Consider an array of numbers. Provide an algorithm that finds the maximum size sub$-$array that is increasing $($the entries may not be contiguous. It may be any set but you need to keep the order$).$ For example in the array $7,2,6,4,1,7,2,10$ the maximum non contiguous array is $2,4,7,10.$ In all algorithms, always explain them and analyze their time complexity. The complexity should be as small as possible.