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merge_sort(num_list) length <-- length of num_list // if there is more than 1 number in the list, if length > 1 // divide the list into two lists half as long shorter_list_A <-- first half of num_list shorter_list_B <-- second half of num_list // Perform a merge sort on each shorter list result_A <-- merge_sort(shorter_list_A) result_B <-- merge_sort(shorter_list_B) // Merge the results of the two sorted sublists sorted_list <-- merge(result_A, result_B) // Return the sorted list return sorted_list else // If there s only 1 number in the list, // just return it return num_list end Let s follow the execution of merge_sort when one calls it with this list of numbers: NUMS = { 1, 6, 4, 2 } 1 First, we call merge_sort passing the list NUMS This is what we call the top-level of recursion, level 0..

b. Trace of the heap sort:

a[0] 44 99 77 88 44 88 22 77 33 66 22 55 33 44 33 22 a[1] 88 99 44 88 a[2] 55 a[3] 99 88 a[4] 66 a[5] 33 a[6] 22 a[7] 88 a[8] 77

CHAP. 2]

44 99 77 88

77 66 44 22

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But what we ve also seen in these last months is the same partisan spectacle that only hardens the disdain many Americans have toward their own government. Instead of honest debate, we ve seen scare tactics. Some have dug into unyielding ideological camps that offer no hope of compromise. Too many have used this as an opportunity to score short-term political points, even if it robs the country of our opportunity to solve a long-term challenge. And out of this blizzard of charges and counter-charges, confusion has reigned. Well, the time for bickering is over. The time for games has passed. [Applause.] Now is the season for action. Now is when we must bring the best ideas of both parties together, and show the American people that we can still do what we were sent here to do. Now is the time to deliver on health care. Now is the time to deliver on health care. The plan I m announcing tonight would meet three basic goals. It will provide more security and stability to those who have health insurance. It will provide insurance for those who don t. And it will slow the growth of health care costs for our families, our businesses, and our government. [Applause.] It s a plan that asks everyone to take responsibility for meeting this challenge not just government, not just insurance companies, but everybody, including employers and individuals. And it s a plan that incorporates ideas from senators and congressmen, from Democrats and Republicans and yes, from some of my opponents in both the primary and general election. Here are the details that every American needs to know about this plan. First, if you are among the hundreds of millions of Americans who already have health insurance

2 merge_sort calls merge_sort again, passing a list of the first two numbers in NUMS This will sort the front half of the list This is level 1 of recursion 3 Now merge_sort calls merge_sort again, passing only the first number in NUMS This is level 2 4 Now merge_sort simply returns; it s down to one element in the list, merge_sort returns to level 1 5 Now merge_sort calls merge_sort again, passing only the second of the first two numbers in NUMS This is level 2 6 Again, merge_sort simply returns; it s down to one element in the list, merge_sort returns to level 1 7 At level 1 of recursion, merge_sort now has result_A and result_B merge_sort calls merge to put those two numbers in order, and then it returns the sorted pair of numbers back to level 0 The first half of the list is sorted.

44 88 22 77 33 66 55

22 44 33

8 From level 0, merge_sort calls merge_sort again, passing a list of the last two numbers in NUMS This will sort the back half of NUMS It s back to level 1 of recursion 9 merge_sort calls merge_sort again, passing only the first of the last two numbers of NUMS This is level 2 of recursion again 10 Since the list contains only one number, merge_sort simply returns back to level 1 11 merge_sort calls merge_sort again, passing only the last of the numbers of NUMS This is level 2 of recursion again 12 Since the list contains only one number, merge_sort simply returns back to level 1 13 At level 1 of recursion, merge_sort now has result_A and result_B merge_sort calls merge to put the two lists in order, and then it returns the sorted set of two numbers back to level 0.

c. Trace of the bubble sort:

a[0] 44 a[1] 88 55 a[2] 55 88

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