Program to calculate Bitonicity of an Array

Given an array of N 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 bt = 0 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++

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// 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














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// 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














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# 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#














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// 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














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<?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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