# Check if Array forms an increasing-decreasing sequence or vice versa

• Difficulty Level : Medium
• Last Updated : 01 Apr, 2022

Given an array arr[] of N integers, the task is to find if the array can be divided into 2 sub-array such that the first sub-array is strictly increasing and the second sub-array is strictly decreasing or vice versa. If the given array can be divided then print “Yes” else print “No”.

Examples:

Input: arr[] = {3, 1, -2, -2, -1, 3}
Output: Yes
Explanation:
First sub-array {3, 1, -2} which is strictly decreasing and second sub-array is {-2, 1, 3} is strictly increasing.

Input: arr[] = {1, 1, 2, 3, 4, 5}
Output: No
Explanation:
The entire array is increasing.

Naive Approach: The naive idea is to divide the array into two subarrays at every possible index and explicitly check if the first subarray is strictly increasing and the second subarray is strictly decreasing or vice-versa. If we can break any subarray then print “Yes” else print “No”
Time Complexity: O(N2
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, traverse the array and check for the strictly increasing sequence and then check for strictly decreasing subsequence or vice-versa. Below are the steps:

1. If arr[1] > arr[0], then check for strictly increasing then strictly decreasing as:
• Check for every consecutive pair until at any index i arr[i + 1] is less than arr[i].
• Now from index i + 1 check for every consecutive pair check if arr[i + 1] is less than arr[i] till the end of the array or not. If at any index i, arr[i] is less than arr[i + 1] then break the loop.
• If we reach the end in the above step then print “Yes” Else print “No”.
2. If arr[1] < arr[0], then check for strictly decreasing then strictly increasing as:
• Check for every consecutive pair until at any index i arr[i + 1] is greater than arr[i].
• Now from index i + 1 check for every consecutive pair check if arr[i + 1] is greater than arr[i] till the end of the array or not. If at any index i, arr[i] is greater than arr[i + 1] then break the loop.
• If we reach the end in the above step then print “Yes” Else print “No”.

Below is the implementation of above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to check if the given array``// forms an increasing decreasing``// sequence or vice versa``bool` `canMake(``int` `n, ``int` `ar[])``{``    ``// Base Case``    ``if` `(n == 1)``        ``return` `true``;``    ``else` `{` `        ``// First subarray is``        ``// strictly increasing``        ``if` `(ar[0] < ar[1]) {` `            ``int` `i = 1;` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i < n``                   ``&& ar[i - 1] < ar[i]) {``                ``i++;``            ``}` `            ``// Check for strictly``            ``// decreasing condition``            ``// & find the break point``            ``while` `(i + 1 < n``                   ``&& ar[i] > ar[i + 1]) {``                ``i++;``            ``}` `            ``// If i is equal to``            ``// length of array``            ``if` `(i >= n - 1)``                ``return` `true``;``            ``else``                ``return` `false``;``        ``}` `        ``// First subarray is``        ``// strictly Decreasing``        ``else` `if` `(ar[0] > ar[1]) {``            ``int` `i = 1;` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i < n``                   ``&& ar[i - 1] > ar[i]) {``                ``i++;``            ``}` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i + 1 < n``                   ``&& ar[i] < ar[i + 1]) {``                ``i++;``            ``}` `            ``// If i is equal to``            ``// length of array - 1``            ``if` `(i >= n - 1)``                ``return` `true``;``            ``else``                ``return` `false``;``        ``}` `        ``// Condition if ar[0] == ar[1]``        ``else` `{``            ``for` `(``int` `i = 2; i < n; i++) {``                ``if` `(ar[i - 1] <= ar[i])``                    ``return` `false``;``            ``}``            ``return` `true``;``        ``}``    ``}``}` `// Driver Code``int` `main()``{``    ``// Given array arr[]``    ``int` `arr[] = { 1, 2, 3, 4, 5 };``    ``int` `n = ``sizeof` `arr / ``sizeof` `arr[0];` `    ``// Function Call``    ``if` `(canMake(n, arr)) {``        ``cout << ``"Yes"``;``    ``}``    ``else` `{``        ``cout << ``"No"``;``    ``}` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;``class` `GFG{` `// Function to check if the given array``// forms an increasing decreasing``// sequence or vice versa``static` `boolean` `canMake(``int` `n, ``int` `ar[])``{``    ``// Base Case``    ``if` `(n == ``1``)``        ``return` `true``;``    ``else``    ``{` `        ``// First subarray is``        ``// strictly increasing``        ``if` `(ar[``0``] < ar[``1``])``        ``{` `            ``int` `i = ``1``;` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i < n && ar[i - ``1``] < ar[i])``            ``{``                ``i++;``            ``}` `            ``// Check for strictly``            ``// decreasing condition``            ``// & find the break point``            ``while` `(i + ``1` `< n && ar[i] > ar[i + ``1``])``            ``{``                ``i++;``            ``}` `            ``// If i is equal to``            ``// length of array``            ``if` `(i >= n - ``1``)``                ``return` `true``;``            ``else``                ``return` `false``;``        ``}` `        ``// First subarray is``        ``// strictly Decreasing``        ``else` `if` `(ar[``0``] > ar[``1``])``        ``{``            ``int` `i = ``1``;` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i < n && ar[i - ``1``] > ar[i])``            ``{``                ``i++;``            ``}` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i + ``1` `< n && ar[i] < ar[i + ``1``])``            ``{``                ``i++;``            ``}` `            ``// If i is equal to``            ``// length of array - 1``            ``if` `(i >= n - ``1``)``                ``return` `true``;``            ``else``                ``return` `false``;``        ``}` `        ``// Condition if ar[0] == ar[1]``        ``else``        ``{``            ``for` `(``int` `i = ``2``; i < n; i++)``            ``{``                ``if` `(ar[i - ``1``] <= ar[i])``                    ``return` `false``;``            ``}``            ``return` `true``;``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Given array arr[]``    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5` `};``    ``int` `n = arr.length;` `    ``// Function Call``    ``if` `(!canMake(n, arr)) {``        ``System.out.print(``"Yes"``);``    ``}``    ``else``    ``{``        ``System.out.print(``"No"``);``    ``}``}``}` `// This code is contributed by Rohit_ranjan`

## Python3

 `# Python3 program for the above approach` `# Function to check if the given array``# forms an increasing decreasing``# sequence or vice versa``def` `canMake(n, ar):``    ` `    ``# Base Case``    ``if` `(n ``=``=` `1``):``        ``return` `True``;``    ``else``:` `        ``# First subarray is``        ``# strictly increasing``        ``if` `(ar[``0``] < ar[``1``]):` `            ``i ``=` `1``;` `            ``# Check for strictly``            ``# increasing condition``            ``# & find the break point``            ``while` `(i < n ``and` `ar[i ``-` `1``] < ar[i]):``                ``i ``+``=` `1``;` `            ``# Check for strictly``            ``# decreasing condition``            ``# & find the break point``            ``while` `(i ``+` `1` `< n ``and` `ar[i] > ar[i ``+` `1``]):``                ``i ``+``=` `1``;` `            ``# If i is equal to``            ``# length of array``            ``if` `(i >``=` `n ``-` `1``):``                ``return` `True``;``            ``else``:``                ``return` `False``;` `        ``# First subarray is``        ``# strictly Decreasing``        ``elif` `(ar[``0``] > ar[``1``]):``            ``i ``=` `1``;` `            ``# Check for strictly``            ``# increasing condition``            ``# & find the break point``            ``while` `(i < n ``and` `ar[i ``-` `1``] > ar[i]):``                ``i ``+``=` `1``;` `            ``# Check for strictly``            ``# increasing condition``            ``# & find the break point``            ``while` `(i ``+` `1` `< n ``and` `ar[i] < ar[i ``+` `1``]):``                ``i ``+``=` `1``;` `            ``# If i is equal to``            ``# length of array - 1``            ``if` `(i >``=` `n ``-` `1``):``                ``return` `True``;``            ``else``:``                ``return` `False``;` `        ``# Condition if ar[0] == ar[1]``        ``else``:``            ``for` `i ``in` `range``(``2``, n):``                ``if` `(ar[i ``-` `1``] <``=` `ar[i]):``                    ``return` `False``;` `            ``return` `True``;` `# Driver Code` `# Given array arr``arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``];``n ``=` `len``(arr);` `# Function Call``if` `(canMake(n, arr)``=``=``False``):``    ``print``(``"Yes"``);``else``:``    ``print``(``"No"``);` `# This code is contributed by PrinciRaj1992`

## C#

 `// C# program for the above approach``using` `System;``class` `GFG{` `// Function to check if the given array``// forms an increasing decreasing``// sequence or vice versa``static` `bool` `canMake(``int` `n, ``int` `[]ar)``{``    ``// Base Case``    ``if` `(n == 1)``        ``return` `true``;``    ``else``    ``{` `        ``// First subarray is``        ``// strictly increasing``        ``if` `(ar[0] < ar[1])``        ``{` `            ``int` `i = 1;` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i < n && ar[i - 1] < ar[i])``            ``{``                ``i++;``            ``}` `            ``// Check for strictly``            ``// decreasing condition``            ``// & find the break point``            ``while` `(i + 1 < n && ar[i] > ar[i + 1])``            ``{``                ``i++;``            ``}` `            ``// If i is equal to``            ``// length of array``            ``if` `(i >= n - 1)``                ``return` `true``;``            ``else``                ``return` `false``;``        ``}` `        ``// First subarray is``        ``// strictly Decreasing``        ``else` `if` `(ar[0] > ar[1])``        ``{``            ``int` `i = 1;` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i < n && ar[i - 1] > ar[i])``            ``{``                ``i++;``            ``}` `            ``// Check for strictly``            ``// increasing condition``            ``// & find the break point``            ``while` `(i + 1 < n && ar[i] < ar[i + 1])``            ``{``                ``i++;``            ``}` `            ``// If i is equal to``            ``// length of array - 1``            ``if` `(i >= n - 1)``                ``return` `true``;``            ``else``                ``return` `false``;``        ``}` `        ``// Condition if ar[0] == ar[1]``        ``else``        ``{``            ``for` `(``int` `i = 2; i < n; i++)``            ``{``                ``if` `(ar[i - 1] <= ar[i])``                    ``return` `false``;``            ``}``            ``return` `true``;``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``// Given array []arr``    ``int` `[]arr = { 1, 2, 3, 4, 5 };``    ``int` `n = arr.Length;` `    ``// Function Call``    ``if` `(!canMake(n, arr))``    ``{``        ``Console.Write(``"Yes"``);``    ``}``    ``else``    ``{``        ``Console.Write(``"No"``);``    ``}``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output:

`No`

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

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