subsequence

I'm a bit confused between subarray, subsequence & subset if I have {1,2,3,4} then subsequence can be {1,2,4} OR {2,4} etc. So basically I can omit some elements but keep the order. subarray would be( say subarray of size 3) {1,2,3} {2,3,4} Then what would be the subset? I'm bit confused between these 3. Wilson In my opinion, if the given pattern is array, the so called subarray means contiguous subsequence . For example, if given {1, 2, 3, 4}, subarray can be {1, 2, 3} {2, 3, 4} etc. While the given pattern is a sequence, subsequence contain elements whose subscripts are increasing in the

I'm practicing algorithms and one of my tasks is to count the number of all longest increasing sub-sequences for given 0 < n <= 10^6 numbers. Solution O(n^2) is not an option. I have already implemented finding a LIS and its length ( LIS Algorithm ), but this algorithm switches numbers to the lowest possible. Therefore, it's impossible to determine if sub-sequences with a previous number (the bigger one) would be able to achieve the longest length, otherwise I could just count those switches, I guess. Any ideas how to get this in about O(nlogn) ? I know that it should be solved using dynamic