Binary Insertion Sort

// C program for implementation of binary insertion sort
#include <stdio.h>

// A binary search based function to find the position
// where item should be inserted in a[low..high]
int binarySearch(int a[], int item, int low, int high)
{
    if (high <= low)
        return (item > a[low])?  (low + 1): low;

    int mid = (low + high)/2;

    if(item == a[mid])
        return mid+1;

    if(item > a[mid])
        return binarySearch(a, item, mid+1, high);
    return binarySearch(a, item, low, mid-1);
}

// Function to sort an array a[] of size 'n'
void insertionSort(int a[], int n)
{
    int i, loc, j, k, selected;

    for (i = 1; i < n; ++i)
    {
        j = i - 1;
        selected = a[i];

        // find location where selected sould be inseretd
        loc = binarySearch(a, selected, 0, j);

        // Move all elements after location to create space
        while (j >= loc)
        {
            a[j+1] = a[j];
            j--;
        }
        a[j+1] = selected;
    }
}

// Driver program to test above function
int main()
{
    int a[] = {37, 23, 0, 17, 12, 72, 31,
              46, 100, 88, 54};
    int n = sizeof(a)/sizeof(a[0]), i;

    insertionSort(a, n);

    printf("Sorted array: \n");
    for (i = 0; i < n; i++)
        printf("%d ",a[i]);

    return 0;
}

// Java Program implementing
// binary insertion sort

import java.util.Arrays;
class GFG
{
    public static void main(String[] args)
    {
        final int[] arr = {37, 23, 0, 17, 12, 72, 31,
                             46, 100, 88, 54 };

        new GFG().sort(arr);

        for(int i=0; i<arr.length; i++)
            System.out.print(arr[i]+" ");
    }

    public void sort(int array[])
    {
        for (int i = 1; i < array.length; i++)
        {
            int x = array[i];

            // Find location to insert using binary search
            int j = Math.abs(Arrays.binarySearch(array, 0, i, x) + 1);

            //Shifting array to one location right
            System.arraycopy(array, j, array, j+1, i-j);

            //Placing element at its correct location
            array[j] = x;
        }
    }
}

// Code contributed by Mohit Gupta_OMG 

# Python Program implementation  
# of binary insertion sort

def binary_search(arr, val, start, end):
    # we need to distinugish whether we should insert
    # before or after the left boundary.
    # imagine [0] is the last step of the binary search
    # and we need to decide where to insert -1
    if start == end:
        if arr[start] > val:
            return start
        else:
            return start+1

    # this occurs if we are moving beyond left's boundary
    # meaning the left boundary is the least position to
    # find a number greater than val
    if start > end:
        return start

    mid = (start+end)/2
    if arr[mid] < val:
        return binary_search(arr, val, mid+1, end)
    elif arr[mid] > val:
        return binary_search(arr, val, start, mid-1)
    else:
        return mid

def insertion_sort(arr):
    for i in xrange(1, len(arr)):
        val = arr[i]
        j = binary_search(arr, val, 0, i-1)
        arr = arr[:j] + [val] + arr[j:i] + arr[i+1:]
    return arr

print("Sorted array:")
print insertion_sort([37, 23, 0, 17, 12, 72, 31,
                        46, 100, 88, 54])

# Code contributed by Mohit Gupta_OMG 

// C# Program implementing
// binary insertion sort
using System;

class GFG {
    
    public static void Main()
    {
        int []arr = {37, 23, 0, 17, 12, 72, 31,
                             46, 100, 88, 54 };

        sort(arr);

        for(int i = 0; i < arr.Length; i++)
            Console.Write(arr[i] + " ");
    }

    public static void sort(int []array)
    {
        for (int i = 1; i < array.Length; i++)
        {
            int x = array[i];

            // Find location to insert using
            // binary search
            int j = Math.Abs(Array.BinarySearch(
                              array, 0, i, x) + 1);

            // Shifting array to one location right
            System.Array.Copy(array, j, array,
                                         j+1, i-j);

            // Placing element at its correct
            // location
            array[j] = x;
        }
    }
}

// This code is contributed by nitin mittal.