Exam 14: Sorting and Searching

Selection sort has O(n²) complexity. If a computer can sort 1,000 elements in 4 seconds, approximately how many seconds will it take the computer to sort 1,000 times that many, or 1,000,000 elements?

Find the simplest order of growth of the following expression: n³ + log(n⁵).

In the worst case, quicksort is a(n) ____ algorithm.

Which function has a faster growth rate: θ(n^1/2) or θ(log(n))?

Consider the swap method shown below from the SelectionSorter class. If we modified it as shown in the swap2 method shown below, what would be the effect on the sort method? Private static void swap(int[] a, int i, int j) { Int temp = a[i]; A[i] = a[j]; A[j] = temp; } Private static void swap2(int[] a, int i, int j) { A[i] = a[j]; A[j] = a[i]; }

Complete the following code that is intended to provide a comparator interface that will be used to create an object that implements the Comparator interface so that object can compare Auto objects. ___________________________ { Int compare(Auto a, Auto b); }

Which of the following classes implement the Comparable interface? I Date II Collections III String

Consider an array with n elements. If we visit each element n times, how many total visits will there be?

Binary search is an ____ algorithm.

Consider the minimumPosition method from the SelectionSorter class. Complete the code to write a maximumPosition method that returns the index of the largest element in the range from index from to the end of the array. Private static int minimumPosition(int[] a, int from) { Int minPos = from; For (int i = from + 1; i < a.length; i++) { If (a[i] < a[minPos]) { minPos = i; } } Return minPos; } Private static int maximumPosition(int[] a, int from) { Int maxPos = from; For (int i = from + 1; i < a.length; i++) { ________________ } Return maxPos; }

In big-Oh notation, suppose an algorithm requires an order of n³ element visits. How does doubling the number of elements affect the number of visits?

In big-Oh notation, when we consider the order of the number of visits an algorithm makes, what do we ignore? I power of two terms II the coefficients of the terms III all lower order terms

The following code is an example of a ___ search. Public static int search(int[] a, int v) { For (int i = 0; i < a.length; i++) { If (a[i] == v) { return i; } } Return -1; }

After 9 iterations of selection sort working on an array of 10 elements, what must hold true?

Assume we are using quicksort to sort an array in ascending order. What can we conclude about the indexes of two pivot elements placed in consecutive recursive calls?

A binary search is generally ____ a linear search.

In the textbook, we determined that the merge method requires a total of 5n visits. We found that the number of visits required to sort an array of n elements is T(n) = T(n / 2) + T(n / 2) + 5n. What does T(n / 2) describe?

Which of the sorts in the textbook can be characterized by the fact that the best case will have a running time of θ(n) if the data is already sorted? I quicksort II selection sort III insertion sort

Suppose the call obj1.compareTo(obj2) returns 0. What can definitely be concluded from the return value? I obj1 and obj2 are the same object II obj1 and obj2 objects cannot be compared III the properties of obj1 and obj2 that are being compared have identical values

A search technique where, in each step, you split the size of the search in half is called a____ search.