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Questions and Answers
What is the primary advantage of using a linked list over an array?
What is the primary advantage of using a linked list over an array?
- Faster insertion and deletion of elements (correct)
- Fixed memory allocation
- Dynamic memory allocation
- Faster access to elements
What does Big O notation measure?
What does Big O notation measure?
- The average-case time complexity of an algorithm
- The space complexity of an algorithm
- The worst-case time complexity of an algorithm (correct)
- The best-case time complexity of an algorithm
Which of the following algorithms exhibits the greedy choice property?
Which of the following algorithms exhibits the greedy choice property?
- Longest Common Subsequence
- Activity Selection Problem (correct)
- Merge Sort
- Fibonacci Series
What is the time complexity of a binary search algorithm?
What is the time complexity of a binary search algorithm?
What is the primary advantage of using dynamic programming over a naive recursive approach?
What is the primary advantage of using dynamic programming over a naive recursive approach?
Which data structure is best suited for implementing a hierarchy of elements?
Which data structure is best suited for implementing a hierarchy of elements?
What is the time complexity of the Merge Sort algorithm?
What is the time complexity of the Merge Sort algorithm?
Which of the following is a characteristic of the Divide and Conquer paradigm?
Which of the following is a characteristic of the Divide and Conquer paradigm?
What is the time complexity of the Fibonacci Series using dynamic programming?
What is the time complexity of the Fibonacci Series using dynamic programming?
Which data structure is best suited for implementing a Last-In-First-Out (LIFO) stack?
Which data structure is best suited for implementing a Last-In-First-Out (LIFO) stack?
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Study Notes
Algorithms
Data Structures
- Arrays: a collection of elements of the same data type stored in contiguous memory locations
- Linked Lists: a dynamic collection of elements, where each element points to the next element
- Stacks: a LIFO (Last In First Out) data structure, where elements are added and removed from the top
- Queues: a FIFO (First In First Out) data structure, where elements are added to the end and removed from the front
- Trees: a hierarchical data structure, where each node has a value and zero or more child nodes
- Graphs: a non-linear data structure, where nodes are connected by edges
Time Complexity
- Big O Notation: a measure of an algorithm's performance, describing the worst-case running time
- Best Case: the minimum time an algorithm takes to complete
- Average Case: the average time an algorithm takes to complete
- Worst Case: the maximum time an algorithm takes to complete
- Time Complexity Classes:
- O(1) - constant time complexity
- O(log n) - logarithmic time complexity
- O(n) - linear time complexity
- O(n log n) - linearithmic time complexity
- O(n^2) - quadratic time complexity
- O(2^n) - exponential time complexity
- O(n!) - factorial time complexity
Greedy Algorithms
- Greedy Choice Property: an optimal solution to a problem can be constructed by making locally optimal choices
- Optimal Substructure: an optimal solution to a problem can be constructed from optimal solutions of its subproblems
- Examples:
- Huffman Coding
- Activity Selection Problem
- Coin Changing Problem
Dynamic Programming
- Dynamic Programming: breaking down a problem into smaller subproblems, solving each only once, and storing the solutions to subproblems to avoid redundant computation
- Memoization: storing the solutions to subproblems to avoid redundant computation
- Tabulation: building up a table of solutions to subproblems
- Examples:
- Fibonacci Series
- Longest Common Subsequence
- Knapsack Problem
Divide and Conquer
- Divide and Conquer: breaking down a problem into smaller subproblems, solving each, and combining the solutions to solve the original problem
- Examples:
- Merge Sort
- Quick Sort
- Binary Search
- Characteristics:
- Divide: break the problem into smaller subproblems
- Conquer: solve each subproblem
- Combine: combine the solutions to the subproblems to solve the original problem
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