Basic algorithms in Computer Science mathamatics (Discrete Mathamatics)

1. Longest Increasing Sub-sequence in an Array
In Longest Increasing Subsequence (LIS) problem, find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order

 Ex: Input : arr[] = {3, 10, 2, 1, 20,4,56,78,90}
 Output : Length of LIS = 6
 The longest increasing subsequence is 3, 10, 20, 56, 78, 90

Usage :Replace Your array with arr array and run it, static int [] arr ={3, 10, 2, 1, 20,4,56,78,90};

2. Pancake Problem

Suppose you are given a stack of n pancakes of different sizes. You want to sort the pancakes so that smaller pancakes are on top of larger pancakes. The only operation you can perform is a flip — insert a spatula under the top k pancakes, for some integer k between 1 and n, and flip them all.