Check if Array forms an increasing-decreasing sequence or vice versa
Last Updated :
12 Jul, 2025
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:
- 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".
- 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 <bits/stdc++.h>
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 false;
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 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 false;
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 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 False;
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# 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 false;
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
<script>
// Javascript program for the above approach
// Function to check if the given array
// forms an increasing decreasing
// sequence or vice versa
function canMake(n, ar)
{
// Base Case
if (n == 1)
return false;
else
{
// First subarray is
// strictly increasing
if (ar[0] < ar[1])
{
let 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])
{
let 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(let i = 2; i < n; i++)
{
if (ar[i - 1] <= ar[i])
return false;
}
return true;
}
}
}
// Driver Code
// Given array arr[]
let arr = [ 1, 2, 3, 4, 5 ];
let n = arr.length;
// Function Call
if (!canMake(n, arr))
{
document.write("Yes");
}
else
{
document.write("No");
}
// This code is contributed by sravan kumar
</script>
Time Complexity: O(N)
Auxiliary Space: O(1)
Method3: Simple and efficient approach
Approach: we create a function divide array and iterates in the array and uses two flags increasing and decreasing to track if an increasing and decreasing sub-array has been found. If both flags are true at any point in the iteration, then we print yes and If both flags are not true after iterating through the entire array, then we print false.
Below is the implementation of above approach:
C++
#include <bits/stdc++.h>
using namespace std;
// Function to check if array can be divided into increasing and decreasing sub-arrays
string Divide_Array(int arr[], int N) {
bool increasing = false; // Flag to track increasing sub-array
bool decreasing = false; // Flag to track decreasing sub-array
// traverse through the array
for (int i = 1; i < N; i++) {
if (arr[i] > arr[i - 1]) {
increasing = true;
} else if (arr[i] < arr[i - 1]) {
decreasing = true;
}
// If both increasing and decreasing flags are true, array can be divided
if (increasing && decreasing) {
return "Yes";
}
}
// If both increasing and decreasing flags are not true, array cannot be divided
return "No";
}
int main() {
// Given array arr[]
int arr[] = { 1, 2, 3, 4, 5 };
int N= sizeof arr / sizeof arr[0];
// Function Call
string result = Divide_Array(arr, N);
cout << result << endl;
return 0;
}
import java.util.*;
public class Main {
// Function to check if array can be divided into increasing and decreasing sub-arrays
static String divideArray(int[] arr, int N) {
boolean increasing = false; // Flag to track increasing sub-array
boolean decreasing = false; // Flag to track decreasing sub-array
// Traverse through the array
for (int i = 1; i < N; i++) {
if (arr[i] > arr[i - 1]) {
increasing = true;
} else if (arr[i] < arr[i - 1]) {
decreasing = true;
}
// If both increasing and decreasing flags are true, array can be divided
if (increasing && decreasing) {
return "Yes";
}
}
// If both increasing and decreasing flags are not true, array cannot be divided
return "No";
}
// Driver Code
public static void main(String[] args) {
// Given array arr[]
int[] arr = { 1, 2, 3, 4, 5 };
int N = arr.length;
String result = divideArray(arr, N);
System.out.println(result);
}
}
# Function to check if array can be divided into increasing and decreasing sub-arrays
def divide_array(arr):
increasing = False # Flag to track increasing sub-array
decreasing = False # Flag to track decreasing sub-array
# Traverse through the array
for i in range(1, len(arr)):
if arr[i] > arr[i - 1]:
increasing = True
elif arr[i] < arr[i - 1]:
decreasing = True
# If both increasing and decreasing flags are true, array can be divided
if increasing and decreasing:
return "Yes"
# If both increasing and decreasing flags are not true, array cannot be divided
return "No"
# Driver code
if __name__ == "__main__":
# Given array arr[]
arr = [1, 2, 3, 4, 5]
# Function Call
result = divide_array(arr)
print(result)
using System;
class Program {
// Function to check if the array can be divided into
// increasing and decreasing sub-arrays
static string DivideArray(int[] arr, int N)
{
bool increasing
= false; // Flag to track increasing sub-array
bool decreasing
= false; // Flag to track decreasing sub-array
// Traverse through the array
for (int i = 1; i < N; i++) {
if (arr[i] > arr[i - 1]) {
increasing = true;
}
else if (arr[i] < arr[i - 1]) {
decreasing = true;
}
// If both increasing and decreasing flags are
// true, the array can be divided
if (increasing && decreasing) {
return "Yes";
}
}
// If both increasing and decreasing flags are not
// true, the array cannot be divided
return "No";
}
static void Main()
{
// Given array arr[]
int[] arr = { 1, 2, 3, 4, 5 };
int N = arr.Length;
// Function Call
string result = DivideArray(arr, N);
Console.WriteLine(result);
Console.ReadKey();
}
}
// Function to check if an array can be divided into increasing and decreasing sub-arrays
function divideArray(arr) {
let increasing = false; // Flag to track increasing sub-array
let decreasing = false; // Flag to track decreasing sub-array
// Traverse through the array
for (let i = 1; i < arr.length; i++) {
if (arr[i] > arr[i - 1]) {
increasing = true;
} else if (arr[i] < arr[i - 1]) {
decreasing = true;
}
// If both increasing and decreasing flags are true, the array can be divided
if (increasing && decreasing) {
return "Yes";
}
}
// If both increasing and decreasing flags are not true, the array cannot be divided
return "No";
}
// Main function
function main() {
// Given array arr[]
const arr = [1, 2, 3, 4, 5];
// Function Call
const result = divideArray(arr);
console.log(result);
}
// Call the main function to execute the code
main();
// This code is contributed by shivamgupta310570
Time Complexity: O(N), where N is the size of an array
Auxiliary Space: O(1), as we are not using any extra space .
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem