slide errors

src/teaching/cse-250/2022fa/slide/11b-RecursionAnalysis.erb

@@ -5,6 +5,10 @@ date: Sept 21, 2022
 textbook: Ch. 15
 ---
 
+<section>
+  <p>Warm up...</p>
+</section>
+
 <section>
   <h4 class="slide_title">Fibonacci</h4>
 
@@ -24,7 +28,7 @@ textbook: Ch. 15
     T(n-1) + T(n-2) + \Theta(1) & \textbf{otherwise}
   \end{cases}$$
 
-  <p>Solve for $T(n)$</p>
+  <p>Test Hypothesis: $T(n) \in O(2^n)$</p>
 </section>
 
 <section>
@@ -60,6 +64,40 @@ textbook: Ch. 15
   <p><b>Output:</b> An array with elements in sorted order.</p>
 </section>
 
+<section>
+  <h4 class="slide_title">Merge Sort</h4>
+  
+  <svg data-src="graphics/11b/merge_example.svg"/>
+</section>
+
+<section>
+  <h4 class="slide_title">Merge Sort</h4>
+
+  <p style="font-size: 90%;"><b>Observation:</b> Merging two sorted arrays can be done in $O(n)$.</p>
+</section>
+
+<section>
+  <h4 class="slide_title">Merge Sort</h4>
+
+  <pre><code class="scala">
+  def merge[A: Ordering](left: Seq[A], right: Seq[A]): Seq[A] = {
+    val output = ArrayBuffer[A]()
+  
+    val leftItems = left.iterator.buffered
+    val rightItems = right.iterator.buffered
+  
+    while(leftItems.hasNext || rightItems.hasNext) {
+      if(!left.hasNext)          { output.append(right.next) }
+      else if(!right.hasNext)    { output.append(left.next) }
+      else if(Ordering[A].lt( left.head, right.head ))
+                                 { output.append(left.next) }
+      else                       { output.append(right.next) }
+    }
+    output.toSeq
+  }
+  </code></pre>
+</section>
+
 <section>
   <h4 class="slide_title">Merge Sort</h4>
 
@@ -110,34 +148,6 @@ textbook: Ch. 15
   </ol>
 </section>
 
-<section>
-  <h4 class="slide_title">Merge Sort</h4>
-  
-  <svg data-src="graphics/11b/merge_example.svg"/>
-</section>
-
-<section>
-  <h4 class="slide_title">Merge Sort</h4>
-
-  <pre><code class="scala">
-  def merge[A: Ordering](left: Seq[A], right: Seq[A]): Seq[A] = {
-    val output = ArrayBuffer[A]()
-  
-    val leftItems = left.iterator.buffered
-    val rightItems = right.iterator.buffered
-  
-    while(leftItems.hasNext || rightItems.hasNext) {
-      if(!left.hasNext)          { output.append(right.next) }
-      else if(!right.hasNext)    { output.append(left.next) }
-      else if(Ordering[A].lt( left.head, right.head ))
-                                 { output.append(left.next) }
-      else                       { output.append(right.next) }
-    }
-    output.toSeq
-  }
-  </code></pre>
-</section>
-
 <section>
   <h4 class="slide_title">Merge Sort</h4>