How to resolve the algorithm Floyd's triangle step by step in the Mathematica / Wolfram Language programming language

Published on 22 June 2024 08:30 PM
#Wolfram

How to resolve the algorithm Floyd's triangle step by step in the Mathematica / Wolfram Language programming language

Table of Contents

Problem Statement

Floyd's triangle   lists the natural numbers in a right triangle aligned to the left where

The first few lines of a Floyd triangle looks like this:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Floyd's triangle step by step in the Mathematica / Wolfram Language programming language

The provided Wolfram code is a function that generates a sequence of numbers. Let's break down the code step by step:

Function Definition:

f=Function[n,

This line defines a function named f that takes one argument, n. This function will generate a sequence of numbers based on the input n.

Sequence Generation:

Most/@(Range@@@Partition[FindSequenceFunction[{1,2,4,7,11}]/@Range[n+1],2,1])]

This part of the code generates the sequence of numbers. Let's break it down into smaller parts:

  • FindSequenceFunction[{1,2,4,7,11}]: This part finds a sequence function that generates the sequence 1, 2, 4, 7, 11. In this case, the sequence function is #^2-1, where # represents the position in the sequence.
  • /@Range[n+1]: This part applies the found sequence function to the range of numbers from 1 to n+1.
  • Partition[..., 2, 1]: This part partitions the list into pairs of consecutive elements, effectively creating a list of 2-tuples.
  • Range@@@...: This part generates a list of ranges based on the pairs of consecutive elements.
  • Most/@...: This part takes the first element from each range, effectively removing the second elements of the pairs.

Example Usage:

TableForm[f@5, TableAlignments->Right, TableSpacing->{1,1}]
TableForm[f@14, TableAlignments->Right, TableSpacing->{1,1}]

These lines demonstrate how to use the f function to generate and display sequences of numbers.

  • f@5: This generates a sequence of numbers based on n=5.
  • TableForm[..., TableAlignments->Right, TableSpacing->{1,1}]: This格式schemas the sequence into a table, aligning the numbers to the right and adding spacing for readability.

When you run this code, it will generate and display two tables of sequences of numbers, one for n=5 and one for n=14. The generated sequences follow the pattern of the original sequence 1, 2, 4, 7, 11, where each subsequent number is obtained by applying the function #^2-1 to the previous number.

Source code in the wolfram programming language

f=Function[n,
	Most/@(Range@@@Partition[FindSequenceFunction[{1,2,4,7,11}]/@Range[n+1],2,1])]
TableForm[f@5,TableAlignments->Right,TableSpacing->{1,1}]
TableForm[f@14,TableAlignments->Right,TableSpacing->{1,1}]

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