# What is Tim Sort

**Timsort**is a hybrid stable sorting algorithm that is commonly used in programming languages such as Python and Java. It was developed by Tim Peters in 2002 for use in the Python programming language and is based on a combination of merge sort and insertion sort.

Timsort is designed to be efficient for both small and large data sets. It works by dividing the input array into small sub-arrays, sorting these sub-arrays using insertion sort, and then merging the sorted sub-arrays using a modified merge sort algorithm.

One of the key features of Timsort is its ability to recognize and exploit patterns in the data being sorted. For example, if the input data is already partially sorted or contains runs of ordered elements, Timsort can take advantage of these patterns to improve performance.

In Simple Terms:

Timsort is a way of putting a list of things in order from smallest to largest (or vice versa). It works by breaking the list down into smaller parts and then sorting each of those parts using a simple method called insertion sort.

Once the smaller parts are sorted, Timsort combines them back together using a modified version of another sorting algorithm called merge sort.

The really cool thing about Timsort is that it's smart enough to look for patterns in the list that can make it sort faster. For example, if there are already some parts of the list that are already sorted, Timsort will recognize that and take advantage of it to make the sorting process faster.

## Who invented it?

**was invented by Tim Peters, a software developer and contributor to the Python programming language, in 2002. He developed Timsort as a replacement for the existing sorting algorithm used in Python, which was not well-suited to sorting real-world data sets.**

Timsort

Timsort

Peters named the algorithm after himself, combining his first name with the word "sort". Since its creation, Timsort has been widely adopted in many programming languages, including Java, C++, and PHP, and is considered to be one of the most efficient and versatile sorting algorithms available.

## Pseudocode

```
function timsort(array):
// Set the minimum size of a run
minrun = calculate_minrun(len(array))
// Divide the array into runs using insertion sort
runs = []
for i = 0 to len(array) - 1 by minrun:
run = insertion_sort(array[i:i+minrun])
runs.append(run)
// Merge adjacent runs until the entire array is sorted
while len(runs) > 1:
new_runs = []
for i = 0 to len(runs) - 2 by 2:
merged_run = merge(runs[i], runs[i+1])
new_runs.append(merged_run)
if len(runs) % 2 == 1:
new_runs.append(runs[-1])
runs = new_runs
return runs[0]
```

In this pseudocode, the calculate_minrun function is a helper function that determines the minimum size of a run based on the length of the input array. The insertion_sort function is a simple implementation of insertion sort, and the merge function is a modified version of the merge function used in merge sort.

## Sample Code

```
// C++ code snippet
const int MIN_RUN = 32;
void insertion_sort(vector
```& array, int start, int end) {
for (int i = start + 1; i < end; i++) {
int key = array[i];
int j = i - 1;
while (j >= start && array[j] > key) {
array[j+1] = array[j];
j--;
}
array[j+1] = key;
}
}
int calculate_minrun(int n) {
int r = 0;
while (n >= MIN_RUN) {
r |= n & 1;
n >>= 1;
}
return n + r;
}
void merge_runs(vector& array, vector>& runs) {
while (runs.size() > 1) {
int n = runs.size();
int i = 0;
while (i < n - 2 && runs[i].second <= runs[i+1].second + runs[i+2].second) {
if (runs[i].second < runs[i+2].second) {
i++;
}
merge(array.begin() + runs[i].first,
array.begin() + runs[i+1].first,
array.begin() + runs[i+1].first + runs[i+1].second,
array.begin() + runs[i+2].first + runs[i+2].second,
array.begin() + runs[i].first);
runs[i].second += runs[i+1].second;
runs.erase(runs.begin() + i + 1);
n--;
}
int j = 0;
for (; j < n - 1; j += 2) {
merge(array.begin() + runs[j].first,
array.begin() + runs[j].first + runs[j].second,
array.begin() + runs[j+1].first,
array.begin() + runs[j+1].first + runs[j+1].second,
array.begin() + runs[j].first);
runs[j].second += runs[j+1].second;
}
if (j == n - 1) {
runs[j-1].second += runs[j].second;
runs.pop_back();
}
}
}
void timsort(vector& array) {
int n = array.size();
int minrun = calculate_minrun(n);
vector> runs;
for (int i = 0; i < n; i += minrun) {
int end = min(i + minrun, n);
insertion_sort(array, i, end);
runs.push_back(make_pair(i, end - i));
}
merge_runs(array, runs);
}
int main() {
vector array = {5, 1, 3, 8, 6, 4, 2, 9, 7};
timsort(array);
for (int i = 0; i < array.size(); i++) {
cout << array[i] << " ";
}
cout << endl;
return 0;
}

```
# Python code snippet
def insertion_sort(array, start, end):
for i in range(start + 1, end):
key = array[i]
j = i - 1
while j >= start and array[j] > key:
array[j+1] = array[j]
j -= 1
array[j+1] = key
def calculate_minrun(n):
r = 0
while n >= 32:
r |= n & 1
n >>= 1
return n + r
def merge_runs(array, runs):
while len(runs) > 1:
n = len(runs)
i = 0
while i < n - 2 and runs[i][1] <= runs[i+1][1] + runs[i+2][1]:
if runs[i][1] < runs[i+2][1]:
i += 1
merge(array, runs[i][0], runs[i+1][0], runs[i+2][0] + runs[i+2][1])
runs[i] = (runs[i][0], runs[i][1] + runs[i+1][1])
runs.pop(i+1)
n -= 1
j = 0
for j in range(0, n - 1, 2):
merge(array, runs[j][0], runs[j][0] + runs[j][1],
runs[j+1][0], runs[j+1][0] + runs[j+1][1])
runs[j] = (runs[j][0], runs[j][1] + runs[j+1][1])
if j == n - 2:
runs[j] = (runs[j][0], runs[j][1] + runs[j+1][1])
runs.pop()
def timsort(array):
n = len(array)
minrun = calculate_minrun(n)
runs = [(i, min(i+minrun, n)-i) for i in range(0, n, minrun)]
for run in runs:
insertion_sort(array, run[0], run[0]+run[1])
merge_runs(array, runs)
def merge(array, start1, end1, start2, end2):
merged = []
i = start1
j = start2
while i < end1 and j < end2:
if array[i] <= array[j]:
merged.append(array[i])
i += 1
else:
merged.append(array[j])
j += 1
merged += array[i:end1]
merged += array[j:end2]
array[start1:end2] = merged
array = [5, 1, 3, 8, 6, 4, 2, 9, 7]
timsort(array)
print(array)
```

```
import java.util.Arrays;
public class Timsort {
private static final int MIN_MERGE = 32;
public static void insertionSort(int[] array, int start, int end) {
for (int i = start + 1; i < end; i++) {
int key = array[i];
int j = i - 1;
while (j >= start && array[j] > key) {
array[j+1] = array[j];
j--;
}
array[j+1] = key;
}
}
public static int calculateMinrun(int n) {
int r = 0;
while (n >= MIN_MERGE) {
r |= (n & 1);
n >>= 1;
}
return n + r;
}
public static void mergeRuns(int[] array, int[][] runs) {
while (runs.length > 1) {
int n = runs.length;
int i = 0;
while (i < n - 2 && runs[i][1] <= runs[i+1][1] + runs[i+2][1]) {
if (runs[i][1] < runs[i+2][1]) {
i++;
}
merge(array, runs[i][0], runs[i+1][0], runs[i+2][0] + runs[i+2][1]);
runs[i][1] += runs[i+1][1];
System.arraycopy(runs, i+2, runs, i+1, n-i-2);
n -= 1;
}
for (int j = 0; j < n - 1; j += 2) {
merge(array, runs[j][0], runs[j][0] + runs[j][1],
runs[j+1][0], runs[j+1][0] + runs[j+1][1]);
runs[j][1] += runs[j+1][1];
}
if (j == n - 2) {
merge(array, runs[j][0], runs[j][0] + runs[j][1],
runs[j+1][0], runs[j+1][0] + runs[j+1][1]);
runs[j][1] += runs[j+1][1];
}
runs = Arrays.copyOf(runs, (n + 1) / 2);
}
}
public static void timsort(int[] array) {
int n = array.length;
int minrun = calculateMinrun(n);
int[][] runs = new int[(n + minrun - 1) / minrun][2];
for (int i = 0; i < runs.length; i++) {
int start = i * minrun;
int end = Math.min(start + minrun, n);
runs[i] = new int[] {start, end - start};
}
for (int[] run : runs) {
insertionSort(array, run[0], run[0] + run[1]);
}
mergeRuns(array, runs);
}
public static void merge(int[] array, int start1, int end1, int start2, int end2) {
int[] merged = new int[end2 - start1];
int i = start1;
int j = start2;
int k = 0;
while (i < end1 && j < end2) {
if (array[i] <= array[j]) {
merged[k++] = array[i++];
} else {
merged[k++] = array[j++];
}
}
while (i < end1) {
merged[k++] = array[i++];
}
while (j < end2) {
merged[k++] = array[j++];
}
System.arraycopy(merged, 0, array, start1, end2 - start1);
}
public static void main(String[] args) {
List
``` list = Arrays.asList(5, 1, 3, 8, 6, 4, 2, 9, 7);
int[] array = list.stream().mapToInt(Integer::intValue).toArray();
timsort(array);
System.out.println(Arrays.toString(array));
}
}

## Time and Space Complexity

- The time complexity of Timsort is O(n log n) in the worst case and average case, and O(n) in the best case (when the input array is already sorted or nearly sorted). This makes Timsort one of the fastest sorting algorithms for many real-world applications.
- The space complexity of Timsort is O(n), as it requires additional memory to store the merged subarrays during the merge step. However, Timsort's space usage is optimized to be as efficient as possible by reusing the input array, rather than allocating new memory for temporary arrays. This makes Timsort very memory efficient and suitable for use on large datasets.

## Advantages

- Timsort is a fast sorting algorithm that can handle a wide range of input sizes, making it suitable for use in many real-world applications.
- Timsort is stable, meaning that it maintains the relative order of equal elements in the input array. This is an important property for certain applications.
- Timsort is optimized to take advantage of existing order in the input array, making it particularly fast for partially sorted or nearly sorted input data.
- Timsort has a worst-case time complexity of O(n log n), which is the same as other popular sorting algorithms such as Merge Sort and Quick Sort.

## Disadvantages

- Timsort requires additional memory to store temporary arrays during the merge step, which can be a disadvantage on systems with limited memory resources.
- Timsort has a more complex implementation than other simple sorting algorithms such as Bubble Sort or Insertion Sort, which can make it more difficult to understand and implement correctly.
- While Timsort has a worst-case time complexity of O(n log n), it may not always be the fastest algorithm for very small datasets, as simpler sorting algorithms such as Bubble Sort or Insertion Sort may be more efficient for very small inputs.