CS61B Spring’15 Discussion 11.  In-Place Sort: ◦ Keeps sorted items in original array (destructive) ◦ No equivalent for linked list-based input  Stable.

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Presentation transcript:

CS61B Spring’15 Discussion 11

 In-Place Sort: ◦ Keeps sorted items in original array (destructive) ◦ No equivalent for linked list-based input  Stable Sort: ◦ Keeps elements with equal keys in same relative order in output as in input

Intuition: Insert x into correct position in S.

 Question 1(a): Insertion Sort

 Question 1(a): Insertion Sort | | | | | | | |

Question 3.  Worst-Case Runtime:  Best-Case Runtime:  In-Place?  Stable?

Algorithm For each position i :  Find smallest element x from i to end.  Swap x and arr[i]

 Question 1(b): Selection Sort

 Question 1(b): Selection Sort | | | | | | |873

Question 3.  Worst-Case Runtime:  Best-Case Runtime:  In-Place?  Stable?

How? See Q4: MergeTwo

 Question 1(c): Merge Sort

 Question 1(c): Merge Sort

Question 3.  Worst-Case Runtime:  Best-Case Runtime:  In-Place?  Stable?

Algorithm  Create max-heap with bottomUpHeap().  Repeatedly deleteMax() and place element at end of array. 1.Start with first internal node and do reverse level-order traversal. 2.Bubble down to fix heap. 1.Start with first internal node and do reverse level-order traversal. 2.Bubble down to fix heap. Sort:

 Question 1(d): Heap Sort

 Question 1(d): Heap Sort

 Question 1(d): Heap Sort

 Question 1(d): Heap Sort

 Question 1(d): Heap Sort

 Question 1(d): Heap Sort

Question 3.  Worst-Case Runtime:  Best-Case Runtime:  In-Place?  Stable?

 Question 1(e). Give an example of a situation when using insertion sort is more efficient than using merge sort.

 Which sorting algorithm?

 Which sorting algorithm?  Selection Sort

 Which sorting algorithm?

 Which sorting algorithm?  Insertion Sort

 Which sorting algorithm?

 Which sorting algorithm?  Merge Sort

 Which sorting algorithm?

 Which sorting algorithm?  Insertion Sort

 Create new array for result.  Initialize three counters (for indices)  Merge while both arrays have unmerged elements.  Array b is done, so append rest of a.  Array a is done, so append rest of b.

public static int[] mergeTwo(int[] a, int[] b) { int[] merged = new int[a.length + b.length]; int aIndex = 0; // Current index in a. int bIndex = 0; // Current index in b. int mergedIndex = 0; // Current index in merged. while (aIndex < a.length && bIndex < b.length) { if (a[aIndex] < b[bIndex]) { merged[mergedIndex] = a[aIndex]; aIndex++; } else { merged[mergedIndex] = b[bIndex]; bIndex++; } mergedIndex++; } // Continued on next slide.

while (aIndex < a.length) { merged[mergedIndex] = a[aIndex]; aIndex++; mergedIndex++; } while (bIndex < b.length) { merged[mergedIndex] = b[bIndex]; bIndex++; mergedIndex++; }