# Maximum Length Bitonic Subarray | Set 2 (O(n) time and O(1) Space)

• Difficulty Level : Hard
• Last Updated : 12 Jul, 2022

Given an array A[0 … n-1] containing n positive integers, a subarray A[i … j] is bitonic if there is a k with i <= k <= j such that A[i] = .. A[j – 1] > = A[j]. Write a function that takes an array as argument and returns the length of the maximum length bitonic subarray.

We have discussed O(n) time and O(n) space approach in below post.
Maximum Length Bitonic Subarray | Set 1 (O(n) time and O(n) space)

In this set, we will discuss solution taking constant extra space.

The idea is to check longest bitonic subarray starting at A[i]. From A[i], first we will check for end of ascent and then end of descent.Overlapping of bitonic subarrays is taken into account by recording a nextStart position when it finds two equal values when going down the slope of the current subarray. If length of this subarray is greater than max_len, we will update max_len. We continue this process till end of array is reached.

Implementation:

## C++

 `// C++ program to find length of longest bitonic``// subarray. O(n) time and O(1) extra space``#include ``using` `namespace` `std;` `// Function to find length of longest bitonic``// subarray``int` `bitonic(``int` `*A, ``int` `n)``{``    ``// if A is empty``    ``if` `(n == 0)``        ``return` `0;``        ` `    ``// initializing max_len``    ``int` `maxLen=1;``        ` `    ``int` `start=0;``    ``int` `nextStart=0;``        ` `    ``int` `j =0;``    ``while` `(j < n-1)``    ``{``        ``// look for end of ascent      ``        ``while` `(j=A[j+1]){``                ` `            ``// adjusting nextStart;``            ``// this will be necessarily executed at least once,``            ``// when we detect the start of the descent``            ``if` `(jA[j+1])``                ``nextStart=j+1;``                ` `            ``j++;``        ``}``            ` `        ``// updating maxLen, if required``        ``maxLen = max(maxLen,j-(start-1));``            ` `        ``start=nextStart;``    ``}``        ` `    ``return` `maxLen;``}` `int` `main()``{``    ``int` `A[] = {12, 4, 78, 90, 45, 23};``    ``int` `n = ``sizeof``(A)/``sizeof``(A);``    ``printf``(``"Length of max length Bitonic "``            ``"Subarray is %d"``, bitonic(A, n));``    ``return` `0;``}`

## Java

 `// Java program to find length of longest bitonic``// subarray O(n) time and O(1) extra space` `public` `class` `MaxLengthBitonic``{``    ``// Method to find length of longest bitonic``    ``// subarray``    ``static` `int` `maxLenBitonic(``int``[] A,``int` `n)``    ``{``        ``// if A is empty``        ``if` `(n == ``0``)``            ``return` `0``;``        ` `        ``// initializing max_len``        ``int` `maxLen=``1``;``        ` `        ``int` `start=``0``;``        ``int` `nextStart=``0``;``        ` `        ``int` `j =``0``;``        ``while` `(j < n-``1``)``        ``{``            ``// look for end of ascent      ``            ``while` `(j=A[j+``1``]){``                ` `                ``// adjusting nextStart;``                ``// this will be necessarily executed at least once,``                ``// when we detect the start of the descent``                ``if` `(jA[j+``1``])``                    ``nextStart=j+``1``;``                ` `                ``j++;``            ``}``            ` `            ``// updating maxLen, if required``            ``maxLen = Math.max(maxLen,j-(start-``1``));``            ` `            ``start=nextStart;``        ``}``        ` `        ``return` `maxLen;``    ``}``    ` `    ``public` `static` `void`  `main(String[] args)``    ``{``        ``int` `A[] = {``12``, ``4``, ``78``, ``90``, ``45``, ``23``};``        ``System.out.println(``"Length of maximal length bitonic "` `+``                            ``"subarray is "` `+ maxLenBitonic(A,A.length));` `    ``}``}``// This code is contributed by Markus Schott`

## Python3

 `# Python3 program to find length of longest bitonic``# subarray. O(n) time and O(1) extra space` `# Function to find length of longest``# bitonic subarray``def` `bitonic(A, n):` `    ``# if A is empty``    ``if` `(n ``=``=` `0``):``        ``return` `0``;``        ` `    ``# initializing max_len``    ``maxLen ``=` `1``;``        ` `    ``start ``=` `0``;``    ``nextStart ``=` `0``;``        ` `    ``j ``=` `0``;``    ``while` `(j < n ``-` `1``):``    ` `        ``# look for end of ascent    ``        ``while` `(j < n ``-` `1` `and` `A[j] <``=` `A[j ``+` `1``]):``            ``j ``=` `j ``+` `1``;``            ` `        ``# look for end of descent``        ``while` `(j < n ``-` `1` `and` `A[j] >``=` `A[j ``+` `1``]):``                ` `            ``# adjusting nextStart;``            ``# this will be necessarily executed``            ``# at least once, when we detect the``            ``# start of the descent``            ``if` `(j < n ``-` `1` `and` `A[j] > A[j ``+` `1``]):``                ``nextStart ``=` `j ``+` `1``;``                ` `            ``j ``=` `j ``+` `1``;``        ` `        ``# updating maxLen, if required``        ``maxLen ``=` `max``(maxLen, j ``-` `(start ``-` `1``));``            ` `        ``start ``=` `nextStart;``    ` `    ``return` `maxLen;` `# Driver Code``A ``=` `[``12``, ``4``, ``78``, ``90``, ``45``, ``23``];``n ``=` `len``(A);``print``(``"Length of max length Bitonic Subarray is"``,``                                  ``bitonic(A, n));` `# This code is contributed by Shivi_Aggarwal`

## C#

 `// C# program to find length of longest bitonic``// subarray O(n) time and O(1) extra space``using` `System;` `class` `MaxLengthBitonic``{``    ``// Method to find length of``    ``// longest bitonic subarray``    ``static` `int` `maxLenBitonic(``int``[] A, ``int` `n)``    ``{``        ``// if A is empty``        ``if` `(n == 0)``            ``return` `0;``        ` `        ``// initializing max_len``        ``int` `maxLen = 1;``        ` `        ``int` `start = 0;``        ``int` `nextStart = 0;``        ` `        ``int` `j = 0;``        ``while` `(j < n-1)``        ``{``            ``// look for end of ascent    ``            ``while` `(j < n-1 && A[j] <= A[j+1])``                ``j++;``            ` `            ``// look for end of descent    ``            ``while` `(j < n-1 && A[j] >= A[j+1]){``                ` `                ``// adjusting nextStart;``                ``// this will be necessarily executed at least once,``                ``// when we detect the start of the descent``                ``if` `(j < n-1 && A[j] > A[j+1])``                    ``nextStart=j + 1;``                ` `                ``j++;``            ``}``            ` `            ``// updating maxLen, if required``            ``maxLen = Math.Max(maxLen, j - (start - 1));``            ` `            ``start=nextStart;``        ``}``        ``return` `maxLen;``    ``}``    ` `    ``public` `static` `void` `Main()``    ``{``        ``int` `[]A = {12, 4, 78, 90, 45, 23};``        ``Console.Write(``"Length of maximal length bitonic "` `+``                      ``"subarray is "` `+ maxLenBitonic(A, A.Length));``    ``}``}` `// This code is contributed by nitin mittal.`

## PHP

 `= ``\$A``[``\$j` `+ 1])``        ``{``                ` `            ``// adjusting nextStart;``            ``// this will be necessarily``            ``// executed at least once,``            ``// when we detect the start``            ``// of the descent``            ``if` `(``\$j` `< ``\$n` `- 1 && ``\$A``[``\$j``] >``                          ``\$A``[``\$j` `+ 1])``                ``\$nextStart` `= ``\$j` `+ 1;``            ``\$j``++;``        ``}``            ` `        ``// updating maxLen,``        ``// if required``        ``\$maxLen` `= max(``\$maxLen``, ``\$j` `- (``\$start` `- 1));``        ``\$start` `= ``\$nextStart``;``    ``}``        ` `    ``return` `\$maxLen``;``}` `    ``// Driver Code``    ``\$A` `= ``array``(12, 4, 78, 90, 45, 23);``    ``\$n` `= sizeof(``\$A``);``    ``echo` `"Length of max length Bitonic "``        ``,``"Subarray is "``, bitonic(``\$A``, ``\$n``);` `// This code is contributed by nitin mittal.``?>`

## Javascript

 ``

Output

`Length of max length Bitonic Subarray is 5`

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