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:
- 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 versabool canMake(int n, int ar[]){ // Base Case if (n == 1) return true; else { // First subarray is // stricly 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 Codeint 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 approachimport java.util.*;class GFG{ // Function to check if the given array// forms an increasing decreasing// sequence or vice versastatic boolean canMake(int n, int ar[]){ // Base Case if (n == 1) return true; else { // First subarray is // stricly 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 Codepublic 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 versadef canMake(n, ar): # Base Case if (n == 1): return True; else: # First subarray is # stricly 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 arrarr = [1, 2, 3, 4, 5];n = len(arr); # Function Callif (canMake(n, arr)==False): print("Yes");else: print("No"); # This code is contributed by PrinciRaj1992 |
C#
// C# program for the above approachusing System;class GFG{ // Function to check if the given array// forms an increasing decreasing// sequence or vice versastatic bool canMake(int n, int []ar){ // Base Case if (n == 1) return true; else { // First subarray is // stricly 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 Codepublic 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 |
Output:
No
Time Complexity: O(N)
Auxiliary Space: O(1)
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