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Questions and Answers
What is the time complexity of Insertion Sort in the best case scenario?
What is the time complexity of Insertion Sort in the best case scenario?
Which sorting algorithm has the best time complexity in the average case?
Which sorting algorithm has the best time complexity in the average case?
What is the time complexity of Binary Search in the worst case scenario?
What is the time complexity of Binary Search in the worst case scenario?
Which sorting algorithm is known to be stable?
Which sorting algorithm is known to be stable?
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Which of the following algorithms does NOT use the Divide and Conquer approach?
Which of the following algorithms does NOT use the Divide and Conquer approach?
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Which of the following problems is typically solved using Divide and Conquer?
Which of the following problems is typically solved using Divide and Conquer?
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What is the main disadvantage of the Greedy approach?
What is the main disadvantage of the Greedy approach?
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Which of the following algorithms uses the Greedy approach for finding the shortest path?
Which of the following algorithms uses the Greedy approach for finding the shortest path?
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What is the primary difference between an Adjacency List and an Adjacency Matrix representation of a graph?
What is the primary difference between an Adjacency List and an Adjacency Matrix representation of a graph?
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Which of the following is NOT a property of a balanced binary tree?
Which of the following is NOT a property of a balanced binary tree?
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In the context of sorting algorithms, which of the following is TRUE about stability?
In the context of sorting algorithms, which of the following is TRUE about stability?
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Which sorting algorithm is considered the most efficient in terms of average-case time complexity?
Which sorting algorithm is considered the most efficient in terms of average-case time complexity?
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Which of the following is a common use case for graphs in computer science?
Which of the following is a common use case for graphs in computer science?
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When performing a Binary Search on a sorted list, if the target element is less than the middle element, what is the next step?
When performing a Binary Search on a sorted list, if the target element is less than the middle element, what is the next step?
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Which of the following sorting algorithms would typically be the least suitable for sorting a large dataset with millions of elements?
Which of the following sorting algorithms would typically be the least suitable for sorting a large dataset with millions of elements?
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In an AVL tree, what is the primary purpose of rotations?
In an AVL tree, what is the primary purpose of rotations?
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What is a key characteristic of Divide and Conquer strategies?
What is a key characteristic of Divide and Conquer strategies?
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Which of these is NOT a step in the general Divide and Conquer strategy?
Which of these is NOT a step in the general Divide and Conquer strategy?
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What is a common limitation of the brute force approach when dealing with large-scale problems?
What is a common limitation of the brute force approach when dealing with large-scale problems?
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When would the brute force approach be considered a reasonable choice for solving a problem?
When would the brute force approach be considered a reasonable choice for solving a problem?
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In the context of the knapsack problem, what does the brute force approach involve doing?
In the context of the knapsack problem, what does the brute force approach involve doing?
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How can brute force algorithms impact memory usage, potentially leading to problems?
How can brute force algorithms impact memory usage, potentially leading to problems?
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What is a key disadvantage of the brute force approach in terms of optimization?
What is a key disadvantage of the brute force approach in terms of optimization?
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What is a fundamental principle behind Dynamic Programming, and how does it relate to brute force approaches?
What is a fundamental principle behind Dynamic Programming, and how does it relate to brute force approaches?
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Flashcards
Adjacency List Space Complexity
Adjacency List Space Complexity
O(V + E) represents space usage in graphs.
Weighted Graph
Weighted Graph
A graph where edges have associated weights or costs.
Binary Tree
Binary Tree
Hierarchical structure with at most two children per node.
AVL Tree
AVL Tree
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Breadth-First Search (BFS)
Breadth-First Search (BFS)
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Binary Search
Binary Search
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Merge Sort Stability
Merge Sort Stability
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Quick Sort Worst-Case Time Complexity
Quick Sort Worst-Case Time Complexity
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Insertion Sort
Insertion Sort
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Merge Sort
Merge Sort
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Linear Search
Linear Search
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Divide and Conquer
Divide and Conquer
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Greedy Algorithm
Greedy Algorithm
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Merge Sort Complexity
Merge Sort Complexity
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Dijkstra's Algorithm
Dijkstra's Algorithm
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Dynamic Programming Example
Dynamic Programming Example
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Brute Force Approach
Brute Force Approach
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Limitations of Brute Force
Limitations of Brute Force
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When to Use Brute Force
When to Use Brute Force
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Knapsack Problem
Knapsack Problem
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Time Complexity of Brute Force
Time Complexity of Brute Force
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Memory Usage in Brute Force
Memory Usage in Brute Force
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Study Notes
Chapter 5: Trees and Graphs
- Adjacency List Representation space complexity: O(V + E)
- Weighted Graph: A graph with edges assigned weights or costs
- Binary Tree: A hierarchical data structure where each node has at most two children
- Adjacency Matrix Representation space complexity: O(V2)
- AVL Tree: A type of binary search tree (BST) ensuring a height difference of at most 1 between left and right subtrees of a node
- Breadth-First Search (BFS): Explores all vertices at the current depth before moving to the next depth level in graph traversal
- Balanced Binary Tree: A balanced binary tree has the height difference between left and right subtrees of any node at most 1
- Binary Tree: A hierarchical data structure where each node has at most two children
- Rebalancing in AVL trees: Performed using rotations
- Worst-case time complexity of unbalanced BST operations: O(n)
- Graph Application: Modelling relationships between objects using vertices and edges
- Balanced BST time complexity: O(log n) for search, insertion, and deletion
Chapter 6: Algorithms (Sorting and Searching)
- Stable Sorting Algorithm: Merge Sort
- Partitioning concept: Used in Quick Sort
- Binary Search time complexity (worst case): O(log n)
- Binary Search - next step when greater than middle: Search the right half
- Bubble Sort best-case time complexity: O(n)
- Bubble Sort suitability for large datasets: Not suitable due to high time complexity
- Quick Sort worst-case time complexity: O(n2)
- Selection Sort: Repeatedly finds the smallest element and puts it at the beginning
- Merge Sort best average-case time complexity: Best average case time complexity
- Insertion Sort suitability: Suitable for small datasets or nearly sorted arrays
- Merge Sort average-case time complexity: Best time complexity in average case
- Linear Search worst-case time complexity: O(n)
- Insertion Sort space complexity: Best space complexity
- Selection Sort: Divides input into sorted and unsorted regions
- Binary Search suitability: Optimal for sorted data
- Bubble Sort worst-case time complexity: Worst time complexity in the worst case
- Binary Search: Algorithm requires sorted data
- Hashing time complexity (average): O(1)
- Stable Sorting Algorithm: Merge Sort
Chapter 7: Divide and Conquer and Greedy Algorithms
- Merge Sort recurrence relation: T(n) = 2T(n/2) + O(n)
- Divide and conquer disadvantage: May require more memory due to recursion
- Divide and conquer problem reduction: Problem size is reduced by half in each step
- Divide and conquer typical problem: Multiplying large integers (e.g., Karatsuba algorithm).
- Divide and conquer steps: Divide, conquer, combine
- Non-Divide and Conquer Algorithm: Bubble Sort
- Divide and Conquer Base Case: Point where input is reduced to a trivial problem size
- Merge Sort worst-case time complexity: O(n log n)
- Greedy Algorithm Characteristic: Making locally optimal choices at each step
- Greedy Choice Property: A global optimum can be achieved by selecting a local optimum
- Divide and Conquer Algorithm: Merge Sort
- Greedy Algorithm Pathfinding: Dijkstra's Algorithm
- Characteristic of Divide and Conquer: Dividing the problem into smaller independent subproblems
- Dynamic Programming characteristic: Overlapping subproblems
- Merge Sort time complexity: O(n log n)
- Divide and Conquer Strategy Steps: Divide, Conquer, Combine
- Dynamic Programming applicability: Solving problems with overlapping subproblems
Chapter 8: Brute Force Design Algorithm
- Brute force optimization limitation: Does not leverage problem-specific knowledge, heuristics, or patterns
- Brute force approach applicability: Used when the problem is small or no better algorithm is available
- Brute force application examples: Search problems, optimization problems, cryptography.
- Brute force time complexity limitation: Exponential time complexity, leading to impractical computation for large datasets, especially with large problem sizes.
- Brute force suitability: Suitable when there are a small number of possibilities, no optimal algorithm exists and no patterns to leverage.
- Knapsack problem: Determine maximum value obtainable by selecting a subset of items without exceeding capacity.
- Brute force Knapsack Solution: Trying all possible combinations of items, checking within the weight limit, calculate total values, and keep track of maximum value.
- Brute force memory usage limitation: Storing a large number of intermediate results leads to high memory usage.
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Description
Dive into Chapter 5 on Trees and Graphs, covering key concepts such as adjacency list and matrix representations, binary trees, AVL trees, and traversal techniques like Breadth-First Search (BFS). Understand the importance of space complexity and operational efficiencies in data structures. Enhance your knowledge of algorithms used in graph modeling and tree balancing.
