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

# 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 [tabby title="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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Striver(underscore)79 at Codechef and codeforces D

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