Find the maximum element in an array which is first increasing and then decreasing

Given an array of integers which is initially increasing and then decreasing, find the maximum value in the array. 
Examples :

Input: arr[] = {8, 10, 20, 80, 100, 200, 400, 500, 3, 2, 1}
Output: 500

Input: arr[] = {1, 3, 50, 10, 9, 7, 6}
Output: 50

Corner case (No decreasing part)
Input: arr[] = {10, 20, 30, 40, 50}
Output: 50

Corner case (No increasing part)
Input: arr[] = {120, 100, 80, 20, 0}
Output: 120

Method 1 (Linear Search): We can traverse the array and keep track of maximum and element. And finally return the maximum element. 

Implementation:

C++

// C++ program to find maximum
// element
#include <bits/stdc++.h>
using namespace std;

// function to find the maximum element
int findMaximum(int arr[], int low, int high)
{
    int max = arr[low];
    int i;
    for (i = low + 1; i <= high; i++)
    {
        if (arr[i] > max)
            max = arr[i];

        // break when once an element is smaller than
        // the max then it will go on decreasing
        // and no need to check after that
        else
            break;
    }
    return max;
}

/* Driver code*/
int main()
{
    int arr[] = {1, 30, 40, 50, 60, 70, 23, 20};
    int n = sizeof(arr)/sizeof(arr[0]);
    cout << "The maximum element is " << findMaximum(arr, 0, n-1);
    return 0;
}

// This is code is contributed by rathbhupendra

C

// C program to find maximum
// element
#include <stdio.h>

// function to find the maximum element
int findMaximum(int arr[], int low, int high)
{
int max = arr[low];
int i;
for (i = low+1; i <= high; i++)
{
    if (arr[i] > max)
        max = arr[i];
// break when once an element is smaller than
// the max then it will go on decreasing
// and no need to check after that
    else
        break;
}
return max;
}

/* Driver program to check above functions */
int main()
{
int arr[] = {1, 30, 40, 50, 60, 70, 23, 20};
int n = sizeof(arr)/sizeof(arr[0]);
printf("The maximum element is %d", findMaximum(arr, 0, n-1));
getchar();
return 0;
}

Java

// java program to find maximum
// element

class Main
{
    // function to find the
    // maximum element
    static int findMaximum(int arr[], int low, int high)
    {
       int max = arr[low];
       int i;
       for (i = low; i <= high; i++)
       {
           if (arr[i] > max)
              max = arr[i];
       }
       return max;
    }

    // main function
    public static void main (String[] args)
    {
        int arr[] = {1, 30, 40, 50, 60, 70, 23, 20};
        int n = arr.length;
        System.out.println("The maximum element is "+
                            findMaximum(arr, 0, n-1));
    }
}

Python3

# Python3 program to find
# maximum element

def findMaximum(arr, low, high):
    max = arr[low]
    i = low
    for i in range(high+1):
        if arr[i] > max:
            max = arr[i]
    return max

# Driver program to check above functions */
arr = [1, 30, 40, 50, 60, 70, 23, 20]
n = len(arr)
print ("The maximum element is %d"%
        findMaximum(arr, 0, n-1))

# This code is contributed by Shreyanshi Arun.

C#

// C# program to find maximum
// element
using System;

class GFG
{
    // function to find the
    // maximum element
    static int findMaximum(int []arr, int low, int high)
    {
        int max = arr[low];
        int i;
        for (i = low; i <= high; i++)
        {
            if (arr[i] > max)
                max = arr[i];
        }
        return max;
    }

    // Driver code
    public static void Main ()
    {
        int []arr = {1, 30, 40, 50, 60, 70, 23, 20};
        int n = arr.Length;
        Console.Write("The maximum element is "+
                        findMaximum(arr, 0, n-1));
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP program to Find the maximum
// element in an array which is first
// increasing and then decreasing

function findMaximum($arr, $low, $high)
{
$max = $arr[$low];
$i;
for ($i = $low; $i <= $high; $i++)
{
    if ($arr[$i] > $max)
        $max = $arr[$i];
}
return $max;
}

// Driver Code
$arr = array(1, 30, 40, 50,
             60, 70, 23, 20);
$n = count($arr);
echo "The maximum element is ",
      findMaximum($arr, 0, $n-1);

// This code is contributed by anuj_67.
?>

Javascript

<script>

// Javascript program to find maximum
// element

// function to find the maximum element
function findMaximum(arr, low, high)
{
    var max = arr[low];
    var i;
    for (i = low + 1; i <= high; i++)
    {
        if (arr[i] > max)
            max = arr[i];

        // break when once an element is smaller than
        // the max then it will go on decreasing
        // and no need to check after that
        else
            break;
    }
    return max;
}

/* Driver code*/
var arr = [1, 30, 40, 50, 60, 70, 23, 20];
var n = arr.length;
document.write("The maximum element is " + findMaximum(arr, 0, n-1));

</script>

Output

The maximum element is 70

Time Complexity : O(n)

Auxiliary Space: O(1)

Method 2 (Binary Search – Recursive Solution)

The iterative approach of Binary search to find the maximum element in an array which is first increasing and then decreasing.
The standard binary search approach can be modified in the following ways :-

1. If the mid element is greater than both of its adjacent elements, then mid is the maximum.
2. If the mid element is smaller than its next element then we should try to search on the right half of the array. So, make, high = mid – 1. Example array : {2, 4, 6, 8, 10, 3, 1}
3. If the mid element is greater than the next element, similarly we should try to search on the left half. So, make, low = mid + 1. Example array: {3, 50, 10, 9, 7, 6} 

Implementation:

C++

#include <bits/stdc++.h>
using namespace std;

// Recursive solution for finding bitonic point
int findMaximum(int arr[], int low, int high)
{
      // if there is only one element
    if (low == high)
        return arr[high];

      // finding the mid index
    int mid = low + (high - low) / 2;

      // if the value of mid index is greater than left and right value
    if (arr[mid] > arr[mid - 1] and arr[mid] > arr[mid + 1])
        return arr[mid];

      // if value on mid index is greater than next index
      // shift the search space to right half
    else if (arr[mid] < arr[mid + 1])
        return findMaximum(arr, mid + 1, high);

      // else vice-versa i.e. to left half
    else
        return findMaximum(arr, low, mid - 1);
}

/* Driver code */
int main()
{
    int arr[] = { 1, 3, 50, 10, 9, 7, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "The maximum element is "
         << findMaximum(arr, 0, n - 1);
    return 0;
}

// This is code is contributed by rajdeep999

C

#include <stdio.h>

int findMaximum(int arr[], int low, int high)
{

   /* Base Case: Only one element is present in arr[low..high]*/
   if (low == high)
     return arr[low];

   /* If there are two elements and first is greater then
      the first element is maximum */
   if ((high == low + 1) && arr[low] >= arr[high])
      return arr[low];

   /* If there are two elements and second is greater then
      the second element is maximum */
   if ((high == low + 1) && arr[low] < arr[high])
      return arr[high];

   int mid = (low + high)/2;   /*low + (high - low)/2;*/

   /* If we reach a point where arr[mid] is greater than both of
     its adjacent elements arr[mid-1] and arr[mid+1], then arr[mid]
     is the maximum element*/
   if ( arr[mid] > arr[mid + 1] && arr[mid] > arr[mid - 1])
      return arr[mid];

   /* If arr[mid] is greater than the next element and smaller than the previous
    element then maximum lies on left side of mid */
   if (arr[mid] > arr[mid + 1] && arr[mid] < arr[mid - 1])
     return findMaximum(arr, low, mid-1);
   else // when arr[mid] is greater than arr[mid-1] and smaller than arr[mid+1]
     return findMaximum(arr, mid + 1, high);
}

/* Driver program to check above functions */
int main()
{
   int arr[] = {1, 3, 50, 10, 9, 7, 6};
   int n = sizeof(arr)/sizeof(arr[0]);
   printf("The maximum element is %d", findMaximum(arr, 0, n-1));
   getchar();
   return 0;
}

Java

// java program to find maximum
// element

class Main
{
    // function to find the
    // maximum element
    static int findMaximum(int arr[], int low, int high)
    {

       /* Base Case: Only one element is
          present in arr[low..high]*/
       if (low == high)
         return arr[low];

       /* If there are two elements and
          first is greater then the first
          element is maximum */
       if ((high == low + 1) && arr[low] >= arr[high])
          return arr[low];

       /* If there are two elements and
          second is greater then the second
          element is maximum */
       if ((high == low + 1) && arr[low] < arr[high])
          return arr[high];

       /*low + (high - low)/2;*/
       int mid = (low + high)/2;

       /* If we reach a point where arr[mid]
          is greater than both of its adjacent
          elements arr[mid-1] and arr[mid+1],
          then arr[mid] is the maximum element*/
       if ( arr[mid] > arr[mid + 1] && arr[mid] > arr[mid - 1])
          return arr[mid];

       /* If arr[mid] is greater than the next
          element and smaller than the previous
          element then maximum lies on left side
          of mid */
       if (arr[mid] > arr[mid + 1] && arr[mid] < arr[mid - 1])
         return findMaximum(arr, low, mid-1);
       else
         return findMaximum(arr, mid + 1, high);
    }

    // main function
    public static void main (String[] args)
    {
        int arr[] = {1, 3, 50, 10, 9, 7, 6};
        int n = arr.length;
        System.out.println("The maximum element is "+
                            findMaximum(arr, 0, n-1));
    }
}

Python3

def findMaximum(arr, low, high):
    # Base Case: Only one element is present in arr[low..high]*/
    if low == high:
        return arr[low]

    # If there are two elements and first is greater then
    # the first element is maximum */
    if high == low + 1 and arr[low] >= arr[high]:
        return arr[low];

    # If there are two elements and second is greater then
    # the second element is maximum */
    if high == low + 1 and arr[low] < arr[high]:
        return arr[high]

    mid = (low + high)//2   #low + (high - low)/2;*/

    # If we reach a point where arr[mid] is greater than both of
    # its adjacent elements arr[mid-1] and arr[mid+1], then arr[mid]
    # is the maximum element*/
    if arr[mid] > arr[mid + 1] and arr[mid] > arr[mid - 1]:
        return arr[mid]

    # If arr[mid] is greater than the next element and smaller than the previous
    # element then maximum lies on left side of mid */
    if arr[mid] > arr[mid + 1] and arr[mid] < arr[mid - 1]:
        return findMaximum(arr, low, mid-1)
    else: # when arr[mid] is greater than arr[mid-1] and smaller than arr[mid+1]
        return findMaximum(arr, mid + 1, high)

# Driver program to check above functions */
arr = [1, 3, 50, 10, 9, 7, 6]
n = len(arr)
print ("The maximum element is %d"% findMaximum(arr, 0, n-1))

# This code is contributed by Shreyanshi Arun.

C#

// C# program to find maximum
// element
using System;

class GFG
{
    // function to find the
    // maximum element
    static int findMaximum(int []arr, int low, int high)
    {

    /* Base Case: Only one element is
        present in arr[low..high]*/
    if (low == high)
        return arr[low];

    /* If there are two elements and
        first is greater then the first
        element is maximum */
    if ((high == low + 1) && arr[low] >= arr[high])
        return arr[low];

    /* If there are two elements and
        second is greater then the second
        element is maximum */
    if ((high == low + 1) && arr[low] < arr[high])
        return arr[high];

    /*low + (high - low)/2;*/
    int mid = (low + high)/2;

    /* If we reach a point where arr[mid]
        is greater than both of its adjacent
        elements arr[mid-1] and arr[mid+1],
        then arr[mid] is the maximum element*/
    if ( arr[mid] > arr[mid + 1] && arr[mid] > arr[mid - 1])
        return arr[mid];

    /* If arr[mid] is greater than the next
        element and smaller than the previous
        element then maximum lies on left side
        of mid */
    if (arr[mid] > arr[mid + 1] && arr[mid] < arr[mid - 1])
        return findMaximum(arr, low, mid-1);
    else
        return findMaximum(arr, mid + 1, high);
    }

    // main function
    public static void Main()
    {
        int []arr = {1, 3, 50, 10, 9, 7, 6};
        int n = arr.Length;
        Console.Write("The maximum element is "+
                            findMaximum(arr, 0, n-1));
    }
}
// This code is contributed by Sam007

PHP

<?php
// PHP program to Find the maximum
// element in an array which is
// first increasing and then decreasing

function findMaximum($arr, $low, $high)
{

    /* Base Case: Only one element
       is present in arr[low..high]*/
    if ($low == $high)
        return $arr[$low];

    /* If there are two elements
       and first is greater then
       the first element is maximum */
    if (($high == $low + 1) &&
        $arr[$low] >= $arr[$high])
        return $arr[$low];

    /* If there are two elements
       and second is greater then
       the second element is maximum */
    if (($high == $low + 1) &&
         $arr[$low] < $arr[$high])
        return $arr[$high];

    /*low + (high - low)/2;*/
    $mid = ($low + $high) / 2;

    /* If we reach a point where
       arr[mid] is greater than
       both of its adjacent elements
       arr[mid-1] and arr[mid+1],
       then arr[mid] is the maximum
       element */
    if ( $arr[$mid] > $arr[$mid + 1] &&
         $arr[$mid] > $arr[$mid - 1])
        return $arr[$mid];

    /* If arr[mid] is greater than
       the next element and smaller
       than the previous element then
       maximum lies on left side of mid */
    if ($arr[$mid] > $arr[$mid + 1] &&
        $arr[$mid] < $arr[$mid - 1])
        return findMaximum($arr, $low, $mid - 1);

    // when arr[mid] is greater than
    // arr[mid-1] and smaller than
    // arr[mid+1]
    else
        return findMaximum($arr,
                           $mid + 1, $high);
}

// Driver Code
$arr = array(1, 3, 50, 10, 9, 7, 6);
$n = sizeof($arr);
echo("The maximum element is ");
echo(findMaximum($arr, 0, $n-1));

// This code is contributed by nitin mittal.
?>

Javascript

<script>

function findMaximum( arr, low, high)
{

    /* Base Case: Only one element is present in arr[low..high]*/
    if (low == high)
        return arr[low];

    /* If there are two elements and first is greater then
        the first element is maximum */
    if ((high == low + 1) && arr[low] >= arr[high])
        return arr[low];

    /* If there are two elements and second is greater then
        the second element is maximum */
    if ((high == low + 1) && arr[low] < arr[high])
        return arr[high];

     mid = (low + high)/2;
     /*low + (high - low)/2;*/

    /* If we reach a point where arr[mid] is greater than both of
        its adjacent elements arr[mid-1] and arr[mid+1], then arr[mid]
        is the maximum element*/
    if ( arr[mid] > arr[mid + 1] && arr[mid] > arr[mid - 1])
        return arr[mid];

    /* If arr[mid] is greater than the next
        element and smaller than the previous
        element then maximum lies on left side of mid */
    if (arr[mid] > arr[mid + 1] && arr[mid] < arr[mid - 1])
        return findMaximum(arr, low, mid-1);

        // when arr[mid] is greater than arr[mid-1]
        // and smaller than arr[mid+1]
        return findMaximum(arr, mid + 1, high);
}

/* Driver code */

     arr = new Array(1, 3, 50, 10, 9, 7, 6);
     n = arr.length;
document.write("The maximum element is" + "\n" + findMaximum(arr, 0, n-1));

// This code is contributed by simranarora5sos
 </script>

Output

The maximum element is 50

Time Complexity : O(logn)

Auxiliary Space : O(logn)
This method works only for distinct numbers. For example, it will not work for an array like {0, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 5, 3, 3, 2, 2, 1, 1}. 
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Method 3 (Binary Search – Iterative Solution) 

The iterative approach of Binary search to find the maximum element in an array which is first increasing and then decreasing.
The standard binary search approach can be modified in the following ways :-

1.  If the mid element is greater than both of its adjacent elements, then mid is the maximum.
2.  If the mid element is smaller than its next element then we should try to search on the right half of the array. So, make, high = mid – 1 .Example array : {2, 4, 6, 8, 10, 3, 1}
3.  If the mid element is greater than the next element, similarly we should try to search on the left half. So, make, low = mid + 1. Example array : {3, 50, 10, 9, 7, 6} 

Implementation:

C++

#include <iostream>
using namespace std;

int maxInBitonic(int arr[], int low, int high)
{
    // find out the size of the array
    // for edge case checking
    int n = high + 1;

    // main code goes as follows
    while (low <= high) {
        // find out the mid
        int mid = low + (high - low) / 2;

          // if mid index value is maximum
        if(arr[mid] > arr[mid+1] and arr[mid] > arr[mid-1])
              return arr[mid];

        // reducing search space by moving to right
        else if (arr[mid] < arr[mid + 1])
            low = mid + 1;

        // reducing search space by moving to left
        else
            high = mid - 1;
    }

    return arr[high];
}

// Driver function
int main()
{
    int arr[] = { 1, 3, 50, 10, 9, 7, 6 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "The maximum element is "
         << maxInBitonic(arr, 0, n - 1);
    return 0;
}

// This code is contributed by rajdeep999

Java

import java.util.*;

class GFG{

static int maxInBitonic(int arr[], int l, int r)
{

    while (l <= r) {

        int m = l + (r - l) / 2; // m = (l + r) / 2

        /****Base Cases Starts*****/

         if(l==r)
        return arr[l];

        /* If there are two elements and first is greater
           then the first element is maximum */
        if ((r == l + 1) && arr[l] >= arr[r])
            return arr[l];

        /* If there are two elements and second is greater
           then the second element is maximum */

        if ((r == l + 1) && arr[l] < arr[r])
            return arr[r];

        /* If we reach a point where arr[mid] is greater
           than both of its adjacent elements arr[mid-1] and
           arr[mid+1], then arr[mid] is the maximum
           element*/
        if (arr[m] > arr[m + 1] && arr[m] > arr[m - 1])
            return arr[m];

        /****Base Case ends *****/

        // move to left with l and r=m-1
        if (arr[m] > arr[m + 1] && arr[m] < arr[m - 1])
            r = m - 1;

        else
            l = m + 1; // move to right with l=m+1 and r
    }
    // if we reach here, then element was
    // not present
    return -1;
}

// Driver function
public static void main(String[] args)
{
    int arr[] = { 1, 3, 50, 10, 9, 7, 6 };
    int n = arr.length;
    System.out.print("The maximum element is "
         + maxInBitonic(arr, 0, n - 1));
}
}

// This code is contributed by todaysgaurav

Python3

# Python 3 program for the above approach

def maxInBitonic(arr, l, r) :

    while (l <= r) :

        m = int(l + (r - l) / 2) # m = (l + r) / 2

        #Base Cases Starts*****/

        if(l==r)
        return arr[l];

        # If there are two elements and first is greater
        # then the first element is maximum */
        if ((r == l + 1) and arr[l] >= arr[r]):
            return arr[l]

        # If there are two elements and second is greater
        # then the second element is maximum */

        if ((r == l + 1) and arr[l] < arr[r]):
            return arr[r]

        # If we reach a point where arr[mid] is greater
        # than both of its adjacent elements arr[mid-1] and
        # arr[mid+1], then arr[mid] is the maximum
        # element*/
        if (arr[m] > arr[m + 1] and arr[m] > arr[m - 1]):
            return arr[m]

        #***Base Case ends *****/

        # move to left with l and r=m-1
        if (arr[m] > arr[m + 1] and arr[m] < arr[m - 1]) :
            r = m - 1

        else :
            l = m + 1 # move to right with l=m+1 and r

    # if we reach here, then element was
    # not present
    return -1

# Driver function
arr = [ 1, 3, 50, 10, 9, 7, 6 ]
n = len(arr)
print("The maximum element is ", maxInBitonic(arr, 0, n - 1))

# This code is contributed by splevel62.

C#

using System;

class GFG{

static int maxInBitonic(int []arr, int l, int r)
{

    while (l <= r) {

        int m = l + (r - l) / 2; // m = (l + r) / 2

        /****Base Cases Starts*****/

          if(l==r)
        return arr[l];

        /* If there are two elements and first is greater
           then the first element is maximum */
        if ((r == l + 1) && arr[l] >= arr[r])
            return arr[l];

        /* If there are two elements and second is greater
           then the second element is maximum */

        if ((r == l + 1) && arr[l] < arr[r])
            return arr[r];

        /* If we reach a point where arr[mid] is greater
           than both of its adjacent elements arr[mid-1] and
           arr[mid+1], then arr[mid] is the maximum
           element*/
        if (arr[m] > arr[m + 1] && arr[m] > arr[m - 1])
            return arr[m];

        /****Base Case ends *****/

        // move to left with l and r=m-1
        if (arr[m] > arr[m + 1] && arr[m] < arr[m - 1])
            r = m - 1;

        else
            l = m + 1; // move to right with l=m+1 and r
    }
    // if we reach here, then element was
    // not present
    return -1;
}

// Driver function
public static void Main(String[] args)
{
    int []arr = { 1, 3, 50, 10, 9, 7, 6 };
    int n = arr.Length;
    Console.Write("The maximum element is "
         + maxInBitonic(arr, 0, n - 1));
}
}

// This code is contributed by shivanisinghss2110

Javascript

<script>
// JavaScript program

function maxInBitonic(arr, l, r)
{

    while (l <= r) {

        var m = l + (r - l) / 2; // m = (l + r) / 2

        /****Base Cases Starts*****/

        if(l==r)
        return arr[l];

        /* If there are two elements and first is greater
           then the first element is maximum */
        if ((r == l + 1) && arr[l] >= arr[r])
            return arr[l];

        /* If there are two elements and second is greater
           then the second element is maximum */

        if ((r == l + 1) && arr[l] < arr[r])
            return arr[r];

        /* If we reach a point where arr[mid] is greater
           than both of its adjacent elements arr[mid-1] and
           arr[mid+1], then arr[mid] is the maximum
           element*/
        if (arr[m] > arr[m + 1] && arr[m] > arr[m - 1])
            return arr[m];

        /****Base Case ends *****/

        // move to left with l and r=m-1
        if (arr[m] > arr[m + 1] && arr[m] < arr[m - 1])
            r = m - 1;

        else
            l = m + 1; // move to right with l=m+1 and r
    }
    // if we reach here, then element was
    // not present
    return -1;
}

// Driver function
    var arr = [ 1, 3, 50, 10, 9, 7, 6 ];
    var n = arr.length;
   document.write("The maximum element is "
         + maxInBitonic(arr, 0, n - 1));


// This code is contributed by shivanisinghss2110

</script>

Output

The maximum element is 50

Time Complexity: O(log n)

Auxiliary Space: O(1)