# Trabb Pardo–Knuth Algorithm

• Difficulty Level : Basic
• Last Updated : 13 Jul, 2017

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. This program was written in several early programming language to show the evolution of programming languages.

Just like the “Hello World!” program has the purpose of introducing beginners to programming the TPK has the same purpose and has no practical applications.

```Algorithm:
input 11 numbers into a sequence A
reverse sequence A
for each item in sequence A
call a function to do an operation
if result overflows
else
print result
```

## C

 `// C program to implement TPK algorithm``#include ``#include `` ` `// f(x) = sqrt(|x|) + 5*x**3 ``double` `f (``double` `x)``{``    ``return` `(``sqrt``(``fabs``(x)) + 5.0 * ``pow``(x, 3.0));``}`` ` `int` `main (``int` `argc, ``char``* argv[])``{``    ``double` `y;``    ``int` `i;`` ` `    ``// Read in the values of the array A ``    ``double` `A[11] = {7.9, 7.3, 20.9, 112.0, 5.0, 3.0, 2.9, 9.0, 21.7, 31.2, 4.1};`` ` `    ``// In reverse order, apply "f" ``    ``// to each element of A and print``    ``for` `(i=10; i>=0; i--)``    ``{``        ``y = f (A[i]);``        ``if` `(y > 400.0)``        ``{``            ``printf` `(``"%d TOO LARGE\n"``, i);``        ``}``        ``else``        ``{``            ``printf` `(``"%d %f\n"``, i, y);``        ``}``    ``}``    ``return` `(0);``}`

## Java

 `// Java program to implement TPK algorithm``import` `java.util.*;``import` `java.io.*; ``   ` `public` `class` `TPKA {``    ``public` `static` `void` `main(String... args) {``        ``double``[] input = {``7.9``, ``7.3``, ``20.9``, ``112.0``, ``5.0``, ``3.0``, ``2.9``, ``9.0``, ``21.7``, ``31.2``, ``4.1``};``          ` `        ``for``(``int` `j = ``10``; j >= ``0``; j--) {``            ``double` `y = f(input[j]);``            ``if``( y < ``400.0``) {``                ``System.out.printf(``"%d %.2f\n"``, j, y);``            ``} ``else` `{``                ``System.out.printf(``"%d %s\n"``, j, ``"TOO LARGE"``);``            ``}``        ``}``    ``}``   ` `    ``private` `static` `double` `f(``double` `x) {``        ``return` `Math.pow(Math.abs(x), ``0.5``) + (``5``*(Math.pow(x, ``3``)));``    ``}``}`

## Python

 `# Python program to implement TPK algorithm``def` `f(x):``    ``return` `abs``(x) ``*``*` `0.5` `+` `5` `*` `x``*``*``3`` ` `def` `main():``    ``s ``=` `[``7.9``, ``7.3``, ``20.9``, ``112.0``, ``5.0``, ``3.0``, ``2.9``, ``9.0``, ``21.7``, ``31.2``, ``4.1``]``    ``s.reverse()``    ``i ``=` `10``    ``for` `x ``in` `s:``        ``result ``=` `f(x)``        ``if` `result > ``400``:``            ``print``(``'%d %s'` `%` `(i, ``"TOO LARGE"``))``            ``i ``=` `i``-``1``        ``else``:``            ``print``(``'%d %f'` `%` `(i, result))``            ``i ``=` `i``-``1``    ``print``('')``     ` `if` `__name__ ``=``=` `'__main__'``:``    ``main()`
```Output:
10 346.629846
9 TOO LARGE
8 TOO LARGE
7 TOO LARGE
6 123.647939
5 136.732051
4 TOO LARGE
3 TOO LARGE
2 TOO LARGE
1 TOO LARGE
0 TOO LARGE
```

References: http://cs.fit.edu/~ryan/compare/tpk-c.html

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