Question

2) Write a recursive procedure in pseudocode to implement the binary search algorithm. 3) Explain, how the binary search algorithm can be modified, or used, to insert, a new integer element x, into a sorted list of n intgers.

Answer 1

1.Recursive procedure in pseudocode to implement a binary search algorithm

// C program to implement recursive Binary Search
#include <stdio.h>
int binarySearch(int arr[], int l, int r, int x)
{
   if (r >= l) {
       int mid = l + (r - l) / 2;  
       if (arr[mid] == x)
           return mid;  
       if (arr[mid] > x)
           return binarySearch(arr, l, mid - 1, x);
       return binarySearch(arr, mid + 1, r, x);
   }
   return -1;
}

int main(void)
{
   int arr[] = { 1,2,4,5};
   int n = sizeof(arr) / sizeof(arr[0]);
   int x = 3;
   int result = binarySearch(arr, 0, n - 1, x);
   (result == -1) ? printf("Element is not present in array")
               : printf("Element is present at index %d",
                           result);
   return 0;
}

2. To insert an element into a sorted array using binary search

In order to insert a random number into a sorted array using binary search first, we compare the number with mid, if the mid is greater than that number then right=mid otherwise lenft=mid-1. After this step, we again call the same function as this is a recursive function. This loop is completed when left<right and then we add the number in the place of left.

 public void add(T e, int result) {
        int left, right, mid;


        left = 0;
        right = array.size();


        while(left< right)  {
            mid = (left + right)/2;
            


            if(result > 0) { //If e is lower
                right = mid;
            } else { //If e is higher
                left = mid + 1;
            }
        }

        array.add(left, e);

    }