Find whether a subarray is in form of a mountain or not

Difficulty Level : Hard
Last Updated : 22 Mar, 2020

We are given an array of integers and a range, we need to find whether the subarray which falls in this range has values in the form of a mountain or not. All values of the subarray are said to be in the form of a mountain if either all values are increasing or decreasing or first increasing and then decreasing.
More formally a subarray [a1, a2, a3 … aN] is said to be in form of a mountain if there exist an integer K, 1 <= K <= N such that,
a1 <= a2 <= a3 .. <= aK >= a(K+1) >= a(K+2) …. >= aN
Examples:

Input : Arr[]  = [2 3 2 4 4 6 3 2], Range = [0, 2]
Output :  Yes

Explanation: The output is yes , subarray is [2 3 2], 
so subarray first increases and then decreases

Input:  Arr[] = [2 3 2 4 4 6 3 2], Range = [2, 7]
Output: Yes

Explanation: The output is yes , subarray is [2 4 4 6 3 2], 
so subarray first increases and then decreases


Input: Arr[]= [2 3 2 4 4 6 3 2], Range = [1, 3]
Output: no

Explanation: The output is no, subarray is [3 2 4], 
so subarray is not in the form above stated

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Solution:

Approach:The problem has multiple queries so for each query the solution should be calculated with least possible time complexity. So create two extra spaces of the length of the original array. For every element find the last index on the left side which is increasing i.e. greater than its previous element and find the element on the right side will store the first index on the right side which is decreasing i.e. greater than its next element. If these value can be calculated for every index in constant time then for every given range the answer can be given in constant time.
Algorithm:
1. Create two extra spaces of length n,left and right and a extra variable lastptr
2. Initilize left[0] = 0 and lastptr = 0
3. Traverse the original array from second index to the end
4. For every index check if it is greater than the pervious element, if yes then update the lastptr with the current index.
5. For every index store the lastptr in left[i]
6. initilize right[N-1] = N-1 and lastptr = N-1
7. Traverse the original array from second last index to the start
8. For every index check if it is greater than the next element, if yes then update the lastptr with the current index.
9. For every index store the lastptr in right[i]
10. Now process the queries
11. for every query l, r, if right[l] >= left[r] then print yes else no

Implementation:

C/C++

// C++ program to check whether a subarray is in 
// mountain form or not 
#include <bits/stdc++.h> 
using namespace std; 
  
// Utility method to construct left and right array 
int preprocess(int arr[], int N, int left[], int right[]) 
{ 
    // Initialize first left index as that index only 
    left[0] = 0; 
    int lastIncr = 0; 
  
    for (int i = 1; i < N; i++) 
    { 
        // if current value is greater than previous, 
        // update last increasing 
        if (arr[i] > arr[i - 1]) 
            lastIncr = i; 
        left[i] = lastIncr; 
    } 
  
    // Initialize last right index as that index only 
    right[N - 1] = N - 1; 
    int firstDecr = N - 1; 
  
    for (int i = N - 2; i >= 0; i--) 
    { 
        // if current value is greater than next, 
        // update first decreasing 
        if (arr[i] > arr[i + 1]) 
            firstDecr = i; 
        right[i] = firstDecr; 
    } 
} 
  
// Method returns true if arr[L..R] is in mountain form 
bool isSubarrayMountainForm(int arr[], int left[], 
                             int right[], int L, int R) 
{ 
    // return true only if right at starting range is 
    // greater than left at ending range 
    return (right[L] >= left[R]); 
} 
  
//    Driver code to test above methods 
int main() 
{ 
    int arr[] = {2, 3, 2, 4, 4, 6, 3, 2}; 
    int N = sizeof(arr) / sizeof(int); 
  
    int left[N], right[N]; 
    preprocess(arr, N, left, right); 
  
    int L = 0; 
    int R = 2; 
    if (isSubarrayMountainForm(arr, left, right, L, R)) 
        cout << "Subarray is in mountain form\n"; 
    else
        cout << "Subarray is not in mountain form\n"; 
  
    L = 1; 
    R = 3; 
    if (isSubarrayMountainForm(arr, left, right, L, R)) 
        cout << "Subarray is in mountain form\n"; 
    else
        cout << "Subarray is not in mountain form\n"; 
  
    return 0; 
} 

Java

// Java program to check whether a subarray is in 
// mountain form or not 
class SubArray 
{ 
    // Utility method to construct left and right array 
    static void preprocess(int arr[], int N, int left[], int right[]) 
    { 
        // initialize first left index as that index only 
        left[0] = 0; 
        int lastIncr = 0; 
      
        for (int i = 1; i < N; i++) 
        { 
            // if current value is greater than previous, 
            // update last increasing 
            if (arr[i] > arr[i - 1]) 
                    lastIncr = i; 
            left[i] = lastIncr; 
        } 
      
        // initialize last right index as that index only 
        right[N - 1] = N - 1; 
        int firstDecr = N - 1; 
      
        for (int i = N - 2; i >= 0; i--) 
        { 
            // if current value is greater than next, 
            // update first decreasing 
            if (arr[i] > arr[i + 1]) 
                    firstDecr = i; 
            right[i] = firstDecr; 
        } 
    } 
      
    // method returns true if arr[L..R] is in mountain form 
    static boolean isSubarrayMountainForm(int arr[], int left[], 
                                    int right[], int L, int R) 
    { 
        // return true only if right at starting range is 
        // greater than left at ending range 
        return (right[L] >= left[R]); 
    } 
      
    public static void main(String[] args) 
    { 
        int arr[] = {2, 3, 2, 4, 4, 6, 3, 2}; 
        int N = arr.length; 
        int left[] = new int[N]; 
        int right[] = new int[N]; 
        preprocess(arr, N, left, right); 
        int L = 0; 
        int R = 2; 
          
        if (isSubarrayMountainForm(arr, left, right, L, R)) 
            System.out.println("Subarray is in mountain form"); 
        else
            System.out.println("Subarray is not in mountain form"); 
      
        L = 1; 
        R = 3; 
      
        if (isSubarrayMountainForm(arr, left, right, L, R)) 
            System.out.println("Subarray is in mountain form"); 
        else
            System.out.println("Subarray is not in mountain form"); 
    } 
} 
// This Code is Contributed by Saket Kumar 

Python3

# Python 3 program to check whether a subarray is in 
# mountain form or not 
  
# Utility method to construct left and right array 
def preprocess(arr, N, left, right): 
    # initialize first left index as that index only 
    left[0] = 0
    lastIncr = 0
  
    for i in range(1,N): 
        # if current value is greater than previous, 
        # update last increasing 
        if (arr[i] > arr[i - 1]): 
            lastIncr = i 
        left[i] = lastIncr 
  
    # initialize last right index as that index only 
    right[N - 1] = N - 1
    firstDecr = N - 1
  
    i = N - 2
    while(i >= 0): 
        # if current value is greater than next, 
        # update first decreasing 
        if (arr[i] > arr[i + 1]): 
            firstDecr = i 
        right[i] = firstDecr 
        i -= 1
  
# method returns true if arr[L..R] is in mountain form 
def isSubarrayMountainForm(arr, left, right, L, R): 
      
    # return true only if right at starting range is 
    # greater than left at ending range 
    return (right[L] >= left[R]) 
  
# Driver code  
if __name__ == '__main__': 
    arr = [2, 3, 2, 4, 4, 6, 3, 2] 
    N = len(arr) 
  
    left = [0 for i in range(N)] 
    right = [0 for i in range(N)] 
    preprocess(arr, N, left, right) 
  
    L = 0
    R = 2
    if (isSubarrayMountainForm(arr, left, right, L, R)): 
        print("Subarray is in mountain form") 
    else: 
        print("Subarray is not in mountain form") 
  
    L = 1
    R = 3
    if (isSubarrayMountainForm(arr, left, right, L, R)): 
        print("Subarray is in mountain form") 
    else: 
        print("Subarray is not in mountain form") 
  
# This code is contributed by 
# Surendra_Gangwar 

C#

// C# program to check whether  
// a subarray is in mountain  
// form or not 
using System; 
  
class GFG 
{ 
      
    // Utility method to construct  
    // left and right array 
    static void preprocess(int []arr, int N,  
                           int []left, int []right) 
    { 
        // initialize first left  
        // index as that index only 
        left[0] = 0; 
        int lastIncr = 0; 
      
        for (int i = 1; i < N; i++) 
        { 
            // if current value is  
            // greater than previous, 
            // update last increasing 
            if (arr[i] > arr[i - 1]) 
                    lastIncr = i; 
            left[i] = lastIncr; 
        } 
      
        // initialize last right  
        // index as that index only 
        right[N - 1] = N - 1; 
        int firstDecr = N - 1; 
      
        for (int i = N - 2; i >= 0; i--) 
        { 
            // if current value is  
            // greater than next, 
            // update first decreasing 
            if (arr[i] > arr[i + 1]) 
                    firstDecr = i; 
            right[i] = firstDecr; 
        } 
    } 
      
    // method returns true if 
    // arr[L..R] is in mountain form 
    static bool isSubarrayMountainForm(int []arr, int []left, 
                                       int []right, int L, int R) 
    { 
        // return true only if right at  
        // starting range is greater  
        // than left at ending range 
        return (right[L] >= left[R]); 
    } 
      
      
    // Driver Code 
    static public void Main () 
    { 
        int []arr = {2, 3, 2, 4, 
                     4, 6, 3, 2}; 
        int N = arr.Length; 
        int []left = new int[N]; 
        int []right = new int[N]; 
        preprocess(arr, N, left, right); 
          
        int L = 0; 
        int R = 2; 
          
        if (isSubarrayMountainForm(arr, left,  
                                   right, L, R)) 
            Console.WriteLine("Subarray is in " +  
                                "mountain form"); 
        else
            Console.WriteLine("Subarray is not " +  
                              "in mountain form"); 
      
        L = 1; 
        R = 3; 
      
        if (isSubarrayMountainForm(arr, left,  
                                   right, L, R)) 
            Console.WriteLine("Subarray is in " +  
                                "mountain form"); 
        else
            Console.WriteLine("Subarray is not " +  
                              "in mountain form"); 
    } 
} 
  
// This code is contributed by aj_36 

Output:

Subarray is in mountain form
Subarray is not in mountain form

Complexity Analysis:
- Time Complexiity:O(n).
  Only two traversals are needed so the time complexity is O(n).
- Space Complexity:O(n).
  Two extra space of length n is required so the space complexity is O(n).

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Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C/C++

Java

Python3

C#