Sorting

The Bubble Sort

The bubble sort makes multiple passes through a list. It compares adjacent items and exchanges those that are out of order. Each pass through the list places the next largest value in its proper place. In essence, each item “bubbles” up to the location where it belongs.

Swap

temp = alist[i]#把I值賦給TEMP儲存起來
alist[i] = alist[j]#把J的值賦給I
alist[j] = temp#在temp的值給J

def bubbleSort(alist):
    for passnum in range(len(alist)-1,0,-1):
        #range([start], stop[, step])
        #從後最後一個到第一個
        #8,7,6,5,4,3,2,1
        for i in range(passnum):#
            print(alist[i])#打印8個，打印7個。。。以此類推
            #一對一對往後比較，對換
            if alist[i]>alist[i+1]:#當前一個數字比後一個數字大的時候 換位
                temp=alist[i]
                alist[i]=alist[i+1]
                alist[i+1]=temp

#test
alist = [54,26,93,17,77,31,44,55,20]
bubbleSort(alist)
print(alist)

冒泡排序，2個循環嵌套
1，列表倒敘循環，找到元素個數
2，再從左到右循環，比較前後2個元素的值

時間
To analyze the bubble sort, we should note that regardless of how the items are arranged in the initial list, n−1 passes will be made to sort a list of size n. Table 1 shows the number of comparisons for each pass. The total number of comparisons is the sum of the first n−1 integers. Recall that the sum of the first n integers is 12n2+12n. The sum of the first n−1 integers is 12n2+12n−n, which is 12n2−12n. This is still O(n2) comparisons. In the best case, if the list is already ordered, no exchanges will be made. However, in the worst case, every comparison will cause an exchange. On average, we exchange half of the time.

Short bubble
A bubble sort can be modified to stop early if it finds that the list has become sorted. This means that for lists that require just a few passes, a bubble sort may have an advantage in that it will recognize the sorted list and stop. ActiveCode 2 shows this modification, which is often referred to as the short bubble.

def shortBubbleSort(alist):
    exchange=True
    passnum=len(alist)-1
    while passnum>0 and exchange:#遞歸停止
        for i in range(passnum):
            if alist[i]>alist[i+1]:
            #當知道不用換位的時候，passnum-1
                exchange=True
                temp=alist[i]
                alist[i]=alist[i+1]
                alist[i+1]=temp
                print(alist)
        passnum=passnum-1

alist=[20,30,40,90,50,60,70,80,100,110]
shortBubbleSort(alist)
print(alist)

Q-42: Suppose you have the following list of numbers to sort:
[19, 1, 9, 7, 3, 10, 13, 15, 8, 12] which list represents the partially sorted list after three complete passes of bubble sort?
[1, 3, 7, 9, 10, 8, 12, 13, 15, 19]