Merge branch 'master' of gram.cse.buffalo.edu:ODIn/Website
commit
0b5b8a5528
GPG Key ID:
3E5F9B3ABD3FDB60
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@ -269,11 +269,15 @@ schedule:
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- date: 09/21/22
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topic: Linked Lists and Iterators
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dow: Wed
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section_a:
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slides: slide/lec10a.pdf
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section_b:
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slides: slide/9b-LinkedListIterator.html
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- date: 09/23/22
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topic: Recursion Intro
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dow: Fri
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section_a:
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||||
slides: slide/lec11a.pdf
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section_b:
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slides: slide/10b-Recursion.html
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- week: 5
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|
@ -286,11 +290,10 @@ schedule:
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- date: 09/28/22
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topic: Recursive Analysis (contd...)
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dow: Wed
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due: WA0
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due: WA1
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- date: 09/30/22
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topic: Data-Bounded Analysis
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dow: Fri
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due: WA1
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- week: 6
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lectures:
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- date: 10/03/22
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|
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@ -1,7 +1,7 @@
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---
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template: templates/cse250_2022_slides.erb
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title: Recursion
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date: Sept 21, 2022
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date: Sept 23, 2022
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textbook: Ch. 15
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---
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@ -10,10 +10,30 @@ textbook: Ch. 15
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<attribution><a href="https://www.etsy.com/listing/916447505/ukrainian-nesting-doll-nesting-dolls">Ukranian Nesting Doll Nesting Dolls Handmade Dolls | Etsy</a>
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</section>
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|
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<section>
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<p>Computational problems can be recursive too!</p>
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</section>
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|
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<section>
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<h4 class="slide_title">Factorial</h4>
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|
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<pre><code>
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<p class="fragment">
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$439!$ <span class="fragment">$= 439 \cdot 438!$</span>
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</p>
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</section>
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<section>
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<h4 class="slide_title">Factorial</h4>
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<p><b>Recursive Case: </b> $n! = n \cdot (n-1)!$</p>
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<p class="fragment"><b>Base Case: </b> $1! = 1$</p>
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|
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</section>
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|
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<section>
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<h4 class="slide_title">Factorial</h4>
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<pre><code class="scala">
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def factorial(n: Int): Long =
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if(n <= 1){ 1 }
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else { n * factorial(n-1) }
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@ -24,12 +44,12 @@ textbook: Ch. 15
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<h4 class="slide_title">Factorial</h4>
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|
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<b>Base Case:</b>
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<pre><code>
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<pre><code class="scala">
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if(n <= 1){ 1 }
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</code></pre>
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|
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<b>Recursive Case:</b>
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<pre><code>
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<pre><code class="scala">
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else { n * factorial(n-1) }
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</code></pre>
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</section>
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|
@ -51,11 +71,18 @@ textbook: Ch. 15
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|||
|
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<section>
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<h4 class="slide_title">Fibonacci</h4>
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|
||||
<p><b>Base Cases:</b> $\texttt{fib}(1) = 1$, $\texttt{fib}(2) = 1$</p>
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<p><b>Recursive Cases:</b> $\texttt{fib}(n) = \texttt{fib}(n-1) + \texttt{fib}(n-2)$</p>
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</section>
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|
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<pre><code>
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def fibb(n: Int): Long =
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<section>
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<h4 class="slide_title">Fibonacci</h4>
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|
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<pre><code class="scala">
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def fib(n: Int): Long =
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if(n < 2){ 1 }
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else { fibb(n-1) + fibb(n-2) }
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else { fib(n-1) + fib(n-2) }
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</code></pre>
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</section>
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|
|
@ -63,13 +90,13 @@ textbook: Ch. 15
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<h4 class="slide_title">Fibonacci</h4>
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|
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<b>Base Case:</b>
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<pre><code>
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<pre><code class="scala">
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if(n < 2){ 1 }
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</code></pre>
|
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|
||||
<b>Recursive Case:</b>
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<pre><code>
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else { fibb(n-1) + fibb(n-2) }
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<pre><code class="scala">
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else { fib(n-1) + fib(n-2) }
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</code></pre>
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</section>
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|
|
@ -82,32 +109,71 @@ textbook: Ch. 15
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<section>
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<h4 class="slide_title">Towers of Hanoi</h4>
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|
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<pre><code>
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<p><b>Task:</b> Move $n$ blocks from <b>A</b> to <b>C</b></p>
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<p><b><u>Base Case</u></b> ($n=1$)
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<ol>
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<li>Move the block from <b>A</b> to <b>C</b></li>
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</ol>
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</p>
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<p><b><u>Recursive Case</u></b> ($n \geq 2$)
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<ol>
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<li>Move $n-1$ blocks from <b>A</b> to <b>B</b></li>
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<li>Move the bottom block from <b>A</b> to <b>C</b></li>
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<li>Move $n-1$ blocks from <b>B</b> to <b>C</b></li>
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</ol>
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||||
</p>
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|
||||
</section>
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<section>
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<h4 class="slide_title">Towers of Hanoi</h4>
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|
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<pre><code class="scala">
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var towers = Array(new Stack(), new Stack(), new Stack())
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def moveFrom(fromTower: Int, toTower: Int, numDisks: Int): Unit =
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def move(fromTower: Int, toTower: Int, numDisks: Int): Unit =
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{
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val otherTower = (Set(0, 1, 2) - fromTower - toTower).head
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if(numDisks < 0){
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return
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} else if(numDisks == 1){
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moveTopDisk(from = fromTower, to = toTower)
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if(numDisks == 1){
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moveOne(from = fromTower, to = toTower)
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} else {
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moveFrom(fromTower, otherTower, numDisks-1)
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moveTopDisk(from = fromTower, to = toTower)
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moveFrom(otherTower, toTower, numDisks-1)
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move(fromTower, otherTower, numDisks-1)
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moveOne(from = fromTower, to = toTower)
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move(otherTower, toTower, numDisks-1)
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||||
}
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||||
}
|
||||
</code></pre>
|
||||
</section>
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|
||||
<section>
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||||
<p>How do we get the complexity of recursive algorithms?</p>
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||||
</section>
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||||
|
||||
<section>
|
||||
<h4 class="slide_title">Factorial</h4>
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||||
|
||||
<p>What's the complexity? (in terms of <tt>n</tt>)</p>
|
||||
|
||||
<pre><code>
|
||||
<pre><code class="scala">
|
||||
def factorial(n: Int): Long =
|
||||
if(n <= 1){ 1 }
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||||
else { n * factorial(n-1) }
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||||
</code></pre>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Idea:</b> Write down a recursive runtime growth function</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Factorial</h4>
|
||||
|
||||
<p>What's the complexity? (in terms of <tt>n</tt>)</p>
|
||||
|
||||
<pre><code class="scala">
|
||||
def factorial(n: Int): Long =
|
||||
if(n <= 1){ 1 }
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else { n * factorial(n-1) }
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|
|
@ -124,13 +190,16 @@ textbook: Ch. 15
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Fibonacci</h4>
|
||||
<h4 class="slide_title">Factorial</h4>
|
||||
<p>
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||||
<b><u>Base Case</u></b> ($n \leq 0$)
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||||
$$\Theta(1)$$
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||||
</p>
|
||||
|
||||
<b>Base Case:</b>
|
||||
$$\Theta(1) \textbf{ if } n < 2$$
|
||||
|
||||
<b>Recursive Case"</b>
|
||||
$$T(n-1) + \Theta(1) \textbf{ otherwise}$$
|
||||
<p>
|
||||
<b><u>Recursive Case</u></b> ($n > 0$)
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$$T(n-1) + \Theta(1)$$
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
|
@ -152,30 +221,30 @@ textbook: Ch. 15
|
|||
<p><b>Approach:</b>
|
||||
<ol>
|
||||
<li>Generate a Hypothesis (🔮)</li>
|
||||
<li>Prove the Hypothesis for the Base Case (🏡)</li>
|
||||
<li>Prove the Hypothesis Inductively (🏢)</li>
|
||||
<li>Prove the Hypothesis for the Base Case</li>
|
||||
<li>Prove the Hypothesis Inductively</li>
|
||||
</ol>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Generate a Hypothesis (🔮)</h4>
|
||||
<h4 class="slide_title">Generate a Hypothesis</h4>
|
||||
|
||||
<p><b>Approach:</b> Write out the rule for increasing $n$</p>
|
||||
|
||||
<p>
|
||||
$\Theta(1)$,
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||||
<span class="fragment">$2\Theta(1)$ </span>
|
||||
<span class="fragment">$3\Theta(1)$ </span>
|
||||
<span class="fragment">$4\Theta(1)$ </span>
|
||||
<span class="fragment">$5\Theta(1)$ </span>
|
||||
<span class="fragment">$6\Theta(1)$ </span>
|
||||
<span class="fragment">$7\Theta(1)$ </span>
|
||||
<span class="fragment">$2\Theta(1)$, </span>
|
||||
<span class="fragment">$3\Theta(1)$, </span>
|
||||
<span class="fragment">$4\Theta(1)$, </span>
|
||||
<span class="fragment">$5\Theta(1)$, </span>
|
||||
<span class="fragment">$6\Theta(1)$, </span>
|
||||
<span class="fragment">$7\Theta(1)$, $\ldots$ </span>
|
||||
</p>
|
||||
|
||||
<p class="fragment">What's the pattern?</p>
|
||||
|
||||
<p class="fragment"><b>Hypothesis: </b> $T(n) \in O(n)$ (there is some $c > 0$ such that $T(n) \leq c \cdot n$)</p>
|
||||
<p class="fragment"><b>Hypothesis: </b> $T(n) \in O(n)$<br> (there is some $c > 0$ such that $T(n) \leq c \cdot n$)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
|
@ -192,16 +261,16 @@ textbook: Ch. 15
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case (🏡)</h4>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case</h4>
|
||||
|
||||
<p>$T(1) \leq c \cdot 1$</p>
|
||||
<p class="fragment">$T(1) \leq c$</p>
|
||||
<p class="fragment">$c_0 \leq c$</p>
|
||||
<p class="fragment">True for any $c \geq c_0</p>
|
||||
<p class="fragment">True for any $c \geq c_0$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case+1 (🏡)</h4>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case+1</h4>
|
||||
|
||||
<p>$T(2) \leq c \cdot 2$</p>
|
||||
<p class="fragment">$T(1) + c_1 \leq 2c$</p>
|
||||
|
|
@ -211,21 +280,21 @@ textbook: Ch. 15
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case+2 (🏡)</h4>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case+2</h4>
|
||||
|
||||
<p>$T(3) \leq c \cdot 3$</p>
|
||||
<p class="fragment">$T(2) + c_1 \leq 3c$</p>
|
||||
<p class="fragment">We know there's a $c$ s.t. $T(2) \leq 2c$, so if we show that $2c + c_1 \leq 3c$, then $T(2) + c_1 \leq 2c + c_1 \leq 3c$</p>
|
||||
<p class="fragment">We know there's a $c$ s.t. $T(2) \leq 2c$,<br>... so if we show that $2c + c_1 \leq 3c$, then $T(2) + c_1 \leq 2c + c_1 \leq 3c$</p>
|
||||
<p class="fragment">$c_1 \leq c$</p>
|
||||
<p class="fragment">True for any $c \geq c_1$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case+3 (🏡)</h4>
|
||||
<h4 class="slide_title">Prove the Hypothesis for the Base Case+3</h4>
|
||||
|
||||
<p>$T(4) \leq c \cdot 4$</p>
|
||||
<p>$T(3) + c_1 \leq 4c$</p>
|
||||
<p>We know there's a $c$ s.t. $T(3) \leq 3c$, so if we show that $3c + c_1 \leq 4c$, then $T(3) + c_1 \leq 3c + c_1 \leq 4c$</p>
|
||||
<p>We know there's a $c$ s.t. $T(3) \leq 3c$, <br>...so if we show that $3c + c_1 \leq 4c$, then $T(3) + c_1 \leq 3c + c_1 \leq 4c$</p>
|
||||
<p>$c_1 \leq c$</p>
|
||||
<p>True for any $c \geq c_1$</p>
|
||||
</section>
|
||||
|
|
@ -235,22 +304,29 @@ textbook: Ch. 15
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Prove the Hypothesis Inductively (🏢)</h4>
|
||||
<h4 class="slide_title">Prove the Hypothesis Inductively</h4>
|
||||
|
||||
<p><b>Approach:</b> Assume the hypothesis is true for any $n' < n$; use that to prove for $n$</p>
|
||||
|
||||
<p class="fragment"><b>Assume: </b>There is a $c > 0$ s.t. $T(n-1) \leq c\cdot (n-1)$</p>
|
||||
<p class="fragment"><b>Prove: </b>There is a $c > 0$ s.t. $T(n) \leq c\cdot n$</p>
|
||||
<p class="fragment">$T(n-1) + c_1 \leq c \cdot n$</p>
|
||||
<p class="fragment">By the inductive assumption, there is a $c$ s.t. $T(n-1) \leq (n-1)c$, so if we show that $(n-1)c + c_1 \leq nc$, then $T(n-1) + c_1 \leq (n-1)c + c_1 \leq nc$</p>
|
||||
<p class="fragment">$c_1 \leq c$</p>
|
||||
<p class="fragment">True for any $c \geq c_1$</p>
|
||||
<p><b>Approach:</b> Assume the hypothesis is true for any $n' < n$;<br> use that to prove for $n$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Prove the Hypothesis Inductively</h4>
|
||||
|
||||
<div style="font-size: 90%">
|
||||
<p><b>Assume: </b>There is a $c > 0$ s.t. $T(n-1) \leq c\cdot (n-1)$</p>
|
||||
<p><b>Prove: </b>There is a $c > 0$ s.t. $T(n) \leq c\cdot n$</p>
|
||||
<p class="fragment">$T(n-1) + c_1 \leq c \cdot n$</p>
|
||||
<p class="fragment" style="font-size: 80%">By the inductive assumption, there is a $c$ s.t. $T(n-1) \leq (n-1)c$, so if we show that $(n-1)c + c_1 \leq nc$, then $T(n-1) + c_1 \leq (n-1)c + c_1 \leq nc$</p>
|
||||
<p class="fragment">$(n-1)c + c_1 - (n-1)c \leq nc - (n-1)c$</p>
|
||||
<p class="fragment">$c_1 \leq c $</p>
|
||||
<p class="fragment">True for any $c \geq c_1$</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Factorial</h4>
|
||||
|
||||
<pre><code>
|
||||
<pre><code class="scala">
|
||||
def factorial(n: Int): Long =
|
||||
if(n <= 1){ 1 }
|
||||
else { n * factorial(n-1) }
|
||||
|
|
@ -260,19 +336,20 @@ textbook: Ch. 15
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">The Call Stack</h4>
|
||||
<svg data-src="graphics/10b/callstack.svg"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">Tail Recursion</h4>
|
||||
|
||||
<pre><code>
|
||||
<pre><code class="scala">
|
||||
def factorial(n: Int): Long =
|
||||
if(n <= 1){ 1 }
|
||||
else { n * factorial(n-1) }
|
||||
</code></pre>
|
||||
<p class="fragment">↳ the compiler can (sometimes) figure this out on its own ↴</p>
|
||||
<pre><code>
|
||||
<p class="fragment" style="font-size: 80%">↳ the compiler can (sometimes) figure this out on its own ↴</p>
|
||||
<pre><code class="scala">
|
||||
def factorial(n: Int): Long =
|
||||
{
|
||||
var total = 1l
|
||||
|
|
@ -300,10 +377,10 @@ textbook: Ch. 15
|
|||
<h4 class="slide_title">Fibonacci</h4>
|
||||
|
||||
<p>What's the complexity? (in terms of <tt>n</tt>)</p>
|
||||
<pre><code>
|
||||
def fibb(n: Int): Long =
|
||||
<pre><code class="scala">
|
||||
def fib(n: Int): Long =
|
||||
if(n < 2){ 1 }
|
||||
else { fibb(n-1) + fibb(n-2) }
|
||||
else { fib(n-1) + fib(n-2) }
|
||||
</code></pre>
|
||||
</section>
|
||||
|
||||
|
|
@ -311,7 +388,7 @@ textbook: Ch. 15
|
|||
<h4 class="slide_title">Fibonacci</h4>
|
||||
|
||||
$$T(n) = \begin{cases}
|
||||
\Theta(1) & \textbf{if } n < 2
|
||||
\Theta(1) & \textbf{if } n < 2\\
|
||||
T(n-1) + T(n-2) + \Theta(1) & \textbf{otherwise}
|
||||
\end{cases}$$
|
||||
|
||||
|
|
|
|||
|
|
@ -13,8 +13,8 @@ textbook: "Ch. 7"
|
|||
<dd><b>Cons:</b> $O(n)$ <tt>remove</tt>, <tt>insert</tt>, <tt>append</tt></dd>
|
||||
|
||||
<dt>ArrayBuffer[T]</dt>
|
||||
<dd><b>Pros:</b> $O(1)$ <tt>apply</tt>, <tt>update</tt>, <tt>remove</tt></dd>
|
||||
<dd><b>Cons:</b> Amortized $O(1)$ <tt>insert</tt>, <tt>append</tt></dd>
|
||||
<dd><b>Pros:</b> $O(1)$ <tt>apply</tt>, <tt>update</tt>, Amortized $O(1)$ <tt>append</tt></dd>
|
||||
<dd><b>Cons:</b> $O(n)$ <tt>remove</tt>, <tt>insert</tt></dd>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>List[T] (linked list)</dt>
|
||||
|
|
@ -24,6 +24,10 @@ textbook: "Ch. 7"
|
|||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<svg data-src="graphics/09b/linked-list-example.svg"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
|
|
@ -44,8 +48,6 @@ textbook: "Ch. 7"
|
|||
</code></pre>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">The <tt>mutable.Seq</tt> ADT</h4>
|
||||
|
||||
|
|
@ -73,8 +75,8 @@ textbook: "Ch. 7"
|
|||
def length: Int =
|
||||
{
|
||||
var i = 0
|
||||
var curr = head
|
||||
while(curr.isDefined){ i += 1; curr = curr.get.next }
|
||||
var current = head
|
||||
while(current.isDefined){ i += 1; curr = curr.get.next }
|
||||
return i
|
||||
}
|
||||
</code></pre>
|
||||
|
|
@ -99,43 +101,59 @@ textbook: "Ch. 7"
|
|||
<p class="fragment"><b>Complexity: </b> $O(1)$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
<p><tt>apply(2)</tt>.</p>
|
||||
|
||||
<svg data-src="graphics/09b/linked-list-apply.svg"/>
|
||||
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
<p>Implementing <tt>apply</tt>.</p>
|
||||
|
||||
<pre class="fragment"><code class="scala">
|
||||
<pre><code class="scala">
|
||||
def apply(idx: Int): T =
|
||||
{
|
||||
var i = 0
|
||||
var curr = head
|
||||
while(i < idx){
|
||||
if(curr.isEmpty) { throw IndexOutOfBoundsException(idx) }
|
||||
i += 1; curr = curr.get.next
|
||||
var current = head
|
||||
for(i <- 0 until idx){
|
||||
if(current.isEmpty) { throw IndexOutOfBoundsException(idx) }
|
||||
current = current.get.next
|
||||
}
|
||||
if(curr.isEmpty) { throw IndexOutOfBoundsException(idx) }
|
||||
return curr
|
||||
if(current.isEmpty) { throw IndexOutOfBoundsException(idx) }
|
||||
return current
|
||||
}
|
||||
</code></pre>
|
||||
|
||||
<p class="fragment"><b>Complexity: </b> $O(n)$ <span class="fragment">(or $\Theta(\texttt{idx})$)</span></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
<p><tt>insert(1, "D")</tt>.</p>
|
||||
|
||||
<svg data-src="graphics/09b/linked-list-insert.svg"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
<p>Implementing <tt>insert</tt>.</p>
|
||||
|
||||
<pre class="fragment"><code class="scala">
|
||||
<pre style="transform: scale(0.8); margin-top: -50px; margin-bottom: -50px;"><code class="scala">
|
||||
def insert(idx: Int, value: T): Unit =
|
||||
{
|
||||
if(idx == 0){
|
||||
head = Some( new SinglyLinkedListNode(value, head) )
|
||||
} else {
|
||||
var i = 1; var curr = head
|
||||
while(i < idx){
|
||||
var current = head
|
||||
for(i <- 0 until idx){
|
||||
if(curr.isEmpty) { throw IndexOutOfBoundsException(idx) }
|
||||
i += 1; curr = curr.get.next
|
||||
curr = curr.get.next
|
||||
}
|
||||
curr.next = Some( new SinglyLinkedListNode(value, curr.next) )
|
||||
}
|
||||
|
|
@ -146,6 +164,10 @@ textbook: "Ch. 7"
|
|||
<p class="fragment"><b>Complexity: </b> $O(n)$ <span class="fragment">(or $\Theta(\texttt{idx})$)</span></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Let's use <tt>apply()</tt></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
|
|
@ -153,7 +175,7 @@ textbook: "Ch. 7"
|
|||
def sum(list: List[Int]): Unit =
|
||||
{
|
||||
val total: Int = 0
|
||||
for(i <- 0 until list.size){ total += list(i) }
|
||||
for(i <- 0 until list.length){ total += list(i) }
|
||||
return total
|
||||
}
|
||||
</code></pre>
|
||||
|
|
@ -185,10 +207,10 @@ textbook: "Ch. 7"
|
|||
def sum(list: List[Int]): Unit =
|
||||
{
|
||||
val total: Int = 0
|
||||
val curr = list.head
|
||||
while(curr.isDefined){
|
||||
total += curr.get.value
|
||||
curr = curr.get.next
|
||||
val current = list.head
|
||||
while(current.isDefined){
|
||||
total += current.get.value
|
||||
current = current.get.next
|
||||
}
|
||||
return total
|
||||
}
|
||||
|
|
@ -219,7 +241,6 @@ textbook: "Ch. 7"
|
|||
<section>
|
||||
<h4 class="slide_title">Iterator[T]</h4>
|
||||
|
||||
<p>(Sort of) a "reference" to a collection element.</p>
|
||||
<dl>
|
||||
<dt><tt>hasNext: Boolean</tt></dt>
|
||||
<dd>Returns <tt>true</tt> if there are more items to retrieve.</dd>
|
||||
|
|
@ -229,19 +250,29 @@ textbook: "Ch. 7"
|
|||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>An iterator is:
|
||||
<ul>
|
||||
<li>A reference to an element of the collection</li>
|
||||
<li>A way to get to the next<sup class="fragment" data-fragment-index=1 style="font-size: 50%">1</sup> element of the collection.</li>
|
||||
</ul>
|
||||
</p>
|
||||
<p class="fragment" data-fragment-index=1>1: For some definition of next.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">ListIterator[T] : Iterator[T]</h4>
|
||||
|
||||
<pre><code class="scala">
|
||||
class ListIterator[T](
|
||||
var curr: Option[SinglyLinkedListNode[T]]
|
||||
var current: Option[SinglyLinkedListNode[T]]
|
||||
)
|
||||
{
|
||||
def hasNext: Boolean = curr.isDefined
|
||||
def hasNext: Boolean = current.isDefined
|
||||
def next: T =
|
||||
{
|
||||
val ret = curr.get.value
|
||||
curr = curr.get.next
|
||||
val ret = current.get.value
|
||||
current = current.get.next
|
||||
return ret
|
||||
}
|
||||
}
|
||||
|
|
@ -250,14 +281,24 @@ textbook: "Ch. 7"
|
|||
|
||||
<section>
|
||||
<p>... back to LinkedLists</p>
|
||||
|
||||
<p class="fragment">How about positional operations:<br><tt style="font-size: 80%;">insertAfter(pos: SinglyLinkedListNode[T], value: T)</tt></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
<p>How would you implement a positional <tt>insertAfter</tt>?</p>
|
||||
<p><tt>insertAfter(pos, "D")</tt></p>
|
||||
|
||||
<pre class="fragment"><code class="scala">
|
||||
<svg data-src="graphics/09b/linked-list-insertPositional.svg"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4 class="slide_title">mutable.List[T] : mutable.Seq[T]</h4>
|
||||
|
||||
<p>Implementing a positional <tt>insertAfter</tt></p>
|
||||
|
||||
<pre><code class="scala">
|
||||
def insertAfter(pos: SinglyLinkedListNode[T], value: T) =
|
||||
{
|
||||
pos.next = Some(
|
||||
|
|
@ -266,6 +307,11 @@ textbook: "Ch. 7"
|
|||
length += 1
|
||||
}
|
||||
</code></pre>
|
||||
|
||||
<p>What is the complexity?
|
||||
<span class="fragment">$\Theta(1)$</span>
|
||||
</p>
|
||||
|
||||
</section>
|
||||
|
||||
<section>
|
||||
|
|
@ -320,12 +366,10 @@ textbook: "Ch. 7"
|
|||
def insertAfter(pos: DoublyLinkedListNode[T], value: T) =
|
||||
{
|
||||
val newNode = new DoublyLinkedListNode(value, prev = Some(pos))
|
||||
if(pos.next.isDefined){
|
||||
pos.next.prev = Some(newNode)
|
||||
newNode.next = pos.next
|
||||
} else {
|
||||
last = newNode
|
||||
}
|
||||
if(pos.next.isDefined){ pos.next.prev = Some(newNode)
|
||||
newNode.next = pos.next }
|
||||
else { last = newNode
|
||||
newNode.next = None }
|
||||
pos.next = Some(newNode)
|
||||
length += 1
|
||||
}
|
||||
|
|
|
|||
|
|
@ -0,0 +1,328 @@
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Reference in New Issue