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

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 <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

// 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

# 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#

// 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

Javascript

<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>

Output

No

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;
}

Java

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);
    }
}

Python3

# 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)

C#

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();
    }
}

Javascript

// 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

Output

No

Time Complexity: O(N), where N is the size of an array
Auxiliary Space: O(1), as we are not using any extra space .