Longest increasing subsequence or LIS problem is a classical dynamic programming problem which refers to finding the length of the longest subsequence from an array such that all the elements of the sequence are in strictly increasing order. Longest Increasing Subsequence [This section was originally written by Anand Sarwate] 33.1 Introduction In this paper we will investigate the connection between random matrices and ﬁnding the longest increasing subsequence of a permutation. We will introduce a model for the problem using a simple card game. a longest increasing subsequence, since they ... subsequence of the original permutation! An interacting particle process Start with zero particles. At each step, pick a random point U in [0,1]; simultaneously, let the nearest particle (if any) to the right of U disappear. Lemma 1 implies: the number of particles af-. Given [10, 9, 2, 5, 3, 7, 101, 18], The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4 After you are done modifying the input array in-place, return the new length of the array Similarly, decreasing order sequence is considered Bitonic with the increasing part as empty This function searches for the longest ascending subsequence of a permutation using a dynamic.