Question

1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.

Answer 1

#include <bits/stdc++.h>

using namespace std;

int binarySearch(int arr[], int low, int high)

{

if(high >= low)

{

int mid = (low + high)/2;

if(mid == arr[mid])

return mid;

if(mid > arr[mid])

return binarySearch(arr, (mid + 1), high);

else

return binarySearch(arr, low, (mid -1));

}

return -1;

}

int main()

{

int arr[100000],i,n,k;

cout<<"Enter no of distinct elements in the array : ";

cin>>n;

cout<<"Enter the elements in ascending order"<<endl;

for(i=0;i<n;i++)

cin>>arr[i];

k=binarySearch(arr,0,n);

cout<<k<<" // ar["<<k<<"] = "<<k<<endl;

return 0;

}

The above program returns a Fixed Point in the array, if there is any Fixed Point present in array, else returns -1. Fixed Point in an array is an index i such that arr[i] is equal to i.