The bubble sort makes multiple passes through a list. It comparesadjacent items and exchanges those that are out of order. Each passthrough the list places the next largest value in its proper place. Inessence, each item 'bubbles' up to the location where it belongs.
Figure 1 shows the first pass of a bubble sort. The shadeditems are being compared to see if they are out of order. If there aren items in the list, then there are (n-1) pairs of items thatneed to be compared on the first pass. It is important to note that oncethe largest value in the list is part of a pair, it will continually bemoved along until the pass is complete.
At the start of the second pass, the largest value is now in place.There are (n-1) items left to sort, meaning that there will be(n-2) pairs. Since each pass places the next largest value inplace, the total number of passes necessary will be (n-1). Aftercompleting the (n-1) passes, the smallest item must be in thecorrect position with no further processing required. ActiveCode 1shows the complete bubbleSort function. It takes the list as aparameter, and modifies it by exchanging items as necessary.
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The exchange operation, sometimes called a 'swap,' is slightly differentin Python than in most other programming languages. Typically, swappingtwo elements in a list requires a temporary storage location (anadditional memory location). A code fragment such as
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List: 1, 2, 3 Modified list: 1, 2, 3, 5 Using Collections class methods There are various methods in Collections class that can be used to instantiate a list. Ii ©2012 Brian Heinold Licensed under aCreative Commons Attribution-Noncommercial-Share Alike 3.0 Unported Li-cense.
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will exchange the ith and jth items in the list. Without thetemporary storage, one of the values would be overwritten.
In Python, it is possible to perform simultaneous assignment. Thestatement a,b=b,a will result in two assignment statements beingdone at the same time (see Figure 2). Using simultaneousassignment, the exchange operation can be done in one statement.
Lines 5-7 in ActiveCode 1 perform the exchange of the (i) and((i+1)th) items using the three–step procedure describedearlier. Note that we could also have used the simultaneous assignmentto swap the items.
Figure 2: Exchanging Two Values in Python¶
The following activecode example shows the complete bubbleSort function working on the listshown above.
The following animation shows bubbleSort in action.
To analyze the bubble sort, we should note that regardless of how theitems are arranged in the initial list, (n-1) passes will bemade to sort a list of size n. Table 1 shows the numberof comparisons for each pass. The total number of comparisons is the sumof the first (n-1) integers. Recall that the sum of the firstn integers is (frac{1}{2}n^{2} + frac{1}{2}n). The sum ofthe first (n-1) integers is(frac{1}{2}n^{2} + frac{1}{2}n - n), which is(frac{1}{2}n^{2} - frac{1}{2}n). This is still(O(n^{2})) comparisons. In the best case, if the list is alreadyordered, no exchanges will be made. However, in the worst case, everycomparison will cause an exchange. On average, we exchange half of thetime.
Pass | Comparisons |
|---|---|
1 | (n-1) |
2 | (n-2) |
3 | (n-3) |
… Adobe photoshop lightroom cc 2019 v2 2 1. | … |
(n-1) | (1) |
A bubble sort is often considered the most inefficient sorting methodsince it must exchange items before the final location is known. These'wasted' exchange operations are very costly. However, because thebubble sort makes passes through the entire unsorted portion of thelist, it has the capability to do something most sorting algorithmscannot. In particular, if during a pass there are no exchanges, then weknow that the list must be sorted. A bubble sort can be modified to stopearly if it finds that the list has become sorted. This means that forlists that require just a few passes, a bubble sort may have anadvantage in that it will recognize the sorted list and stop.ActiveCode 2 shows this modification, which is often referredto as the short bubble.
In Python, it is possible to perform simultaneous assignment. Thestatement a,b=b,a will result in two assignment statements beingdone at the same time (see Figure 2). Using simultaneousassignment, the exchange operation can be done in one statement.
Lines 5-7 in ActiveCode 1 perform the exchange of the (i) and((i+1)th) items using the three–step procedure describedearlier. Note that we could also have used the simultaneous assignmentto swap the items.
Figure 2: Exchanging Two Values in Python¶
The following activecode example shows the complete bubbleSort function working on the listshown above.
The following animation shows bubbleSort in action.
To analyze the bubble sort, we should note that regardless of how theitems are arranged in the initial list, (n-1) passes will bemade to sort a list of size n. Table 1 shows the numberof comparisons for each pass. The total number of comparisons is the sumof the first (n-1) integers. Recall that the sum of the firstn integers is (frac{1}{2}n^{2} + frac{1}{2}n). The sum ofthe first (n-1) integers is(frac{1}{2}n^{2} + frac{1}{2}n - n), which is(frac{1}{2}n^{2} - frac{1}{2}n). This is still(O(n^{2})) comparisons. In the best case, if the list is alreadyordered, no exchanges will be made. However, in the worst case, everycomparison will cause an exchange. On average, we exchange half of thetime.
Pass | Comparisons |
|---|---|
1 | (n-1) |
2 | (n-2) |
3 | (n-3) |
… Adobe photoshop lightroom cc 2019 v2 2 1. | … |
(n-1) | (1) |
A bubble sort is often considered the most inefficient sorting methodsince it must exchange items before the final location is known. These'wasted' exchange operations are very costly. However, because thebubble sort makes passes through the entire unsorted portion of thelist, it has the capability to do something most sorting algorithmscannot. In particular, if during a pass there are no exchanges, then weknow that the list must be sorted. A bubble sort can be modified to stopearly if it finds that the list has become sorted. This means that forlists that require just a few passes, a bubble sort may have anadvantage in that it will recognize the sorted list and stop.ActiveCode 2 shows this modification, which is often referredto as the short bubble.
Self Check
- [1, 9, 19, 7, 3, 10, 13, 15, 8, 12]
- This answer represents three swaps. A pass means that you continue swapping all the way to the end of the list.
- [1, 3, 7, 9, 10, 8, 12, 13, 15, 19]
- Very Good
- [1, 7, 3, 9, 10, 13, 8, 12, 15, 19]
- A bubble sort contines to swap numbers up to index position passnum. But remember that passnum starts at the length of the list - 1.
- [1, 9, 19, 7, 3, 10, 13, 15, 8, 12]
- You have been doing an insertion sort, not a bubble sort.
Q-2: 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?
