A Practical Introduction to Data Structures and Algorithm Analysis

24 Chap. 1 Data Structures and Algorithms1.18 Imagine that you are a programmer who must write a function to sort anarray of about 1000 integers from lowest value to highest value. Write downat least five approaches to sorting the array. Do not write algorithms in Javaor pseudocode. Just write a sentence or two for each approach to describehow it would work.1.19 Think of an algorithm to find the maximum value in an (unsorted) array.Now, think of an algorithm to find the second largest value in the array.Which is harder to implement? Which takes more time to run (as measuredby the number of comparisons performed)? Now, think of an algorithm tofind the third largest value. Finally, think of an algorithm to find the middlevalue. Which is the most difficult of these problems to solve?1.20 An unsorted list of integers allows for constant-time insert simply by addinga new integer at the end of the list. Unfortunately, searching for the integerwith key value X requires a sequential search through the unsorted list untilyou find X, which on average requires looking at half the list. On the otherhand, a sorted array-based list of n integers can be searched in log n time byusing a binary search. Unfortunately, inserting a new integer requires a lot oftime because many integers might be shifted in the array if we want to keepit sorted. How might data be organized to support both insertion and searchin log n time?