TimSort

TimSort is a sorting algorithm based on Insertion Sort and Merge Sort.

1. A stable sorting algorithm works in O(n Log n) time
2. Used in Java’s Arrays.sort() as well as Python’s sorted() and sort().
3. First sort small pieces using Insertion Sort, then merges the pieces using merge of merge sort.

We divides the Array into blocks known as Run. We sort those runs using insertion sort one by one and then merge those runs using combine function used in merge sort. If size of Array is less than run, then Array get sorted just by using Insertion Sort. The size of run may vary from 32 to 64 depending upon size of array. Note that merge function performs well when sizes subarrays are powers of 2. The idea is based on the fact that insertion sort performs well for small arrays.

Details of below implementation :

• We consider size of run as 32.
• We one by one sort pieces of size equal to run
• After sorting individual pieces, we merge them one by one. We double the size of merged subarrays after every iteration.

// C++ program to perform TimSort.
#include<bits/stdc++.h>
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;
}

Output:

Given Array is
5  21  7  23  19
After Sorting Array is
5  7  19  21  23

References :
https://svn.python.org/projects/python/trunk/Objects/listsort.txt
https://en.wikipedia.org/wiki/Timsort#Minimum_size_.28minrun.29

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