Comparision of Sorting Algorithms
This table summarizes the performance of different algorithms as measured by executing them on a NodeJS server. These results are in no way exhaustive as only one type of data was tested, however they do provide a glimpse at how each algorithm performs.
All tests were ran on the same list of 10000 integers. First on a list of randomly sorted data, then worst case where all the items are sorted but in reverse order, then the best case where all the items are sorted in the correct order. The values shown are - time the script took to run in milliseconds, the number of comparisons the algorithm performed, and the number of swaps it performed.
| Algorithm | Time (ms) | Comparisons | Swaps |
|---|---|---|---|
| Bubble (random) | 300 | 100k | 25k |
| Bubble (reversed) | 193 | 100k | 50k |
| Bubble (sorted) | 1 | 10k | 0 |
| Selection (random) | 144 | 50k | 10k |
| Selection (reversed) | 149 | 50k | 7k |
| Selection (sorted) | 142 | 50k | 0 |
| Insertion (random) | 59 | 25k | 25k |
| Insertion (reversed) | 84 | 50k | 50k |
| Insertion (sorted) | 1 | 10k | 0 |
| Quick (random) | 26 | 191k | 116k |
| Quick (reversed) | 15 | 166k | 99k |
| Quick (sorted) | 8 | 161k | 0 |
| Merge (random) | 13 | 121k | |
| Merge (reversed) | 9 | 69k | |
| Merge (sorted) | 9 | 75k |
Observations
From the above data we can see how each algorithm performs at sorting 10k integers in a NodeJS server. Of course the performance will be different depending on the server hardware, and different still when executed in a browser, and different still when executed in different languages, but it should provide a general idea of how the performance of each algorithm compares against the others.
As noted at the beginning of this module - the Bubble Sort is a terrible algorithm, but it’s extremely simple, fast to write and implement, consumes hardly any additional memory, and might be okay as a quick and dirty solution for prototyping or quickly sorting small datasets.
The Selection Sort and Insertion Sort algorithms are very similar to the Bubble Sort in that they consume very little additional memory, and are fairly slow to execute, however they both reduce the number of operations as compared to the Bubble Sort, which means faster execution times, and less energy consumption. These are important factors to remember, especially when running our code in cloud resources that bill by the amount of compute resources used.
Truly understanding why the Insertion Sort is so much more performant than the Bubble Sort or Selection Sort is a key takeaway from this module. The code didn’t change significantly (as it does with Quick Sort or Merge Sort), but the approach to eliminating unnecessary comparisons and swaps is what makes this algorithm so much better in practice, even though in theory the Big O for Insertion Sort is the same as for the Bubble Sort.
When we begin looking at Quick Sort and Merge Sort we begin to see a whole different pattern emerge. This pattern consumes additional memory in order to temporarily place unsorted items somewhere. With previous algorithms you can imagine having to sort a deck of cards while holding them in your hands. You can see how swapping two cards doesn’t require significant additional resources - perhaps palming the card being moved, or temporarily placing it at the front of the stack. These approaches are excellent when we don’t have additional memory to work with, and need to be able to sort our data in place.
With Quick Sort and Merge Sort you can imagine having a large desk in front of you where you can place cards as you go through the unsorted pile. You can begin sorting them as you go, and then merging the sorted piles as you complete the process. This approach allows you to perform the sorting much faster, but does require that you have access to additional storage space (desk, or disk, or RAM).
There are other algorithms that build upon these basic ones by adding small improvements to the seeking and swapping logic - such as finding sequences of sorted elements that can be skipped when swapping unsorted items, or eliminating the need to swap items if they are known to be in the right order.
There are also completely different algorithms that use unique approaches to break the data into segments, or combine several basic algorithms to utilize the strength of each - for example breaking the data into buckets (similar to Quick Sort or Merge Sort), and then using an Insertion Sort to sort the buckets themselves, and then using a Merge Sort to combine them.
I encourage you to expore all the different algorithms and evaluate their strenghts and weaknesses - whether it’s code size, memory consumption, or compute use. By reading about the approach and recreating it in your preferred language you will gain a better appreciation for algorithms, and hopefully think about this tutorial next time you execute data.sort().
Data
This is the random list of 10k integers that was used for testing the algorithms to produce the results in the table above:
[212,69,940,36,196,966,878,94,121,113,62,755,930,817,900,463,645,805,946,334,655,212,676,793,738,554,430,406,623,866,359,856,612,707,565,419,557,653,914,942,874,310,109,643,38,171,251,745,197,741,535,708,79,181,480,33,920,144,103,943,533,426,641,800,156,417,930,982,635,776,6,220,555,404,434,356,328,400,831,679,472,679,106,205,161,165,506,395,958,150,211,372,807,982,666,350,541,872,991,723,666,548,101,623,605,96,890,575,906,68,752,371,476,748,290,605,416,619,996,705,190,358,145,296,498,600,541,92,957,90,603,334,132,274,26,873,40,578,168,508,754,810,547,635,119,701,510,558,373,478,438,723,376,728,190,914,78,363,45,593,393,436,170,873,762,532,945,554,166,756,959,226,446,703,971,808,124,609,953,644,333,287,702,876,554,767,444,888,708,661,370,460,655,532,916,743,818,607,82,348,217,115,568,160,243,571,494,430,335,323,66,923,526,792,574,617,906,45,110,506,596,479,936,952,839,166,827,44,974,645,80,888,629,175,777,645,941,746,369,44,653,897,811,677,819,433,8,651,245,465,338,795,171,185,353,865,1,20,97,243,673,256,254,235,524,823,64,256,401,724,545,27,992,510,340,992,204,407,446,914,448,172,56,651,878,479,128,509,983,317,410,319,782,243,966,723,796,401,252,370,890,187,10,359,547,572,652,39,19,409,4,645,901,887,372,390,11,321,580,225,281,779,183,352,203,213,716,645,120,774,694,671,655,832,148,293,100,534,603,981,200,988,897,219,11,21,871,93,907,619,769,980,505,864,336,221,351,427,706,568,738,191,464,123,773,322,319,533,785,497,418,551,307,879,641,873,420,570,375,669,607,160,852,724,400,55,316,968,613,371,299,359,103,757,506,511,922,229,444,346,289,595,670,425,495,280,879,966,391,739,222,791,498,839,248,253,601,872,499,655,65,576,701,532,117,358,980,890,953,432,382,499,351,868,654,805,857,447,369,32,825,145,821,21,272,891,744,230,964,708,732,604,323,720,441,313,664,240,802,815,32,986,365,980,529,914,136,592,474,650,101,841,723,617,223,363,377,817,705,930,649,119,683,337,691,315,712,310,460,723,927,168,694,743,155,446,426,925,0,334,314,208,92,157,245,609,835,664,195,894,118,762,187,712,765,987,69,495,643,700,973,538,907,21,334,5,53,481,482,953,484,640,994,459,803,477,559,188,728,851,813,214,596,129,877,614,536,449,118,777,793,449,462,232,858,296,350,97,931,77,937,861,834,709,278,158,33,438,700,629,84,758,375,543,741,544,336,959,928,223,452,36,419,906,596,668,723,344,784,402,836,949,714,768,707,84,954,654,710,719,406,623,417,469,313,511,646,598,630,357,550,868,357,873,700,172,870,574,428,872,656,891,427,149,645,613,227,594,801,626,206,450,838,326,177,671,3,576,969,83,529,674,728,180,46,647,78,99,391,501,829,713,344,735,612,736,516,419,895,829,834,519,617,42,140,478,360,999,809,434,553,899,116,863,275,24,542,533,321,512,927,735,723,657,395,831,258,784,443,513,363,805,316,465,823,935,895,542,670,896,449,65,743,705,507,791,612,300,101,208,980,206,269,793,990,580,754,296,453,909,641,393,966,629,854,211,139,451,717,587,775,529,326,735,577,60,203,419,435,729,48,88,53,718,441,385,898,158,533,647,351,263,632,536,875,54,107,402,952,108,681,829,959,826,617,579,771,251,292,747,932,871,273,9,170,64,585,994,673,647,386,648,538,791,409,448,823,747,294,676,406,622,453,205,146,209,579,646,766,110,315,288,637,881,522,703,752,223,685,298,484,811,680,305,808,166,142,108,962,254,689,53,379,533,767,749,321,830,360,959,202,35,940,521,291,742,105,149,157,362,600,315,421,763,162,36,353,13,191,594,625,479,680,126,941,514,690,923,571,704,919,147,569,489,331,259,941,424,683,87,879,715,154,885,963,820,48,311,800,650,739,384,659,7,568,903,906,250,187,155,702,46,304,728,82,330,454,780,284,801,36,922,23,780,17,302,244,262,409,718,488,636,781,723,619,161,709,986,790,9,661,887,613,689,337,528,483,669,940,919,131,467,616,511,161,395,135,599,312,231,438,405,984,228,790,445,36,547,155,820,633,991,780,488,538,700,68,207,649,326,907,371,759,847,760,167,347,605,194,97,637,422,198,987,700,139,968,618,386,926,643,578,355,546,730,117,157,266,34,268,397,518,263,957,510,780,480,824,742,243,473,444,572,923,999,238,477,231,699,483,138,229,75,868,554,259,984,282,550,836,94,107,761,635,161,321,598,990,890,266,13,8,23,767,177,322,62,647,727,169,712,646,56,654,64,851,489,874,925,725,374,273,632,322,987,354,932,517,454,151,383,530,618,955,355,46,698,87,12,325,431,370,367,229,193,229,552,756,489,454,925,276,254,856,726,441,58,866,782,726,555,652,717,158,636,420,582,630,324,772,567,605,798,876,795,534,993,180,947,292,261,739,846,290,47,412,63,109,918,749,246,400,877,84,747,973,571,529,622,528,738,257,299,378,864,750,793,461,158,149,621,856,798,395,314,336,513,697,324,766,124,59,577,13,388,437,767,741,330,685,618,286,385,717,718,882,61,689,208,506,428,756,772,295,590,462,82,827,190,921,835,262,608,55,39,44,735,524,243,306,842,21,631,381,207,940,828,319,17,773,967,431,193,485,851,436,385,736,47,323,662,432,272,267,719,355,164,743,437,106,951,163,674,260,383,906,569,845,412,855,581,177,83,348,152,601,428,727,813,374,962,989,708,336,195,123,187,960,113,738,43,676,120,386,285,665,17,328,613,628,635,828,859,380,436,167,202,662,245,62,926,392,856,804,547,645,857,674,884,762,503,3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reversed:
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sorted:
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