How to resolve the algorithm Cartesian product of two or more lists step by step in the Maxima programming language

Published on 12 May 2024 09:40 PM
#Maxima

How to resolve the algorithm Cartesian product of two or more lists step by step in the Maxima programming language

Table of Contents

Problem Statement

Show one or more idiomatic ways of generating the Cartesian product of two arbitrary lists in your language. Demonstrate that your function/method correctly returns: and, in contrast: Also demonstrate, using your function/method, that the product of an empty list with any other list is empty. For extra credit, show or write a function returning the n-ary product of an arbitrary number of lists, each of arbitrary length. Your function might, for example, accept a single argument which is itself a list of lists, and return the n-ary product of those lists. Use your n-ary Cartesian product function to show the following products:

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Step by Step solution about How to resolve the algorithm Cartesian product of two or more lists step by step in the Maxima programming language

Source code in the maxima programming language

cartesian_product({1,2},{3,4});
/* {[1,3],[1,4],[2,3],[2,4]} */
cartesian_product({3,4},{1,2});
/* {[3,1],[3,2],[4,1],[4,2]} */
cartesian_product({1,2},{});
/* {} */
cartesian_product({},{1,2});
/* {} */


cartesian_product_list([1,2],[3,4]);
/* [[1,3],[1,4],[2,3],[2,4]] */
cartesian_product_list([3,4],[1,2]);
/* [[3,1],[3,2],[4,1],[4,2]] */
cartesian_product_list([1,2],[]);
/* [] */
cartesian_product_list([],[1,2]);
/* [] */


create_list([i,j],i,[1,2],j,[3,4]);
/* [[1,3],[1,4],[2,3],[2,4]] */
create_list([i,j],i,[3,4],j,[1,2]);
/* [[3,1],[3,2],[4,1],[4,2]] */
create_list([i,j],i,[1,2],j,[]);
/* [] */
create_list([i,j],i,[],j,[1,2]);
/* [] */


my_cartesian(lst1,lst2):=create_list([i,j],i,lst1,j,lst2);
n_ary_cartesian(singleargument):=block(lreduce(my_cartesian,singleargument),map(flatten,%%));

[[1776,1789],[7,12],[4,14,23],[0,1]]$
n_ary_cartesian(%);
/* 	[[1776,7,4,0],[1776,7,4,1],[1776,7,14,0],[1776,7,14,1],[1776,7,23,0],[1776,7,23,1],[1776,12,4,0],[1776,12,4,1],[1776,12,14,0],[1776,12,14,1],[1776,12,23,0],[1776,12,23,1],[1789,7,4,0],[1789,7,4,1],[1789,7,14,0],[1789,7,14,1],[1789,7,23,0],[1789,7,23,1],[1789,12,4,0],[1789,12,4,1],[1789,12,14,0],[1789,12,14,1],[1789,12,23,0],[1789,12,23,1]] */

[[1,2,3],[30],[500,100]]$
n_ary_cartesian(%);
/* [[1,30,500],[1,30,100],[2,30,500],[2,30,100],[3,30,500],[3,30,100]] */

[[1,2,3],[],[500,100]]$
n_ary_cartesian(%);
/* [] */

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