?
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In determining if an array has all distinct values, how does the algorithm avoid unnecessary comparisons?
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How many total comparisons are made when checking for distinct values in an array of n elements?
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What happens when the outer loop reaches the last element in the distinct values check?
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Why can we ignore constants when analyzing the time complexity of the maximum value loop?
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What is the worst-case scenario for finding the maximum value in an array?
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How many iterations does the inner loop run when the outer loop is at index i=2 in an array of size n?
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What is the primary operation performed in each iteration of the maximum value loop?
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Study Notes
Algorithm Correctness & Efficiency
- The algorithm should be correct and perform the intended job.
- Efficiency is measured by the time it takes to execute, considering the input size.
- Comparing algorithms using asymptotic complexity measures running time as input grows, using big O notation.
Problem Modeling & Data Structures
- Algorithms often require mathematical models, such as graphs.
- Data structures are used to represent these models within the algorithm.
- Problem decomposition into smaller, manageable sub-problems is a vital strategy.
Generic Algorithm Techniques
- Divide and conquer: Break down the problem into non-overlapping subproblems, combine solutions for the overall solution.
Graph Connectivity
- Determining the paths between cities (nodes) in a graph, representing connections like flights.
- Efficiency depends on both the number of cities (N) and the number of direct flights (F).
Complexity & Scaling
- Input size (N) influences algorithm complexity significantly.
- The number of connections (F) also impacts complexity.
- Determining the realistic size of networks that can be efficiently handled is essential, especially for real-time applications.
Constraints & Efficiency
- Cost (e.g., ticket price) and time are factors in finding the best route.
- Finding paths from A to B with additional constraints, like time limits or maintenance shutdowns, requires adjustments in algorithms.
Big O Notation Example
- For a function like 100n + 5:
- Provided n is bigger than 5, 100n + 5 is smaller than 101n.
- Since n is at least 1, n² is bigger than n, and 101n is smaller than 101n².
- Therefore, 100n + 5 is O(n²).
Finding Array Maximum & Linear Complexity
- To find the maximum value in an array, the worst-case scenario is scanning the entire array.
- Each iteration of the loop performs at least one comparison and a potential assignment.
- Ignoring constants, the algorithm is linear and takes O(n) time.
Distinct Values in an Array
- Determining if an array has all distinct values requires checking for duplicates.
- Two nested loops compare every element with every other element, but the inner loop iterates only up to n-1 for each outer loop iteration to avoid redundancy.
- The algorithm's time complexity is not linear due to the nested loop structure and its total steps sum up as 0+1+2+...+n-2+n-1, which is equal to n(n-1)/2, implying a O(n²) complexity.
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Description
This quiz covers key concepts related to algorithm correctness, efficiency, and the use of data structures in problem modeling. It focuses on techniques such as divide and conquer, and discusses graph connectivity and complexity as it relates to scaling. Test your understanding of algorithm design and analysis!
