Type of array and its maximum element

Given an array, it can be of 4 types
(a) Ascending
(b) Descending
(c) Ascending Rotated
(d) Descending Rotated
Find out which kind of array it is and return the maximum of that array.

Examples :

Input :  arr[] = { 2, 1, 5, 4, 3}
Output : Descending rotated with maximum element 5

Input :  arr[] = { 3, 4, 5, 1, 2}
Output : Ascending rotated with maximum element 5

Asked in : Amazon Interview

Implementation:

1- First, check if the whole array is in 
   increasing order, if yes then print arr[n-1].
   and return.

2- If above statement doesn't run even single
   time that means an array is in decreasing 
   order from starting. Two cases arise:
   
      a) Check if the whole array is in 
         decreasing order, if yes then 
         print arr[0] and return.
     (b) Otherwise, the array is descending
         rotated and the maximum element will
         be the index before which array was 
         decreasing.

3- If first point partially satisfies that 
   means the whole array is not in increasing 
   order that means an array is ascending 
   rotated and the maximum element will be the
   point from where it starts decreasing.

C/C++

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// C++ program to find type of array, ascending
// descending, clockwise rotated or anti-clockwise
// rotated.
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the type of an array
// and maximum element in it.
void findType(int arr[], int n)
{
    int i = 0;
  
    // Check if the array is in ascending order
    while (i < n - 1 && arr[i] <= arr[i + 1])
        i++;
  
    // If i reaches to last index that means
    // all elements are in increasing order
    if (i == n - 1) {
        cout << "Ascending with maximum element = "
             << arr[n - 1] << endl;
        return;
    }
  
    // If first element is greater than next one
    if (i == 0) {
        while (i < n - 1 && arr[i] >= arr[i + 1])
            i++;
  
        // If i reaches to last index
        if (i == n - 1) {
            cout << "Descending with maximum element =  "
                 << arr[0] << endl;
            return;
        }
  
        // If the whole array is not in decreasing order
        // that means it is first decreasing then
        // increasing, i.e., descending rotated, so
        // its maximum element will be the point breaking
        // the order i.e. i so, max will be i+1
        if (arr[0] < arr[i + 1]) {
            cout << "Descending rotated with maximum element = "
                 << max(arr[0], arr[i + 1]) << endl;
            return;
        }
        else {
            cout << "Ascending rotated with maximum element = "
                 << max(arr[0], arr[i + 1]) << endl;
            return;
        }
    }
  
    // If whole array is not increasing that means at some
    // point it is decreasing, which makes it ascending rotated
    // with max element as the decreasing point
    if (i < n - 1 && arr[0] > arr[i + 1]) {
        cout << "Ascending rotated with maximum element =  "
             << max(arr[i], arr[0]) << endl;
        return;
    }
  
    cout << "Descending rotated with maximum element "
         << max(arr[i], arr[0]) << endl;
}
  
// Driver code
int main()
{
    int arr1[] = { 4, 5, 6, 1, 2, 3 }; // Ascending rotated
    int n = sizeof(arr1) / sizeof(arr1[0]);
    findType(arr1, n);
  
    int arr2[] = { 2, 1, 7, 5, 4, 3 }; // Descending rotated
    n = sizeof(arr2) / sizeof(arr2[0]);
    findType(arr2, n);
  
    int arr3[] = { 1, 2, 3, 4, 5, 8 }; // Ascending
    n = sizeof(arr3) / sizeof(arr3[0]);
    findType(arr3, n);
  
    int arr4[] = { 9, 5, 4, 3, 2, 1 }; // Descending
    n = sizeof(arr4) / sizeof(arr4[0]);
    findType(arr4, n);
  
    return 0;
}

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Java

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// Java program to find type of array, ascending
// descending, clockwise rotated or anti-clockwise
// rotated.
import java.io.*;
class GFG {
    public static int max(int a, int b)
    {
        return (a > b) ? a : b;
    }
  
    // Function to find the type of an array
    // and maximum element in it
    public static void findType(int arr[])
    {
        int i = 0;
        int n = arr.length;
  
        // Check if the array is in ascending order
        while (i < n - 1 && arr[i] <= arr[i + 1])
            i++;
  
        // If i reaches to last index that means
        // all elements are in increasing order
        if (i == n - 1) {
            System.out.println("Ascending with maximum element = " + arr[n - 1]);
            return;
        }
  
        // If first element is greater than next one
        if (i == 0) {
            while (i < n - 1 && arr[i] >= arr[i + 1])
                i++;
  
            // If i reaches to last index
            if (i == n - 1) {
                System.out.println("Descending with maximum "
                                   + "element =  " + arr[0]);
                return;
            }
  
            // If the whole array is not in decreasing order
            // that means it is first decreasing then
            // increasing, i.e., descending rotated, so
            // its maximum element will be the point breaking
            // the order i.e. i so, max will be i+1
            if (arr[0] < arr[i + 1]) {
                System.out.println("Descending rotated with"
                                   + " maximum element = " + max(arr[0], arr[i + 1]));
                return;
            }
            else {
                System.out.println("Ascending rotated with"
                                   + " maximum element = " + max(arr[0], arr[i + 1]));
                return;
            }
        }
  
        // If whole array is not increasing that means at some
        // point it is decreasing, which makes it ascending rotated
        // with max element as the decreasing point
        if (i < n - 1 && arr[0] > arr[i + 1]) {
  
            System.out.println("Ascending rotated with maximum"
                               + " element =  " + max(arr[i], arr[0]));
            return;
        }
  
        System.out.println("Descending rotated with maximum "
                           + "element " + max(arr[i], arr[0]));
    }
  
    public static void main(String[] args)
    {
        int arr1[] = { 4, 5, 6, 1, 2, 3 }; // Ascending rotated
        findType(arr1);
  
        int arr2[] = { 2, 1, 7, 5, 4, 3 }; // Descending rotated
        findType(arr2);
  
        int arr3[] = { 1, 2, 3, 4, 5, 8 }; // Ascending
        findType(arr3);
  
        int arr4[] = { 9, 5, 4, 3, 2, 1 }; // Descending
        findType(arr4);
    }
}

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Python3

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# Python3 program to find type of array, ascending 
# descending, clockwise rotated or anti-clockwise 
# rotated.
  
def findType(arr, n) :
  
    i = 0
  
    # Check if the array is in ascending order 
    while (i < n-1 and arr[i] <= arr[i + 1]) :
        i = i + 1
  
    # If i reaches to last index that means 
    # all elements are in increasing order 
    if (i == n-1):
        print(("Ascending with maximum element = "
              + str(arr[n-1])))
        return None
      
  
    # If first element is greater than next one 
    if (i == 0):
        while (i < n-1 and arr[i] >= arr[i + 1]):
            i = i + 1
  
        # If i reaches to last index 
        if (i == n - 1):
            print(("Descending with maximum element = "
                  + str(arr[0])))
            return None
      
  
        # If the whole array is not in decreasing order 
        # that means it is first decreasing then 
        # increasing, i.e., descending rotated, so 
        # its maximum element will be the point breaking 
        # the order i.e. i so, max will be i + 1 
        if (arr[0] < arr[i + 1]):
            print(("Descending rotated with maximum element = " 
                  + str(max(arr[0], arr[i + 1]))))
            return None
        else:
          
            print(("Ascending rotated with maximum element = " 
                  + str(max(arr[0], arr[i + 1]))))
                    
            return None
          
      
  
    # If whole array is not increasing that means at some 
    # point it is decreasing, which makes it ascending rotated 
    # with max element as the decreasing point 
    if (i < n -1 and arr[0] > arr[i + 1]):
      
        print(("Ascending rotated with maximum element = " 
             + str(max(arr[i], arr[0]))))
        return None
      
  
    print(("Descending rotated with maximum element "
          + str(max(arr[i], arr[0]))))
  
# Driver code 
if __name__=='__main__':
    arr1 = [ 4, 5, 6, 1, 2, 3] # Ascending rotated 
    n = len(arr1)
    findType(arr1, n); 
  
    arr2 = [ 2, 1, 7, 5, 4, 3] # Descending rotated 
    n = len(arr2) 
    findType(arr2, n); 
  
    arr3 = [ 1, 2, 3, 4, 5, 8] # Ascending 
    n = len(arr3) 
    findType(arr3, n); 
  
    arr4 = [ 9, 5, 4, 3, 2, 1] # Descending 
    n = len(arr4) 
    findType(arr4, n); 
  
# this code is contributed by YatinGupta

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C#

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// C# program to find type of array, ascending
// descending, clockwise rotated or anti-clockwise
// rotated.
using System;
  
class GFG {
  
    public static int max(int a, int b)
    {
        return (a > b) ? a : b;
    }
  
    // Function to find the type of an array
    // and maximum element in it
    public static void findType(int[] arr)
    {
        int i = 0;
        int n = arr.Length;
  
        // Check if the array is in ascending
        // order
        while (i < n - 1 && arr[i] <= arr[i + 1])
            i++;
  
        // If i reaches to last index that means
        // all elements are in increasing order
        if (i == n - 1) {
            Console.WriteLine("Ascending with "
                              + "maximum element = " + arr[n - 1]);
            return;
        }
  
        // If first element is greater than
        // next one
        if (i == 0) {
            while (i < n - 1 && arr[i] >= arr[i + 1])
                i++;
  
            // If i reaches to last index
            if (i == n - 1) {
                Console.WriteLine("Descending with"
                                  + " maximum element = " + arr[0]);
                return;
            }
  
            // If the whole array is not in
            // decreasing order that means it is
            // first decreasing then increasing,
            // i.e., descending rotated, so its
            // maximum element will be the point
            // breaking the order i.e. i so, max
            // will be i+1
            if (arr[0] < arr[i + 1]) {
                Console.WriteLine("Descending rotated"
                                  + " with maximum element = "
                                  + max(arr[0], arr[i + 1]));
                return;
            }
            else {
                Console.WriteLine("Ascending rotated"
                                  + " with maximum element = "
                                  + max(arr[0], arr[i + 1]));
                return;
            }
        }
  
        // If whole array is not increasing that
        // means at some point it is decreasing,
        // which makes it ascending rotated with
        // max element as the decreasing point
        if (i < n - 1 && arr[0] > arr[i + 1]) {
  
            Console.WriteLine("Ascending rotated"
                              + " with maximum element = "
                              + max(arr[i], arr[0]));
            return;
        }
  
        Console.WriteLine("Descending rotated with"
                          + " maximum element "
                          + max(arr[i], arr[0]));
    }
  
    // Driver code
    public static void Main()
    {
  
        // Ascending rotated
        int[] arr1 = { 4, 5, 6, 1, 2, 3 };
        findType(arr1);
  
        // Descending rotated
        int[] arr2 = { 2, 1, 7, 5, 4, 3 };
        findType(arr2);
  
        // Ascending
        int[] arr3 = { 1, 2, 3, 4, 5, 8 };
        findType(arr3);
  
        // Descending
        int[] arr4 = { 9, 5, 4, 3, 2, 1 };
        findType(arr4);
    }
}
  
// This code is contributed by nitin mittal.

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PHP

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<?php
// PHP program to find type 
// of array, ascending descending, 
// clockwise rotated or anti-clockwise
// rotated.
  
// Function to find the type
// of an array and maximum 
// element in it.
function findType($arr, $n)
{
    $i = 0;
  
    // Check if the array is 
    // in ascending order
    while ($i < $n - 1 and 
           $arr[$i] <= $arr[$i + 1])
        $i++;
  
    // If i reaches to last index 
    // that means all elements are
    // in increasing order
    if ($i == $n - 1)
    {
        echo "Ascending with maximum "
                         "element = "
                    $arr[$n - 1], "\n";
        return ;
    }
  
    // If first element is
    // greater than next one
    if ($i == 0)
    {
        while ($i < $n - 1 and 
               $arr[$i] >= $arr[$i + 1])
            $i++;
  
        // If i reaches to last index
        if ($i == $n - 1)
        {
            echo "Descending with maximum "
                              "element = "
                              $arr[0], "\n";
            return ;
        }
  
        // If the whole array is not in 
        // decreasing order that means 
        // it is first decreasing then
        // increasing, i.e., descending
        // rotated, so its maximum element 
        // will be the point breaking the 
        // order i.e. i so, max will be i+1
        if ($arr[0] < $arr[$i + 1])
        {
            echo "Descending rotated with ".
                      "maximum element = "
                                max($arr[0],
                        $arr[$i + 1]), "\n";
            return ;
        }
        else
        {
            echo "Ascending rotated with " .
                       "maximum element = "
                                max($arr[0], 
                       $arr[$i + 1]), "\n";
            return ;
        }
    }
  
    // If whole array is not increasing 
    // that means at some point it is 
    // decreasing, which makes it 
    // ascending rotated with max element
    // as the decreasing point
    if ($i < $n - 1 and $arr[0] > $arr[$i + 1])
    {
        echo "Ascending rotated with maximum "
                   "element = ", max($arr[$i], 
                                $arr[0]), "\n";
        return;
    }
  
    echo "Descending rotated with maximum " .
                   "element ", max($arr[$i], 
                              $arr[0]), "\n";
}
  
// Driver code
  
// Ascending rotated
$arr1 = array( 4, 5, 6, 1, 2, 3); 
$n = count($arr1);
findType($arr1, $n);
  
// Descending rotated
$arr2 = array( 2, 1, 7, 5, 4, 3); 
$n = count($arr2);
findType($arr2, $n);
  
// Ascending
$arr3 = array( 1, 2, 3, 4, 5, 8); 
$n = count($arr3);
findType($arr3, $n);
  
// Descending
$arr4 = array( 9, 5, 4, 3, 2, 1); 
$n = count($arr4);
findType($arr4, $n);
  
// This code is contributed by anuj_67.
?>

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Output :

Ascending rotated with maximum element = 6
Descending rotated with maximum element = 7
Ascending with maximum element = 8
Descending with maximum element = 9

Time Complexity : O(n)
Auxiliary Space : O(1)

Another approach: Iterate through the array once and store the indices of the first and the last occurrences of the minimum and the maximum element from the array. Now there are four cases:

  1. If the first occurrence of the minimum element is at the beginning of the array and the last occurrence of the maximum element is at the end of the array then the array is in ascending order. For example, {1, 1, 1, 2, 3, 4, 5, 6, 6, 6}.
  2. If the first occurrence of the maximum element is at the beginning of the array and the last occurrence of the minimum element is at the end of the array then the array is in descending order. For example, {6, 6, 6, 5, 4, 3, 2, 1, 1, 1}.
  3. If the first occurrence of the maximum element is equal to the last occurrence of the minimum element + 1 then the array is in descending rotated order. For example, {3, 2, 1, 1, 1, 6, 6, 6, 5, 4}.
  4. If the first occurrence of the minimum element is equal to the last occurrence of the maximum element + 1 then the array is in ascending rotated order. For example, {4, 5, 6, 6, 6, 1, 1, 1, 2, 3}.

Below is the implementation of the above approach:

// C++ implementation of the approach
#include
using namespace std;

// Function to find the type of an array
// and maximum element in it
void findType(int arr[], int n)
{

// To store the minimum and the maximum
// element from the array
int min_element = INT_MAX, max_element = INT_MIN;

// To store the first and the last occurrences
// of the minimum and the maximum
// element from the array
int min_index1, max_index1, max_index2, min_index2;

for (int i = 0; i < n; i++) { // If new minimum is found if (arr[i] < min_element) { // Update the minimum so far // and its occurrences min_element = arr[i]; min_index1 = i; min_index2 = i; } // If current element is equal the found // minimum so far then update the last // occurrence of the minimum element else if (arr[i] == min_element) min_index2 = i; // If new maximum is found if (arr[i] > max_element) {

// Update the maximum so far
// and its occurrences
max_element = arr[i];
max_index1 = i;
max_index2 = i;
}

// If current element is equal the found
// maximum so far then update the last
// occurrence of the maximum element
else if (arr[i] == max_element)
max_index2 = i;
}

// First occurrence of minimum element is at the
// beginning of the array and the last occurrence
// of the maximum element is at the end of the
// array then the array is sorted in ascending
// For example, {1, 1, 1, 2, 3, 4, 5, 6, 6, 6}
if (min_index1 == 0 && max_index2 == n – 1) {
cout << "Ascending with maximum element = " << max_element << endl; } // First occurrence of maximum element is at the // beginning of the array and the last occurrence // of the minimum element is at the end of the // array then the array is sorted in descending // For example, {6, 6, 6, 5, 4, 3, 2, 1, 1, 1} else if (min_index2 == n - 1 && max_index1 == 0) { cout << "Descending with maximum element = " << max_element << endl; } // First occurrence of maximum element is equal // to the last occurrence of the minimum element + 1 // then the array is descending and rotated // For example, {3, 2, 1, 1, 1, 6, 6, 6, 5, 4} else if (max_index1 == min_index2 + 1) { cout << "Descending rotated with maximum element = " << max_element << endl; } // First occurrence of minimum element is equal // to the last occurrence of the maximum element + 1 // then the array is ascending and rotated // For example, {4, 5, 6, 6, 6, 1, 1, 1, 2, 3} else { cout << "Ascending rotated with maximum element = " << max_element << endl; } } // Driver code int main() { int arr[] = { 4, 5, 6, 6, 6, 1, 1, 1, 2, 3 }; int n = sizeof(arr) / sizeof(arr[0]); findType(arr, n); return 0; } Output :

Ascending rotated with maximum element = 6


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