Given an array of 
integers. The task is to find the Bitonicity of the given array.
The Bitonicity of an array arr[] can be defined as:
B[i] = 0, if i = 0.
= B[i-1] + 1, if arr[i] > arr[i-1]
= B[i-1] - 1, if arr[i] < arr[i-1]
= B[i-1], if arr[i] = arr[i-1]
Bitonicity will be last element of array B[].
Examples:
Input : arr[] = {1, 2, 3, 4, 5}
Output : 4
Input : arr[] = {1, 4, 5, 3, 2}
Output : 0
Given that the Bitonicity of an array arr[] can be defined as:
B[i] = 0, if i = 0.
= B[i-1] + 1, if arr[i] > arr[i-1]
= B[i-1] - 1, if arr[i] < arr[i-1]
= B[i-1], if arr[i] = arr[i-1]
Bitonicity will be last element of array B[].
From the above expression it can be deduced that:
- The bitonicity of the array is initially 0.
- It increases by 1 on moving to next element if the next element is greater than previous element.
- It decreases by 1 on moving to next element if the next element is greater than previous element.
The idea is to take a variable 
and start traversing the array, if the next element is greater than current, increment bt by 1 and if the next element is smaller than current then decrement bt by 1.
Below is the implementation of the above approach:
C++
// C++ program to find bitonicity // of an array #include <iostream> using namespace std; // Function to find the bitonicity // of an array int findBitonicity(int arr[], int n) { int bt = 0; for (int i = 1; i < n; i++) { if (arr[i] > arr[i - 1]) bt++; else if (arr[i] < arr[i - 1]) bt--; } return bt; } // Driver Code int main() { int arr[] = { 1, 2, 3, 4, 5, 6, 4, 3 }; int n = sizeof(arr) / sizeof(arr[0]); cout << "Bitonicity = " << findBitonicity(arr, n); return 0; } |
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Java
// Java program to find bitonicity // of an array import java.util.*; import java.lang.*; class GFG { // Function to find the bitonicity // of an array static int findBitonicity(int[] arr, int n) { int bt = 0; for (int i = 1; i < n; i++) { if (arr[i] > arr[i - 1]) bt++; else if (arr[i] < arr[i - 1]) bt--; } return bt; } // Driver Code public static void main(String args[]) { int arr[] = { 1, 2, 3, 4, 5, 6, 4, 3 }; int n = arr.length; System.out.print("Bitonicity = " + findBitonicity(arr, n)); } } // This code is contributed // by Akanksha Rai |
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Python3
# Python3 program to find bitonicity # of an array # Function to find the bitonicity # of an array def findBitonicity(arr, n): bt = 0 for i in range(1, n, 1): if (arr[i] > arr[i - 1]): bt += 1 elif (arr[i] < arr[i - 1]): bt -= 1 return bt # Driver Code if __name__ == '__main__': arr = [1, 2, 3, 4, 5, 6, 4, 3] n = len(arr) print("Bitonicity =", findBitonicity(arr, n)) # This code is contributed by # Surendra_Gangwar |
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C#
// C# program to find bitonicity // of an array using System; class GFG { // Function to find the bitonicity // of an array static int findBitonicity(int[] arr, int n) { int bt = 0; for (int i = 1; i < n; i++) { if (arr[i] > arr[i - 1]) bt++; else if (arr[i] < arr[i - 1]) bt--; } return bt; } // Driver Code public static void Main() { int[] arr = { 1, 2, 3, 4, 5, 6, 4, 3 }; int n = arr.Length; Console.Write("Bitonicity = " + findBitonicity(arr, n)); } } // This code is contributed // by Akanksha Rai |
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PHP
<?php // PHP program to find bitonicity // of an array // Function to find the bitonicity // of an array function findBitonicity(&$arr, $n) { $bt = 0; for ($i = 1; $i < $n; $i++) { if ($arr[$i] > $arr[$i - 1]) $bt++; else if ($arr[$i] < $arr[$i - 1]) $bt--; } return $bt; } // Driver Code $arr = array(1, 2, 3, 4, 5, 6, 4, 3 ); $n = sizeof($arr); echo ("Bitonicity = "); echo findBitonicity($arr, $n); // This code is contributed // by Shivi_Aggarwal ?> |
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Output:
Bitonicity = 3
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