Java Sorting & Searching Study Guide
B
A database containing 2,000 sorted integers must be searched using a binary search algorithm. What is the maximum number of iterations of the binary search method that must occur in order to find a specified value or guarantee that it is not in the database? (A) 8 (B) 11 (C) 20 (D) 100 (E) 2000
B
A list of 120 names has been sorted in alphabetical order. Using a binary search method, what is the minimum number of passes needed to find a specified name or confirm that it is not in the list? (A) 5 (B) 7 (C) 10 (D) 12 (E) 128
C
A list of integers containing [12, 8, 7, 30, 62, 45, 10, 3] is sorted from largest to smallest using a selection sort method. After three passes, what does the list look like? (A) [62, 45, 30, 12, 7, 8, 10, 3] (B) [30, 12, 8, 7, 62, 45, 10, 3] (C) [62, 45, 30, 7, 12, 8, 10, 3] (D) [62, 45, 30, 12, 7, 8, 10, 3] (E) [12, 8, 30, 7, 62, 45, 10, 3]
E
A sorted array of integers containing 2000 elements is to be searched for key using a binary search method. Assuming key is in the array, what is the maximum number of iterations needed to find key? (A) 8 (B) 10 (C) 100 (D) 2000 (E) 11
O(logn)
Algorithm with this complexity has a performance that is directly proportional to the log function of the size of the input data set. Extremely slow-growing function = very efficient algorithm.
O(n^2)
Algorithm with this complexity has a performance that is directly proportional to the size of the input data set, squared.
O(nlogn)
Algorithm with this complexity has a performance that is directly proportional to the size of the input data set, times the log function of itself.
O(n)
Algorithm with this complexity has a performance that is directly proportional to the size of the input data set. Very inefficient algorithm.
Bubble Sort
Compares each item with the next item in the list, and swaps them if needed. Imagine that the largest/smallest item in the array (depending on sorting order) is being raised to the top of the list. Stops when it makes a pass through the entire list without swapping.
D
Consider an array of integers that contains [12, 8, 4, 6, 13, 29, 7]. If the array is sorted from smallest to largest using an insertion sort method, what will be the order of the array after the third iteration of the sorting method? (A) [4, 6, 12, 8, 13, 29, 7] (B) [4, 6, 7, 8, 13, 29, 12] (C) [4, 8, 12, 6, 13, 29, 7] (D) [4, 6, 8, 12, 13, 29, 7] (E) [4, 6, 7, 8, 12, 13, 29]
Binary Search
Finds the index of a targeted value in a SORTED array. Uses a "search space" (initially the entire array) to find the target. Each step, it compares the median value in the search space to the target. Based on the comparison, it can remove half of the search space every step, until the search space consists of only the target value.
Sequential Search
Finds the index of a targeted value in an array, regardless of if it is sorted. Starts from the beginning of the array, and goes through the entire array until it finds the target value.
Selection Sort
Finds the largest/smallest item in the array (depending on sorting order), and then swaps it with the item in the next position to be filled. For example, the first step finds the largest/smallest item in the array, then swaps it with the first item in the array, and so on.
B
How many times would the while loop execute if you first do int[] arr = {2, 10, 23, 31, 55, 86} and then call binarySearch(arr,2)? (A) 1 (B) 2 (C) 3
A
How many times would the while loop execute if you first do int[] arr = {6, 12, 19, 54, 76, 99} and then call binarySearch(arr,76)? (A) 2 (B) 1 (C) 3
A
In which of these cases will an ascending order (from smallest to largest) insertion sort have the fastest run time? I. An array that is in reverse order (from largest to smallest). II. An array that is in sorted order already (from smallest to largest). III. An array that is in random order (not already sorted). (A) II only (B) I only (C) I and II only (D) II and III only (E) III only
Descending Order
Largest to Smallest
O(logn)
Level of complexity of Binary Search (Big O Notation)
O(n^2)
Level of complexity of Bubble, Insertion, and Selection Sort (Big O Notation)
O(nlogn)
Level of complexity of Merge Sort (Big O Notation)
O(n)
Level of complexity of Sequential Search (Big O Notation)
Insertion Sort
Separates the list into sorted and unsorted sections (sorted section initially empty). Compares an item in the unsorted section with the items in the sorted section, and places it in the correct position in the sorted section. After each step, the sorted section gets bigger, and the unsorted section gets smaller, until the entire list is sorted.
Ascending Order
Smallest to Largest
D
The array intArray contains [8, 12, 34, 6, 10, 14, 2, 4]. What are the contents of intArray after 3 passes of insertion sort? (A) [6, 8, 12, 34, 2, 4, 10, 14] (B) [2, 4, 6, 34, 10, 14, 8, 12] (C) [2, 4, 34, 6, 10, 13, 8, 12] (D) [6, 8, 12, 34, 10, 14, 2, 4] (E) [6, 8, 10, 12, 34, 14, 2, 4]
C
Under what condition will a merge sort execute faster? (A) If the data is already sorted in ascending order (B) If the data is already sorted in descending order (C) It will always take the same amount of time to execute
C
Under what condition will a selection sort execute faster? (A) If the data is already sorted in ascending order (B) If the data is already sorted in descending order (C) It will always take the same amount of time to execute
B
Under what condition will an ascending insertion sort execute the slowest? (A) If the data is already sorted in ascending order (B) If the data is already sorted in descending order (C) It will always take the same amount of time to execute
A
Under what condition will an insertion sort execute faster? (A) If the data is already sorted in the correct order (B) It will always take the same amount of time to execute
Merge Sort
Uses the divide and conquer strategy. Recursively breaks the values to be sorted in half, until there is only one value left to be sorted. Then, it merges the two sorted lists back into one list.
C
Which of the following conditions must be true in order to search for a value using binary search? I. The values in the array must be integers. II. The values in the array must be in sorted order. III. The array must not contain duplicate values. (A) I only (B) I and II (C) II only (D) II and III
A
Which of the following correctly shows the iterations of an ascending (from left to right) insertion sort on an array with the following elements: {7,3,8,5,2}? (A) {3,7,8,5,2}, {3,7,8,5,2}, {3,5,7,8,2}, {2,3,5,7,8} (B) {2,3,8,5,7}, {2,3,8,5,7}, {2,3,5,8,7}, {2,3,5,7,8} (C) {3,7,8,5,2}, {3,5,7,8,2}, {2,3,5,7,8} (D) {2,3,8,5,7}, {2,3,5,8,7}, {2,3,5,7,8} (E) {2,7,3,8,5}, {2,3,7,8,5}, {2,3,5,7,8}
D
Which of the following correctly shows the iterations of an ascending (from left to right) selection sort on an array with the following elements: {10, 6, 3, 2, 8}? (A) {6,10,3,2,8}, {3,6,10,2,8}, {2,3,6,10,8}, {2,3,6,8,10} (B) {6,10,3,2,8}, {3,6,10,2,8}, {2,3,6,8,10} (C) {2,6,3,10,8}, {2,3,6,10,8}, {2,3,6,8,10} (D) {2,6,3,10,8}, {2,3,6,10,8}, {2,3,6,10,8}, {2,3,6,8,10}
E
Which of the following is/are true about using insertion sort versus using merge sort? I. Insertion sort requires more storage space than mergesort. II. Insertion sort is only more efficient than mergesort in the case that we have a very small and nearly sorted array. III. Insertion sort is almost always less efficient than mergesort. (A) I only (B) II only (C) III only (D) I and III (E) II and III
C
Which sort should be the fastest most of the time? (A) selection sort (B) insertion sort (C) merge sort
D
Which will cause the longest execution of a sequential search looking for a value in an array of integers? (A) The value is the first one in the array (B) The value is in the middle of the array (C) The value is the last one in the array (D) The value isn't in the array
B
Which will cause the shortest execution of a binary search looking for a value in an array of integers? (A) The value is the first one in the array (B) The value is in the middle of the array (C) The value is the last one in the array (D) The value isn't in the array
A
Which will cause the shortest execution of a sequential search looking for a value in an array of integers? (A) The value is the first one in the array (B) The value is in the middle of the array (C) The value is the last one in the array (D) The value isn't in the array
