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@ -10,7 +10,7 @@ Asymptotic notations are used in computer science to classify algorithms based h
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# big O notation
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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
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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
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## 1 Formal definition
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@ -20,7 +20,7 @@ $f(n) = O(g(n))$ if there is some constant $A$ such that $f(n) < A \times g(n)$
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# big theta notation
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Big theta defines an upper and a lower bound for a the running time (or space) of an algorithm.
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Big theta defines an *upper and a lower* bound for a the running time (or space) of an algorithm.
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## 2 Formal definition
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@ -1,18 +0,0 @@
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---
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title: "big-theta-notation"
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tags:
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- cosc201
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---
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>Big theta means $f(n) = \Theta(g(n))$ if there are constants 0 < B < A such that for all sufficiently large n, ==$B × g(n) ≤ f(n) ≤ A × g(n)$==
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- Upper and lower bound
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- $Θ$ says that $g(n)$ provides **upper** and **lower** bound for $f(n)$
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- "selection sort is $\Theta(n^2)$" -> the maximum number of operations will be bounded both above and below by some constant times $n^2$
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- $f(n) = \Theta(g(n))$ means that f and g have similar growth rates
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- if $f(n) = \Theta(g(n))$ then the opposite is also true
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- usually $f(n)$ is complex but $g(n)$ is very simple
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@ -6,7 +6,6 @@ tags:
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---
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- [[notes/aymptotic-notation]]
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- [[notes/big-theta-notation]]
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- [[notes/induction]]
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- [[notes/analysis-of-recursive-algorithms]]
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- [[notes/union-find]]
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@ -15,4 +14,3 @@ tags:
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- [[notes/heapsort]]
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- [[notes/mergesort]]
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- [[notes/quicksort]]
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@ -10,3 +10,10 @@ tags:
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- [[notes/ethics-in-cs]]
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- [[notes/integrated-development-environments]]
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- [[notes/branch]]
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- [[notes/testing]]
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- [[notes/test-driven-development]]
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- [[notes/unit-testing]]
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- [[notes/debugging]]
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- [[notes/documentation]]
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- [[notes/continuous-integration]]
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-
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@ -10,9 +10,9 @@ tags:
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- [[notes/cosc-202-lectures]]
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- [[notes/cosc-202-outline]]
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## 2 Assignments
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## 1 Assignments
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-
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## 3 Resources
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## 2 Resources
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7
content/templates/induction-proof-template.md
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7
content/templates/induction-proof-template.md
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@ -0,0 +1,7 @@
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We will prove that, for every non-negative integer $n$, *insert property here*
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For $n = 0$, *The property* is true because *explicit verification of this case*
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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*
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Therefore, by induction, *the property* is true for all n.
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