Node-TimSort: Fast Sorting for Node.js

An adaptive and stable sort algorithm based on merging that requires fewer than nlog(n) comparisons when run on partially sorted arrays. The algorithm uses O(n) memory and still runs in O(nlogn) (worst case) on random arrays.
This implementation is based on the original TimSort developed by Tim Peters for Python's lists (code here). TimSort has been also adopted in Java starting from version 7.

# Acknowledgments

- @novacrazy: ported the module to ES6/ES7 and made it available via bower
- @kasperisager: implemented faster lexicographic comparison of small integers

# Usage

Install the package with npm:

npm install --save timsort

And use it:

var TimSort = require('timsort');
var arr = [...];
TimSort.sort(arr);

You can also install it with bower:

bower install timsort

As `array.sort()` by default the `timsort` module sorts according to lexicographical order. You can also provide your own compare function (to sort any object) as:

function numberCompare(a,b) {
return a-b;
}
var arr = [...];
var TimSort = require('timsort');
TimSort.sort(arr, numberCompare);

You can also sort only a specific subrange of the array:

TimSort.sort(arr, 5, 10);
TimSort.sort(arr, numberCompare, 5, 10);

# Performance

A benchmark is provided in `benchmark/index.js`. It compares the `timsort` module against the default `array.sort` method in the numerical sorting of different types of integer array (as described here):

- Random array
- Descending array
- Ascending array
- Ascending array with 3 random exchanges
- Ascending array with 10 random numbers in the end
- Array of equal elements
- Random Array with many duplicates
- Random Array with some duplicates

For any of the array types the sorting is repeated several times and for different array sizes, average execution time is then printed. I run the benchmark on Node v6.3.1 (both pre-compiled and compiled from source, results are very similar), obtaining the following values:

|  | Execution Time (ns) | Speedup
--- | --- | --- | ---
Array Type | Length | TimSort.sort | array.sort <tbody>
Random | 10 | 404 | 1583 | 3.91
100 | 7147 | 4442 | 0.62
1000 | 96395 | 59979 | 0.62
10000 | 1341044 | 6098065 | 4.55
Descending | 10 | 180 | 1881 | 10.41
100 | 682 | 19210 | 28.14
1000 | 3809 | 185185 | 48.61
10000 | 35878 | 5392428 | 150.30
Ascending | 10 | 173 | 816 | 4.69
100 | 578 | 18147 | 31.34
1000 | 2551 | 331993 | 130.12
10000 | 22098 | 5382446 | 243.57
Ascending + 3 Rand Exc | 10 | 232 | 927 | 3.99
100 | 1059 | 15792 | 14.90
1000 | 3525 | 300708 | 85.29
10000 | 27455 | 4781370 | 174.15
Ascending + 10 Rand End | 10 | 378 | 1425 | 3.77
100 | 1707 | 23346 | 13.67
1000 | 5818 | 334744 | 57.53
10000 | 38034 | 4985473 | 131.08
Equal Elements | 10 | 164 | 766 | 4.68
100 | 520 | 3188 | 6.12
1000 | 2340 | 27971 | 11.95
10000 | 17011 | 281672 | 16.56
Many Repetitions | 10 | 396 | 1482 | 3.74
100 | 7282 | 25267 | 3.47
1000 | 105528 | 420120 | 3.98
10000 | 1396120 | 5787399 | 4.15
Some Repetitions | 10 | 390 | 1463 | 3.75
100 | 6678 | 20082 | 3.01
1000 | 104344 | 374103 | 3.59
10000 | 1333816 | 5474000 | 4.10 </tbody>

`TimSort.sort` is faster than `array.sort` on almost of the tested array types. In general, the more ordered the array is the better `TimSort.sort` performs with respect to `array.sort` (up to 243 times faster on already sorted arrays). And also, in general, the bigger the array the more we benefit from using the `timsort` module.

These data strongly depend on Node.js version and the machine on which the benchmark is run. I strongly encourage you to run the benchmark on your own setup with:

npm run benchmark

Please also notice that:

- This benchmark is far from exhaustive. Several cases are not considered and the results must be taken as partial
- inlining is surely playing an active role in `timsort` module's good performance
- A more accurate comparison of the algorithms would require implementing `array.sort` in pure javascript and counting element comparisons

# Stability

TimSort is stable which means that equal items maintain their relative order after sorting. Stability is a desirable property for a sorting algorithm. Consider the following array of items with an height and a weight.

[
{ height: 100, weight: 80 },
{ height: 90, weight: 90 },
{ height: 70, weight: 95 },
{ height: 100, weight: 100 },
{ height: 80, weight: 110 },
{ height: 110, weight: 115 },
{ height: 100, weight: 120 },
{ height: 70, weight: 125 },
{ height: 70, weight: 130 },
{ height: 100, weight: 135 },
{ height: 75, weight: 140 },
{ height: 70, weight: 140 }
]

Items are already sorted by `weight`. Sorting the array according to the item's `height` with the `timsort` module results in the following array:

[
{ height: 70, weight: 95 },
{ height: 70, weight: 125 },
{ height: 70, weight: 130 },
{ height: 70, weight: 140 },
{ height: 75, weight: 140 },
{ height: 80, weight: 110 },
{ height: 90, weight: 90 },
{ height: 100, weight: 80 },
{ height: 100, weight: 100 },
{ height: 100, weight: 120 },
{ height: 100, weight: 135 },
{ height: 110, weight: 115 }
]

Items with the same `height` are still sorted by `weight` which means they preserved their relative order.

`array.sort`, instead, is not guarranteed to be stable. In Node v0.12.7 sorting the previous array by `height` with `array.sort` results in:

[
{ height: 70, weight: 140 },
{ height: 70, weight: 95 },
{ height: 70, weight: 125 },
{ height: 70, weight: 130 },
{ height: 75, weight: 140 },
{ height: 80, weight: 110 },
{ height: 90, weight: 90 },
{ height: 100, weight: 100 },
{ height: 100, weight: 80 },
{ height: 100, weight: 135 },
{ height: 100, weight: 120 },
{ height: 110, weight: 115 }
]

As you can see the sorting did not preserve `weight` ordering for items with the same `height`.