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++

// 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; }

## Java

// 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

## C#

// 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

## PHP

<?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 ?>

Output:

11

Time complexity : O(Log n)

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