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Questions and Answers
What is the primary advantage of using a linked list over an array?
What does Big O notation measure?
Which of the following algorithms exhibits the greedy choice property?
What is the time complexity of a binary search algorithm?
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What is the primary advantage of using dynamic programming over a naive recursive approach?
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Which data structure is best suited for implementing a hierarchy of elements?
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What is the time complexity of the Merge Sort algorithm?
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Which of the following is a characteristic of the Divide and Conquer paradigm?
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What is the time complexity of the Fibonacci Series using dynamic programming?
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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
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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
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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
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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
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Examples:
- Merge Sort
- Quick Sort
- Binary Search
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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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Description
Learn about different data structures such as arrays, linked lists, stacks, queues, trees, and graphs. Understand time complexity with Big O notation and explore algorithms like greedy, dynamic programming, and divide and conquer.
