The TPK algorithm is a simple program introduced by Donald Knuth and Luis Trabb Pardo to illustrate the evolution of computer programming languages. In their 1977 work "The Early Development of Programming Languages", Trabb Pardo and Knuth introduced a small program that involved arrays, indexing, mathematical functions, subroutines, I/O, conditionals and iteration. They then wrote implementations of the algorithm in several early programming languages to show how such concepts were expressed.

To explain the name "TPK", the authors referred to Grimm's law (which concerns the consonants 't', 'p', and 'k'), the sounds in the word "typical", and their own initials (Trabb Pardo and Knuth). In a talk based on the paper, Knuth said:

You can only appreciate how deep the subject is by seeing how good people struggled with it and how the ideas emerged one at a time. In order to study this—Luis I think was the main instigator of this idea—we take one program—one algorithm—and we write it in every language. And that way from one example we can quickly psych out the flavor of that particular language. We call this the TPK program, and well, the fact that it has the initials of Trabb Pardo and Knuth is just a funny coincidence.

Knuth describes it as follows:

We introduced a simple procedure called the “TPK algorithm,” and gave the flavor of each language by expressing TPK in each particular style. […] The TPK algorithm inputs eleven numbers ${\displaystyle a_{0},a_{1},\ldots ,a_{10}}$; then it outputs a sequence of eleven pairs ${\displaystyle (10,b_{10}),(9,b_{9}),\ldots ,(0,b_{0}),}$ where

${\displaystyle b_{i}={\begin{cases}f(a_{i}),&{\text{if }}f(a_{i})\leq 400;\\999,&{\text{if }}f(a_{i})>400;\end{cases}}\quad f(x)={\sqrt {|x|}}+5x^{3}.}$

This simple task is obviously not much of a challenge, in any decent computer language.

In pseudocode: