We must know, we will know !
万物并作，吾以观复

This blog is going to talk about Piecewise linear convex objective functions. Why we study that? Becasue this kind of problems can be cast as “Linear Programming Problems”.

This lecture continues to talk about Dynamic Programming, we are going to introduce RNA secondary stucture problem and squence alignment problem.

We are going to talk about Piecewise linear convex objective functions. But before it, we will give some concepts, convex, concave and affine function.

This blog is going to talk about the general form and standard form, and the transformation between different forms.

This lecture continues to talk about Dynamic Programming, we are going to introduce Knapsack Problem and Fibonacci number problem.

This blog I will share my notes in Penn State MATH 484: Linear Programming.

This blog I will share my notes in Penn State CSE 565: Algorithm Design and Analysis.

In this lecture, we still talk about sorting and we want to ask “How fast can we sort?”. Let’s review the running time of previous learned Algorithms, the Heapsort and Merge Sort can achieve ${ O(n \lg n) }$ in the worst case. Randomized Quicksort can run in ${ O(n \lg n) }$ time on average. And Insetion Sort is ${ O(n^2) }$. All these Algortihms run no faster than ${ O(n \lg n) }$.

So can we do better?