Find bitonic point in given bitonic sequence

You are given a bitonic sequence, the task is to find Bitonic Point in it. A Bitonic Sequence is a sequence of numbers which is first strictly increasing then after a point strictly decreasing.

A Bitonic Point is a point in bitonic sequence before which elements are strictly increasing and after which elements are strictly decreasing. A Bitonic point doesn’t exist if array is only decreasing or only increasing.

Examples :

Input : arr[] = {6, 7, 8, 11, 9, 5, 2, 1}
Output: 11
All elements before 11 are smaller and all
elements after 11 are greater.

Input : arr[] = {-3, -2, 4, 6, 10, 8, 7, 1}
Output: 10

A simple solution for this problem is to use linear search. Element arr[i] is bitonic point if both i-1’th and i+1’th both elements are less than i’th element. Time complexity for this approach is O(n).



An efficient solution for this problem is to use modified binary search.

  • If arr[mid-1] < arr[mid] and arr[mid] > arr[mid+1] then we are done with bitonic point.
  • If arr[mid] < arr[mid+1] then search in right sub-array, else search in left sub-array.

C++

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// C++ program to find bitonic point in a bitonic array.
#include<bits/stdc++.h>
using namespace std;
  
// Function to find bitonic point using binary search
int binarySearch(int arr[], int left, int right)
{
    if (left <= right)
    {
        int mid = (left+right)/2;
  
        // base condition to check if arr[mid] is
        // bitonic point or not
        if (arr[mid-1]<arr[mid] && arr[mid]>arr[mid+1])
            return mid;
  
        // We assume that sequence is bitonic. We go to
        // right subarray if middle point is part of
        // increasing subsequence. Else we go to left
        // subarray.
        if (arr[mid] < arr[mid+1])
            return binarySearch(arr, mid+1,right);
        else
            return binarySearch(arr, left, mid-1);
    }
  
    return -1;
}
  
// Driver program to run the case
int main()
{
    int arr[] = {6, 7, 8, 11, 9, 5, 2, 1};
    int n = sizeof(arr)/sizeof(arr[0]);
    int index = binarySearch(arr, 1, n-2);
    if (index != -1)
       cout << arr[index];
    return 0;
}

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Java














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// Java program to find bitonic 


// point in a bitonic array. 


  


import java.io.*; 


  


class GFG  


{ 


    // Function to find bitonic point  


    // using binary search 


    static int binarySearch(int arr[], int left, 


                                       int right) 


    { 


        if (left <= right) 


        { 


            int mid = (left + right) / 2; 


      


            // base condition to check if arr[mid]  


            // is bitonic point or not 


            if (arr[mid - 1] < arr[mid] &&  


                   arr[mid] > arr[mid + 1]) 


                   return mid; 


      


            // We assume that sequence is bitonic. We go to 


            // right subarray if middle point is part of 


            // increasing subsequence. Else we go to left 


            // subarray. 


            if (arr[mid] < arr[mid + 1]) 


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


            else


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


        } 


      


        return -1; 


    } 


      


    // Driver program  


    public static void main (String[] args)  


    { 


        int arr[] = {6, 7, 8, 11, 9, 5, 2, 1}; 


        int n = arr.length; 


        int index = binarySearch(arr, 1, n - 2); 


        if (index != -1) 


        System.out.println ( arr[index]); 


              


    } 


} 


  


// This code is contributed by vt_m 



















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Python3














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# Python3 program to find bitonic  


# point in a bitonic array. 


  


# Function to find bitonic point  


# using binary search 


def binarySearch(arr, left, right): 


  


    if (left <= right): 


  


        mid = (left + right) // 2; 


  


        # base condition to check if  


        # arr[mid] is bitonic point  


        # or not 


        if (arr[mid - 1] < arr[mid] and arr[mid] > arr[mid + 1]): 


            return mid; 


  


        # We assume that sequence  


        # is bitonic. We go to right  


        # subarray if middle point  


        # is part of increasing  


        # subsequence. Else we go  


        # to left subarray. 


        if (arr[mid] < arr[mid + 1]): 


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


        else: 


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


  


    return -1; 


  


# Driver Code 


arr = [6, 7, 8, 11, 9, 5, 2, 1]; 


n = len(arr); 


index = binarySearch(arr, 1, n-2); 


if (index != -1): 


        print(arr[index]); 


  


# This code is contributed by mits 



















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C#














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// C# program to find bitonic 


// point in a bitonic array. 


using System; 


  


class GFG  


{ 


    // Function to find bitonic point  


    // using binary search 


    static int binarySearch(int []arr, int left, 


                                      int right) 


    { 


        if (left <= right) 


        { 


            int mid = (left + right) / 2; 


      


            // base condition to check if arr[mid]  


            // is bitonic point or not 


            if (arr[mid - 1] < arr[mid] &&  


                arr[mid] > arr[mid + 1]) 


                return mid; 


      


            // We assume that sequence is bitonic. We go 


            // to right subarray if middle point is part of 


            // increasing subsequence. Else we go to left subarray. 


            if (arr[mid] < arr[mid + 1]) 


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


            else


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


        } 


      


        return -1; 


    } 


      


    // Driver program  


    public static void Main ()  


    { 


        int []arr = {6, 7, 8, 11, 9, 5, 2, 1}; 


        int n = arr.Length; 


        int index = binarySearch(arr, 1, n - 2); 


        if (index != -1) 


        Console.Write ( arr[index]); 


    } 


} 


  


// This code is contributed by nitin mittal 



















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PHP














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<?php 


// PHP program to find bitonic  


// point in a bitonic array. 


  


// Function to find bitonic point  


// using binary search 


function binarySearch($arr, $left, $right) 


{ 


    if ($left <= $right) 


    { 


        $mid = ($left + $right) / 2; 


  


        // base condition to check if  


        // arr[mid] is bitonic point  


        // or not 


        if ($arr[$mid - 1] < $arr[$mid] &&  


            $arr[$mid] > $arr[$mid + 1]) 


            return $mid; 


  


        // We assume that sequence  


        // is bitonic. We go to right  


        // subarray if middle point  


        // is part of increasing  


        // subsequence. Else we go  


        // to left subarray. 


        if ($arr[$mid] < $arr[$mid + 1]) 


            return binarySearch($arr, $mid + 1,$right); 


        else


            return binarySearch($arr, $left, $mid - 1); 


    } 


  


    return -1; 


} 


  


    // Driver Code 


    $arr = array(6, 7, 8, 11, 9, 5, 2, 1); 


    $n = sizeof($arr); 


    $index = binarySearch($arr, 1, $n-2); 


    if ($index != -1) 


        echo $arr[$index]; 


  


// This code is contributed by nitin mittal 


?> 



















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Output:


11



Time complexity : O(Log n)


This article is contributed by Shashank Mishra ( Gullu ). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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