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Selection Insertion To understand these three methods, imagine a deck of cards To sort the cards by using exchange, spread them on a table, face up, and then exchange out-of-order cards until the deck is ordered Using selection, spread the cards on the table, select the card of lowest value, take it out of the deck, and hold it in your hand Then, from the remaining cards on the table, select the lowest card and place it behind the one already in your hand This process continues until all the cards are in your hand The cards in your hand will be sorted when you finish the process To sort the cards by using insertion, hold all the cards in your hand Place one card at a time on the table, always inserting it in the correct position The deck will be sorted when you have no cards in your hand Judging Sorting Algorithms There are many different sorting algorithms They all have some merit, but the general criteria for judging a sorting algorithm are How fast can it sort information in an average case How fast are its best and worst cases Does it exhibit natural or unnatural behavior Does it rearrange elements with equal keys Look closely at these criteria now Clearly, how fast a particular algorithm sorts is of great concern The speed with which an array can be sorted is directly related to the number of comparisons and the number of exchanges that take place, with exchanges taking more time A comparison occurs when one array element is compared to another; an exchange happens when two elements are swapped The run times of some sort routines increase exponentially, while others increase logarithmically relative to the number of items being sorted The best- and worst-case run times are important if you expect to encounter one of these situations frequently Often a sort has a good average case but a terrible worst case A sort is said to exhibit natural behavior if it works least when the list is already in order, works harder as the list becomes less ordered, and works hardest when a list is in inverse order How hard a sort works is based on the number of comparisons and exchanges that it makes To understand why rearranging elements with equal keys may be important, imagine a database such as a mailing list, which is sorted on a main key and a subkey The main sort key is the postal code, and within postal codes, the last name is the subkey When a new address is added to the list and the list is re-sorted, you do not want the subkeys (that is, the last names within postal codes) to be rearranged To guarantee that this doesn't happen, a sort must not exchange keys of equal value
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The discussion that follows first examines the representative sorts from each category and then analyzes the efficiency of each Later, you'll see improved sorting methods The Bubble Sort The most well-known (and infamous) sort is the bubble sort Its popularity is derived from its catchy name and its simplicity However, for general-purpose sorting, it is one of the worst sorts ever conceived The bubble sort is an exchange sort It involves the repeated comparison and, if necessary, the exchange of adjacent elements The elements are like bubbles in a tank of water each seeks its own level A simple form of the bubble sort is shown here:
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/* The Bubble Sort */ void bubble(char *items, int count) { register int a, b; register char t; for(a=1; a < count; ++a) for(b=count-1; b >= a; --b) { if(items[b-1] > items[b]) { /* exchange elements */ t = items[b-1]; items[b-1] = items[b]; items[b] = t; } } }
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Here, items is a pointer to the character array to be sorted, and count is the number of elements in the array The bubble sort is driven by two loops Given that there are count elements in the array, the outer loop causes the array to be scanned count times This ensures that, in the worst case, 1 every element is in its proper position when the function terminates The inner loop actually performs the comparisons and exchanges (A slightly improved version of the bubble sort terminates if no exchanges occur, but this adds another comparison in each pass through the inner loop) You can use this version of the bubble sort to sort a character array into ascending order For example, the following short program sorts a string entered by the user:
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