Lecture 2

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Lecture 2

tags: Data Structure NYCU

[TOC]

Reference

Lec02 資料結構 第二週課程

Note

Recursive Algorithms

Type

  • Direct Recursion: 簡單來說就是自己呼叫自己
  • Indirect Recursion: A calls B $\to$ B calls itself

Boundary Condition

Recursive algorithm是會停止的，如果他能夠寫出一個完整的通式或過程，就代表有上限，當達到這個上限時就會停止 :::spoiler Example :::

Application of Recursive Function

  • Permutation Detailed description can browse the original video 如果不用Recursive解決Permutation的問題，可以考慮用For-Loop但是要考慮重複出現的問題 :::spoiler Example

    在這個例子中boundary condition就是只剩下一個字元需要做排列的時候 :::

  • Binary Search :::spoiler Example :::

Performance Analysis

如何判斷一個演算法的好壞

Complexity Theory

  1. Space Complexity

    font>: amount of memory $\to$ $S(P)=c+S_p(I)$ where $c$ is a constant(有多少固定的空間被用掉了，e.g. instruction, simple variables, constants) and $S_p$ is depends on characteristics of instance $I$

  2. Time Complexity

    font>: amount of computer time $\to$ $T(P)=c+T_p(I)$ where $c$ is a constant(有多少固定的時間被用掉了，e.g. compile time) and $S_p$ is program execution depends on characteristics of instance $I$ :::info Run(Execution) Time $T_p(n)=c_aADD(n)+c_sSUB(n)+c_lLDA(n)+c_{st}STA(n)$ where $LDA$ is the time by loading something and $STA$ is the time by storing something :::

How to know how many step in one program? - Purpose: Compute Time Complexity

  1. Use Count Variable :::spoiler Example :::
  2. Use Tabular Method :::spoiler Example ::: :::warning

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