Given an array arr with N elements, the task is to find out the longest sub-array which has the shape of a mountain.
A mountain sub-array consists of elements that are initially in ascending order until a peak element is reached and beyond the peak element all other elements of the sub-array are in decreasing order.
Input: arr = [2, 2, 2]
No sub-array exists that shows the behavior of a mountain sub-array.
Input: arr = [1, 3, 1, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5]
There are two sub-arrays that can be considered as mountain sub-arrays. The first one is from index 0 – 2 (3 elements) and next one is from index 2 – 12 (11 elements). As 11 > 2, our answer is 11.
Go through every possible sub-array and check whether it is a mountain sub-array or not. This might take long time to find the solution and the time complexity for above approach can be estimated as O(N*N) to go through every possible sub-array and O(N) to check whether it is a mountain sub-array or not. Thus, the over all time complexity for the program is O(N3) which is very high.
- If the lenght of the given array is less than 3, print 0 as it is not possible to have a mountain sub-array in such case.
- Set the maximum length to 0 initially.
- Use the two-pointer technique (‘begin’ pointer and ‘end’ pointer) to find out the longest mountain sub-array in the given array.
- When an increasing sub-array is encountered, mark the beginning index of that increasing sub-array in the ‘begin’ pointer.
- If any index value is found in the ‘end’ pointer then reset the values in both the pointers as it marks the beginning of a new mountain sub-array.
- When a decreasing sub-array us encountered, mark the ending index of the mountain sub-array in the ‘end’ pointer.
- Calculate the length of the current mountain sub-array, compare it with the current maximum length of all mountain sub-arrays traversed until now and keep updating the current maximum length.
Below is the implementation of the above described efficient approach:
Time Complexity: O(N)
Auxillary Space Complexity: O(1)
- Find whether a subarray is in form of a mountain or not
- Longest subarray having sum K | Set 2
- Longest subarray such that difference of max and min is at-most K
- Longest subarray having maximum sum
- Longest increasing subarray
- Longest subarray with only one value greater than k
- Longest subarray such that the difference of max and min is at-most one
- Longest subarray with odd product
- Longest subarray with sum divisible by k
- Longest subarray with all elements same
- Longest subarray with sum not divisible by X
- Longest subarray in which all elements are greater than K
- Length of the longest alternating even odd subarray
- Length of the longest alternating subarray
- Length of the longest Subarray with only Even Elements
- Longest common subarray in the given two arrays
- Longest subarray not having more than K distinct elements
- Longest Subarray having strictly positive XOR
- Longest Subarray with Sum greater than Equal to Zero
- Longest Subarray having sum of elements atmost 'k'
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.