Skip to main content

Function to sort an array using insertion sort

Insertion sort is slightly better sorting method among O(n2) algorithms. It is effecient if the elements are almost sorted and if the size is small.

Insertion sort basically works by splitting your elements into two parts. Sorted half and unsorted half. To begin with, Sorted half is empty and unsorted half has all elements. Then one element is removed from unsorted half and added to the sorted half. When adding , this element is inserted at the correct location. This process is continued till we have all the elements in sorted half and unsorted half is empty. Now let us try to understand it with a diagram.
First 17 is removed from unsorted array and added to sorted array. Since there is one element there, it is sorted. Next 4 which is front most element now in unsored array is removed and added to sorted array. But 4 is smaller than 17, so 17 is pushed to right and its place is taken by 4.
   Next 32 is removed from the front of unsorted array and added to sorted array. But here in sorted array to last element 17 is smaller. So 32 is in its correct place. Next 1 is moved from front of unsorted array. In sorted array, 32 is larger and pushed to right. Next 17 is pushed to right and 4 is also pushed to right. Now 1 is placed in 4's position. As you can see, now these 4 elements are sorted. This process continues until all the elements are removed from unsorted array.
   Removing front most element from the array takes O(1) X N elements. And inserting an element takes in worst case O(N) time. Hence complexity is O(N2 ) .
C++ function to insertion sort an array is really very simple and small.

#include<iostream>
using std::cin;
using std::cout;

void insertionSort(int *arr,int size);
void printArray(int *arr,int size);
int main()
{
    int n;
    cout<<"Size of array:";
    cin>>n;
    int a[n];
    cout<<"Elements of array:";
    for(int i=0;i<size;i++)
         cin>>a[i];
     insertionSort(a,n);
     printArray(a,n);
     return 0;
}

void insertionSort(int *arr,int size)
{
   for(int i=1;i<size;i++)
   {
        int val = arr[i];
        int j;
        for(j=i-1;j>=0 && arr[j] >val;j--)
        {
                 arr[j+1]=arr[j];
         }
         arr[j+1]=val;
   }
}


void printArray(int *arr,int size)
{
     for(int i=0;i<size;i++) 
            cout<< arr[i]<<"=====";
 
 }

In the insertionSort function, outer loop is for extracting one element from unsorted array. And inner loop is for inserting it in the sorted array and pushing elements to right as needed.
Writing insertion sort for linked list is much simple as well. You take one more linked list - sortedList. Now remove front element from list and insert it in ascending order in sortedList.
Labels:

Comments

Post a Comment

Popular posts from this blog

Introduction to AVL tree

AVL tree is a balanced binary search tree where the difference between heights of two sub trees is maximum 1. Why balanced tree A binary tree is good data structure because search operation here is of the order of O(logn). But this is true if the tree is balanced - which means the left and right subtrees are almost equal in height. If not balanced, search operation will take longer.  In worst case, if the tree has only one branch, then search is of the order O(n). Look at this example.  Here all nodes have only right children.  To search a value in this tree, we need upto 7 iterations, which is O(n). So this tree is very very inefficient. One way of making the tree efficient is to, balance the tree and make sure that height of two branches of each node are almost equal. Height of a node Height of a node is the distance between the node and its extreme child.  In the above a diagram, height of 37 is 3 and height of left child of 37 is 0 and right child of 37 is 2. Bal...
Post a Comment
Read more

Program to delete a node from linked list

How do you remove a node from a linked list? If you have to delete a node, first you need to search the node. Then you should find its previous node. Then you should link the previous node to the next node. If node containing 8 has to be deleted, then n1 should be pointing to n2. Looks quite simple. Isn't it? But there are at least two special cases you have to consider. Of course, when the node is not found. If the node is first node of the list viz head. If the node to be deleted is head node, then if you delete, the list would be lost. You should avoid that and make the second node as the head node. So it becomes mandatory that you return the changed head node from the function.   Now let us have a look at the code. #include<stdio.h> #include<stdlib.h> struct node { int data; struct node * next; }; typedef struct node * NODEPTR; NODEPTR create_node ( int value) { NODEPTR temp = (NODEPTR) malloc( size...
3 comments
Read more

Balanced brackets

Have you observed something? When ever you are writing code using any IDE, if you write mismatched brackets, immediately an error is shown by IDE. So how does IDE  know if an expression is having balanced brackets? For that, the expression must have equal number of opening and closing brackets of matching types and also they must be in correct order. Let us look at some examples (a+b)*c+d*{e+(f*g)}   - balanced (p+q*[r+u )] - unbalanced (p+q+r+s) ) - unbalanced (m+n*[p+q]+{g+h}) - balanced So we do we write a program to check if an expression is having balanced brackets? We do need to make use of stack to store the brackets. The algorithm is as follows Scan a character - ch from the expression If the character is opening bracket, push it to stack If the character is closing bracket pop a character from stack If popped opening bracket and ch are not of same type ( ( and ) or [ and ] ) stop the function and return false Repeat steps 2 and 3 till all characters are scanned. On...
2 comments
Read more