auto update

This commit is contained in:
Jet Hughes 2022-04-07 11:52:38 +12:00
parent b29e682bbc
commit 53a939f4d6
7 changed files with 20 additions and 26 deletions

View File

@ -10,7 +10,7 @@ Asymptotic notations are used in computer science to classify algorithms based h
# big O notation
Big O defines a bound for the *upper limit* of the running time (or space) of a algorithm. However, it is possible that the actual running time is much less as it does not take into account special cases
Big O defines a bound for the *upper* bound of the running time (or space) of a algorithm. However, it is possible that the actual running time is much less as it does not take into account special cases
## 1 Formal definition
@ -20,7 +20,7 @@ $f(n) = O(g(n))$ if there is some constant $A$ such that $f(n) < A \times g(n)$
# big theta notation
Big theta defines an upper and a lower bound for a the running time (or space) of an algorithm.
Big theta defines an *upper and a lower* bound for a the running time (or space) of an algorithm.
## 2 Formal definition

View File

@ -1,18 +0,0 @@
---
title: "big-theta-notation"
tags:
- cosc201
---
>Big theta means $f(n) = \Theta(g(n))$ if there are constants 0 < B < A such that for all sufficiently large n, ==$B × g(n) f(n) A × g(n)$==
- Upper and lower bound
- $Θ$ says that $g(n)$ provides **upper** and **lower** bound for $f(n)$
- "selection sort is $\Theta(n^2)$" -> the maximum number of operations will be bounded both above and below by some constant times $n^2$
- $f(n) = \Theta(g(n))$ means that f and g have similar growth rates
- if $f(n) = \Theta(g(n))$ then the opposite is also true
- usually $f(n)$ is complex but $g(n)$ is very simple

View File

@ -6,7 +6,6 @@ tags:
---
- [[notes/aymptotic-notation]]
- [[notes/big-theta-notation]]
- [[notes/induction]]
- [[notes/analysis-of-recursive-algorithms]]
- [[notes/union-find]]
@ -15,4 +14,3 @@ tags:
- [[notes/heapsort]]
- [[notes/mergesort]]
- [[notes/quicksort]]

View File

@ -10,3 +10,10 @@ tags:
- [[notes/ethics-in-cs]]
- [[notes/integrated-development-environments]]
- [[notes/branch]]
- [[notes/testing]]
- [[notes/test-driven-development]]
- [[notes/unit-testing]]
- [[notes/debugging]]
- [[notes/documentation]]
- [[notes/continuous-integration]]
-

View File

@ -10,9 +10,9 @@ tags:
- [[notes/cosc-202-lectures]]
- [[notes/cosc-202-outline]]
## 2 Assignments
## 1 Assignments
-
## 3 Resources
## 2 Resources

View File

@ -33,7 +33,7 @@ Four parts
e.g.,
- we will prove that, for every non-negative integer $n$, *insert property here*
- For $n = 0$, *The property* is true because *explicit verification of this case*
- for any $n > 0$, assuming *the property* is true for $n-1$ (or, for all $k < n$), *the property* is true at $n$ because *explain why we can take a step up*
- for any $n > 0$, assuming *the property* is true for $n-1$ (or, for all $k < n$), *the property* is true at $n$ because *explain why we can take a step up*
- Therefore, by induction, *the property* is true for all n.
### 1.3 Checking

View File

@ -0,0 +1,7 @@
We will prove that, for every non-negative integer $n$, *insert property here*
For $n = 0$, *The property* is true because *explicit verification of this case*
For any $n > 0$, assuming *the property* is true for $n-1$ (or, for all $k < n$), *the property* is true at $n$ because *explain why we can take a step up*
Therefore, by induction, *the property* is true for all n.