Binary Insertion Sort
We can use binary search to reduce the number of comparisons in normal insertion sort. Binary Insertion Sort uses binary search to find the proper location to insert the selected item at each iteration.
In normal insertion sort, it takes O(n) comparisons (at nth iteration) in the worst case. We can reduce it to O(log n) by using binary search.
C++
// 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 Codeint 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
// Java Program implementing// binary insertion sortimport 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] + " "); } // Driver Code 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
# Python Program implementation# of binary insertion sortdef 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 middef insertion_sort(arr): for i in range(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 arrprint("Sorted array:")print(insertion_sort([37, 23, 0, 31, 22, 17, 12, 72, 31, 46, 100, 88, 54]))# Code contributed by Mohit Gupta_OMG |
C#
// C# Program implementing// binary insertion sortusing 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] + " "); } // Driver Code 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. |
PHP
<?php// PHP program for implementation of// binary insertion sort// A binary search based function to find// the position where item should be// inserted in a[low..high]function binarySearch($a, $item, $low, $high){ if ($high <= $low) return ($item > $a[$low]) ? ($low + 1) : $low; $mid = (int)(($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, $mid - 1);}// Function to sort an array a of size 'n'function insertionSort(&$a, $n){ $i; $loc; $j; $k; $selected; for ($i = 1; $i < $n; ++$i) { $j = $i - 1; $selected = $a[$i]; // find location where selected // item should be inserted $loc = binarySearch($a, $selected, 0, $j); // Move all elements after location // to create space while ($j >= $loc) { $a[$j + 1] = $a[$j]; $j--; } $a[$j + 1] = $selected; }}// Driver Code$a = array(37, 23, 0, 17, 12, 72, 31, 46, 100, 88, 54); $n = sizeof($a);insertionSort($a, $n);echo "Sorted array:\n";for ($i = 0; $i < $n; $i++) echo "$a[$i] ";// This code is contributed by// Adesh Singh?> |
Output
Sorted array: 0 12 17 23 31 37 46 54 72 88 100
Time Complexity: The algorithm as a whole still has a running worst-case running time of O(n2) because of the series of swaps required for each insertion.
This article is contributed by Amit Auddy. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
