(Homework Solution): 4.20 Bitonic search. An array is bitonic if it is comprised of an increasing sequence of integers

/*** Below is the complete program and sample output in the end . I have used my own bitonic array. You can use whichever biotonic array you want. ust change the elements in the main method.

It is the most optimised version which uses binary search to find the element. In the worst case it will take 3Log(n). comparision to find the element.

Average complexity is O(logn)

**/

#include<iostream>

using namespace std;

/***

The algorithm will be similar to binary Search only.

First we need to find the biotonic point. The array is biotonic as initially it will be increasing and then decresing

So the point where this deviation starts i.e. increasing to dectreasing will be biotonic point.

After finding the biotonic point if the element which we are searching is equal to biotonic point element then we will return that index

If element is greater than the biotonic point then the element will definitely not present in the array

if the element is lessar than the biotonic point then it can present in both the array (left to biotionc and right to biotonic) We can simply use the binary search

in both the parts to find the element.

**/

int findBiotonicArrayPoint(int arr[], int size, int low, int high){

int mid = (high + low)/2;

// at biotonic point both left and right index element will be lessar than that index element

if(arr[mid] > arr[mid-1] && arr[mid] > arr[mid > arr[mid+1]]){

return mid;

}

// for the right part of the array

else if(arr[mid] > arr[mid-1] && arr[mid] < arr[mid+1]){

findBiotonicArrayPoint(arr,size, mid, high);

}

// for the left part of the array

else if(arr[mid] < arr[mid-1] && arr[mid] > arr[mid+1]){

findBiotonicArrayPoint(arr, size, low, mid);

}

}

/* If the element is present in the right to the biotonic then it will be descending order array

*/

int descendingBinarySearch(int arr[], int low, int high, int key){

while(low <= high){

int mid = low + (high – low)/2;

if(arr[mid] == key)

return mid;

if(arr[mid] < key)

high = mid -1;

else

low = mid +1;

}

return -1;

}

/* If the element is present in the left to the biotonic then it will be Ascending order array

*/

int ascendingBinarySearch(int arr[], int low, int high, int key){

while(low <= high){

int mid = low + (high – low)/2;

if(arr[mid] == key)

return mid;

if(arr[mid] > key)

high = mid -1;

else

low = mid +1;

}

return -1;

}

int searchBiotonicArray(int arr[], int n, int key, int index){

// if key is greater than the biotonic point

if( key > arr[index])

return -1;

// equal to biotonic point

else if(key == arr[index])

return index;

// search in both the arrays

else{

int temp = ascendingBinarySearch(arr,0, index-1, key);

if(temp !=-1)

return temp;

return descendingBinarySearch(arr, index +1, n-1, key);

}

}

int main(){

int arr[] = {-8,1,2,3,4,5,-2,-3};

int n = sizeof(arr)/ sizeof(arr[0]);

cout<<“biotonic Array is: “<<endl;

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

cout<<arr[i] <<” “;

}

cout<<endl;

cout<<“Enter the element you want to find:”<<endl;

int key;

cin>>key;

int low = 0;

int high = n-1;

int index = findBiotonicArrayPoint(arr,n, low, high);

int x = searchBiotonicArray(arr,n,key,index);

if(x == -1){

cout<<“Element ” <<key<<” is not present in the array”<<endl;

}

else{

cout<<“Element “<<key<<” is present at index: “<<x<<endl;

}

return 0;

}

/*** Sample output **/