# Maximum length sub-array which satisfies the given conditions

• Difficulty Level : Medium
• Last Updated : 06 Jun, 2021

Given an array arr[] of N integers, the task is to find the maximum length of any sub-array of arr[] which satisfies one of the given conditions:

1. The subarray is strictly increasing.
2. The subarray is strictly decreasing.
3. The subarray is first strictly increasing then strictly decreasing.

Examples:

Input: arr[] = {1, 2, 2, 1, 3}
Output:
{1, 2}, {2, 1} and {1, 3} are the valid subarrays.

Input: arr[] = {5, 4, 3, 2, 1, 2, 3, 4}
Output:
{5, 4, 3, 2, 1} is the required subarray.

Approach: Create an array incEnding[] where incEnding[i] will store the length of the largest increasing subarray of the given array ending at index i. Similarly, create another array decStarting[] where decStarting[i] will store the length of the largest decreasing subarray of the given array starting at the index i. Now start traversing the original array and for every element, assume it to be the mid of the required subarray then the length of the largest required subarray whose mid at index i will be incEnding[i] + decStarting[i] – 1. Note that 1 is subtracted because arr[i] will be counted twice for both the increasing and the decreasing subarray.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the largest``// required sub-array``int` `largestSubArr(``int` `arr[], ``int` `n)``{` `    ``// incEnding[i] will store the length``    ``// of the largest increasing subarray``    ``// ending at arr[i]``    ``int` `incEnding[n] = { 0 };``    ``incEnding = 1;``    ``for` `(``int` `i = 1; i < n; i++) {` `        ``// If current element is greater than``        ``// the previous element then it``        ``// can be a part of the previous``        ``// increasing subarray``        ``if` `(arr[i - 1] < arr[i])``            ``incEnding[i] = incEnding[i - 1] + 1;``        ``else``            ``incEnding[i] = 1;``    ``}` `    ``// decStarting[i] will store the length``    ``// of the largest decreasing subarray``    ``// starting at arr[i]``    ``int` `decStarting[n] = { 0 };``    ``decStarting[n - 1] = 1;``    ``for` `(``int` `i = n - 2; i >= 0; i--) {` `        ``// If current element is greater than``        ``// the next element then it can be a part``        ``// of the decreasing subarray``        ``// with the next element``        ``if` `(arr[i + 1] < arr[i])``            ``decStarting[i] = decStarting[i + 1] + 1;``        ``else``            ``decStarting[i] = 1;``    ``}` `    ``// To store the length of the``    ``// maximum required subarray``    ``int` `maxSubArr = 0;` `    ``// Assume every element to be the mid``    ``// point of the required array``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// 1 has to be subtracted because the``        ``// current element will be counted for``        ``// both the increasing and``        ``// the decreasing subarray``        ``maxSubArr = max(maxSubArr, incEnding[i]``                                       ``+ decStarting[i] - 1);``    ``}` `    ``return` `maxSubArr;``}` `// Driver code``int` `main()``{` `    ``int` `arr[] = { 1, 2, 2, 1, 3 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``cout << largestSubArr(arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the above approach``class` `GFG``{``    ` `    ``// Function to return the largest``    ``// required sub-array``    ``static` `int` `largestSubArr(``int` `arr[], ``int` `n)``    ``{``    ` `        ``// incEnding[i] will store the length``        ``// of the largest increasing subarray``        ``// ending at arr[i]``        ``int` `incEnding[] = ``new` `int``[n];``        ` `        ``int` `i;``        ``for``(i = ``0``; i < n ; i++)``            ``incEnding[i] = ``0``;``            ` `        ``incEnding[``0``] = ``1``;``        ` `        ``for` `(i = ``1``; i < n; i++)``        ``{``    ` `            ``// If current element is greater than``            ``// the previous element then it``            ``// can be a part of the previous``            ``// increasing subarray``            ``if` `(arr[i - ``1``] < arr[i])``                ``incEnding[i] = incEnding[i - ``1``] + ``1``;``            ``else``                ``incEnding[i] = ``1``;``        ``}``    ` `        ``// decStarting[i] will store the length``        ``// of the largest decreasing subarray``        ``// starting at arr[i]``        ``int` `decStarting[] = ``new` `int``[n];``        ` `        ``for``(i = ``0``; i < n ; i++)``            ``decStarting[i] = ``0``;``            ` `        ``decStarting[n - ``1``] = ``1``;``        ` `        ``for` `(i = n - ``2``; i >= ``0``; i--)``        ``{``    ` `            ``// If current element is greater than``            ``// the next element then it can be a part``            ``// of the decreasing subarray``            ``// with the next element``            ``if` `(arr[i + ``1``] < arr[i])``                ``decStarting[i] = decStarting[i + ``1``] + ``1``;``            ``else``                ``decStarting[i] = ``1``;``        ``}``    ` `        ``// To store the length of the``        ``// maximum required subarray``        ``int` `maxSubArr = ``0``;``    ` `        ``// Assume every element to be the mid``        ``// point of the required array``        ``for` `(i = ``0``; i < n; i++)``        ``{``    ` `            ``// 1 has to be subtracted because the``            ``// current element will be counted for``            ``// both the increasing and``            ``// the decreasing subarray``            ``maxSubArr = Math.max(maxSubArr, incEnding[i] +``                                            ``decStarting[i] - ``1``);``        ``}``        ``return` `maxSubArr;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `arr[] = { ``1``, ``2``, ``2``, ``1``, ``3` `};``        ``int` `n = arr.length;``        ` `        ``System.out.println(largestSubArr(arr, n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 implementation of the approach` `# Function to return the largest``# required sub-array``def` `largestSubArr(arr, n) :` `    ``# incEnding[i] will store the length``    ``# of the largest increasing subarray``    ``# ending at arr[i]``    ``incEnding ``=` `[``0``] ``*` `n``    ``incEnding[``0``] ``=` `1``    ``for` `i ``in` `range``(``1``, n) :` `        ``# If current element is greater than``        ``# the previous element then it``        ``# can be a part of the previous``        ``# increasing subarray``        ``if` `(arr[i ``-` `1``] < arr[i]) :``            ``incEnding[i] ``=` `incEnding[i ``-` `1``] ``+` `1``        ``else` `:``            ``incEnding[i] ``=` `1` `    ``# decStarting[i] will store the length``    ``# of the largest decreasing subarray``    ``# starting at arr[i]``    ``decStarting ``=` `[``0``] ``*` `n``    ``decStarting[n ``-` `1``] ``=` `1``    ``for` `i ``in` `range``(n ``-` `2``, ``-``1``, ``-``1``):` `        ``# If current element is greater than``        ``# the next element then it can be a part``        ``# of the decreasing subarray``        ``# with the next element``        ``if` `(arr[i ``+` `1``] < arr[i]) :``            ``decStarting[i] ``=` `decStarting[i ``+` `1``] ``+` `1``        ``else` `:``            ``decStarting[i] ``=` `1` `    ``# To store the length of the``    ``# maximum required subarray``    ``maxSubArr ``=` `0` `    ``# Assume every element to be the mid``    ``# point of the required array``    ``for` `i ``in` `range``(n):` `        ``# 1 has to be subtracted because the``        ``# current element will be counted for``        ``# both the increasing and``        ``# the decreasing subarray``        ``maxSubArr ``=` `max``(maxSubArr, incEnding[i] ``+``                                 ``decStarting[i] ``-` `1``)` `    ``return` `maxSubArr``    ` `# Driver code``arr ``=` `[ ``1``, ``2``, ``2``, ``1``, ``3` `]``n ``=` `len``(arr)` `print``(largestSubArr(arr, n))` `# This code is contributed by``# divyamohan123`

## C#

 `// C# implementation of the above approach``using` `System;        ` `class` `GFG``{``    ` `    ``// Function to return the largest``    ``// required sub-array``    ``static` `int` `largestSubArr(``int` `[]arr, ``int` `n)``    ``{``    ` `        ``// incEnding[i] will store the length``        ``// of the largest increasing subarray``        ``// ending at arr[i]``        ``int` `[]incEnding = ``new` `int``[n];``        ` `        ``int` `i;``        ``for``(i = 0; i < n ; i++)``            ``incEnding[i] = 0;``            ` `        ``incEnding = 1;``        ` `        ``for` `(i = 1; i < n; i++)``        ``{``    ` `            ``// If current element is greater than``            ``// the previous element then it``            ``// can be a part of the previous``            ``// increasing subarray``            ``if` `(arr[i - 1] < arr[i])``                ``incEnding[i] = incEnding[i - 1] + 1;``            ``else``                ``incEnding[i] = 1;``        ``}``    ` `        ``// decStarting[i] will store the length``        ``// of the largest decreasing subarray``        ``// starting at arr[i]``        ``int` `[]decStarting = ``new` `int``[n];``        ` `        ``for``(i = 0; i < n ; i++)``            ``decStarting[i] = 0;``            ` `        ``decStarting[n - 1] = 1;``        ` `        ``for` `(i = n - 2; i >= 0; i--)``        ``{``    ` `            ``// If current element is greater than``            ``// the next element then it can be a part``            ``// of the decreasing subarray``            ``// with the next element``            ``if` `(arr[i + 1] < arr[i])``                ``decStarting[i] = decStarting[i + 1] + 1;``            ``else``                ``decStarting[i] = 1;``        ``}``    ` `        ``// To store the length of the``        ``// maximum required subarray``        ``int` `maxSubArr = 0;``    ` `        ``// Assume every element to be the mid``        ``// point of the required array``        ``for` `(i = 0; i < n; i++)``        ``{``    ` `            ``// 1 has to be subtracted because the``            ``// current element will be counted for``            ``// both the increasing and``            ``// the decreasing subarray``            ``maxSubArr = Math.Max(maxSubArr, incEnding[i] +``                                            ``decStarting[i] - 1);``        ``}``        ``return` `maxSubArr;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main (String[] args)``    ``{``        ``int` `[]arr = { 1, 2, 2, 1, 3 };``        ``int` `n = arr.Length;``        ` `        ``Console.WriteLine(largestSubArr(arr, n));``    ``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output:

`2`

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