Given an array of n integers, find the no of subarrays whose minimal and maximum elements are same. Subarray is defined as non-empty sequence of consecutive elements.
Input: 2 3 1 1 Output: 5 Explanation: The subarrays are (2), (3), (1), (1) and (1, 1) Input: 2 4 5 3 3 3 Output: 9 Explanation: The subarrays are (2), (4), (5), (3), (3, 3), (3, 3, 3), (3), (3, 3) and (3)
The first thing to observe is that only those subarrays whose all elements are same will have the same minimum and maximum. Having different elements clearly means different minimum and maximum. Hence we just need to calculate the number of continuous same elements(say d), then by combinations formula we get the no of subarrays to be –
No of subarrays possible with d elements = ( d * (d+1) / 2 )
where d is number of continuous same elements.
We traverse from 1-n and then from I+1 to n and then find the number of continuous same elements and then add to the result the no subarrays possible.
Time complexity : O(n)
Auxiliary Space : O(1)
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