Tim Sort Algorithm
The Tim Sort Algorithm is a hybrid sorting algorithm that combines the best aspects of two other algorithms - Merge Sort and Insertion Sort - to achieve better performance and efficiency. It was developed by Tim Peters in 2002 for the Python programming language, and since then, it has been adopted as the default sorting algorithm in Python, Java, and other programming languages. Tim Sort's primary advantage is its ability to optimize the sorting process by taking advantage of the naturally occurring runs (sorted subsequences) within the input data.
Tim Sort works by first dividing the input data into small segments called "runs" and then sorting these runs using a variation of Insertion Sort called "Binary Insertion Sort." This step is highly efficient because Insertion Sort performs well on small or partially sorted data. After sorting the runs, Tim Sort merges them using a modified Merge Sort algorithm called "Merge of Merges" that efficiently combines runs while preserving their sorted order. The merging process uses a merge stack that stores the runs, and it continuously merges runs in the stack until certain conditions are met. This combination of steps allows Tim Sort to adapt to the input data's structure and deliver excellent performance on both random and partially sorted data sets.
// C++ program to perform TimSort.
#include <iostream>
using namespace std;
const int RUN = 32;
// this function sorts array from left index to to right index which is of size atmost RUN
void insertionSort(int arr[], int left, int right)
{
for (int i = left + 1; i <= right; i++)
{
int temp = arr[i];
int j = i - 1;
while (arr[j] > temp && j >= left)
{
arr[j+1] = arr[j];
j--;
}
arr[j+1] = temp;
}
}
// merge function merges the sorted runs
void merge(int arr[], int l, int m, int r)
{
// original array is broken in two parts, left and right array
int len1 = m - l + 1, len2 = r - m;
int left[len1], right[len2];
for (int i = 0; i < len1; i++)
left[i] = arr[l + i];
for (int i = 0; i < len2; i++)
right[i] = arr[m + 1 + i];
int i = 0;
int j = 0;
int k = l;
// after comparing, we merge those two array in larger sub array
while (i < len1 && j < len2)
{
if (left[i] <= right[j])
{
arr[k] = left[i];
i++;
}
else
{
arr[k] = right[j];
j++;
}
k++;
}
// copy remaining elements of left, if any
while (i < len1)
{
arr[k] = left[i];
k++;
i++;
}
// copy remaining element of right, if any
while (j < len2)
{
arr[k] = right[j];
k++;
j++;
}
}
// iterative Timsort function to sort the array[0...n-1] (similar to merge sort)
void timSort(int arr[], int n)
{
// Sort individual subarrays of size RUN
for (int i = 0; i < n; i+=RUN)
insertionSort(arr, i, min((i+31), (n-1)));
// start merging from size RUN (or 32). It will merge to form size 64, then 128, 256 and so on ....
for (int size = RUN; size < n; size = 2*size)
{
// pick starting point of left sub array. We are going to merge arr[left..left+size-1] and arr[left+size, left+2*size-1]
// After every merge, we increase left by 2*size
for (int left = 0; left < n; left += 2*size)
{
// find ending point of left sub array
// mid+1 is starting point of right sub array
int mid = left + size - 1;
int right = min((left + 2*size - 1), (n-1));
// merge sub array arr[left.....mid] & arr[mid+1....right]
merge(arr, left, mid, right);
}
}
}
// utility function to print the Array
void printArray(int arr[], int n)
{
for (int i = 0; i < n; i++)
printf("%d ", arr[i]);
printf("\n");
}
// Driver program to test above function
int main()
{
int arr[] = {5, 21, 7, 23, 19};
int n = sizeof(arr)/sizeof(arr[0]);
printf("Given Array is\n");
printArray(arr, n);
timSort(arr, n);
printf("After Sorting Array is\n");
printArray(arr, n);
return 0;
}
