binary Insertion Sort Algorithm
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time.
However, insertion sort provides several advantages:
Simple implementation: Jon Bentley shows a three-line c version, and a five-line optimized version
Efficient for (quite) small data sets, much like other quadratic sorting algorithmsAdaptive, i.e., efficient for data sets that are already substantially sorted: the time complexity is O(kn) when each component in the input is no more than K places away from its sorted position
Stable; i.e., makes not change the relative order of components with equal keys
/* Sorting of array list using binary insertion sort
* Using binary search to find the proper location for
* inserting the selected item at each iteration. */
#include <stdio.h>
/*Displays the array, passed to this method*/
void display(int arr[], int n) {
int i;
for(i = 0; i < n; i++){
printf("%d ", arr[i]);
}
printf("\n");
}
int binarySearch(int arr[], int key, int low, int high) {
if (low >= high)
return (key > arr[low]) ? (low + 1): low;
int mid = low + (high - 1) / 2;
if(arr[mid] == key)
return mid + 1;
else if (arr[mid] > key)
return binarySearch(arr, key, low, mid - 1);
else
return binarySearch(arr, key, mid + 1, high);
}
/*This is where the sorting of the array takes place
arr[] --- Array to be sorted
size --- Array Size
*/
void insertionSort(int arr[], int size) {
int i, j, key, index;
for(i = 0; i < size; i++) {
j = i - 1;
key = arr[i];
/* Use binrary search to find exact key's index */
index = binarySearch(arr, key, 0, j);
/* Move all elements greater than key from [index...j]
* to one position */
while(j >= index) {
arr[j + 1] = arr[j];
j = j - 1;
}
/* Insert key value in right place */
arr[j + 1] = key;
}
}
int main(int argc, const char * argv[]) {
int n;
printf("Enter size of array:\n");
scanf("%d", &n); // E.g. 8
printf("Enter the elements of the array\n");
int i;
int arr[n];
for(i = 0; i < n; i++) {
scanf("%d", &arr[i] );
}
printf("Original array: ");
display(arr, n);
insertionSort(arr, n);
printf("Sorted array: ");
display(arr, n);
return 0;
}
