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Insertion and Deletion of elements in a Sorted Array

In the article Insertion and Deletion of elements in an Array, we saw how data is inserted and deleted in an unsorted array. In that case, we needed two information, the element as well as the position, for insertion while for deletion we needed the position. In the case of sorted arrays insertion and deletion takes pace in a slightly different way.

The following example will clarify this:

Suppose we have the following array:

arr[5]={1,2,3,4,5}

And, we need to insert the element 6, so where it should be inserted? We can’t insert it at any place because then the array might not remain sorted. Therefore, we let the program to automatically calculate the position suitable for the new element, so that the array remains sorted even after insertion.

Now, arr[5]={1,2,3,4,6}

Now, suppose we wish to delete the element 6, in this case we don’t use the position for deletion because we don’t know where the element was placed by the program, so rather than referencing the position for deletion, we reference the element itself.

arr[5]={1,2,3,4}

Therefore, we conclude that while insertion we can use the same process that we used in the case of unsorted array but in spite of us giving the position the program will itself calculate it. Similarly, while deletion we have to reference the element and its position will be found out by the program. The rest of the process remains the same as we did for the insertion and deletion in an unsorted array.

I don’t think there is any need for further discussion on this topic, so we straightaway move on to the example program. The program is self-explanatory, wherever needed I have provided the comments.

  // Example Program to illustrate
  // insertion and deletion of
  // elements in a sorted array
  #include<iostream.h>

  // array has been declared as
  // global so that other functions
  // can also have access to it
  int arr[5]={1,2,3,4,5};
  // function prototype
  void a_insert(int);
  void a_delete(int);

  void main(void)
  {
   int ch;
   int num;

   while(ch!=4)
   {
    cout<<"1> Insert";
    cout<<"\n2> Delete";
    cout<<"\n3> Show";
    cout<<"\n4> Quit\n";

    cin>>ch;

    switch(ch)
    {
     case 1:
     cout<<"enter element:";
     cin>>num;

     a_insert(num);
     break;

     case 2:
     cout<<"enter element.:";
     cin>>num;
     a_delete(num);
     break;

     case 3:
     cout<<"\nArray:";
     for(int i=0;i<5;i++)
       if(arr[i]!=0) cout<<arr[i]<<" ";
     break;
    }
    cout<<"\n";
   }
  }

  // insertion function
  void a_insert(int num)
  {
   int pos;
   // find the position where
   // the element 'num' should
   // be inserted
   for(pos=0;arr[pos]<=num;pos++);
   pos++;

   // insert 'num' at the
   // appropriate position
   for(int i=4; i>=pos;i--)
   arr[i]=arr[i-1];
   arr[i]=num;
  }

  // deletion function
  // THE ELEMENT 'NUM' SHOULD BE
  // IN THE ARRAY
  void a_delete(int num)
  {
   int pos;

   // find the position where
   // the element 'num' is at
   // ---ELEMENT MUST BE IN THE
   // ARRAY---
   for(pos=0;arr[pos]!=num;pos++);
   pos++;

   // delete 'num' from the
   // appropriate position
   for(int i=pos; i<=4;i++)
   arr[i-1]=arr[i];
   arr[i-1]=0;
  }

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