2025-02-Algorithm/notes/midterm.md

Alogorithm Midterm Access

Sorting Problem

Comparison Sorts(Lower bound is \Omega(n \lg n) because decision-tree model)

• Insertion Sort
• Selection Sort
• Merge Sort
• Quick Sort
• Heap Sort

Sorting In Linear Time

• Counting Sort
• Radix Sort

Asymtotic Notation

• $Theta$-notation
• $O$-notation
• $\Omega$-notation

Transitivity, Reflexivity, Symmetry, Transpose Symmetry

Three methods for solving recurrences:

1. Substitution method
2. Recursion-tree method
3. Master method

Getting asymtotic notation by recursion tree is important

Dynamic Programming

• Assembly-line scheduling
• Rod cutting
• Longest-Common Subsequence
• Matrix-chain Multiplication

Greedy Algorithm

• An Activity Selection Problem
• Elements of the greedy strategy
• Huffman codes