How to resolve the algorithm Pascal's triangle step by step in the Ada programming language

Published on 12 May 2024 09:40 PM
#Ada

How to resolve the algorithm Pascal's triangle step by step in the Ada programming language

Table of Contents

Problem Statement

Pascal's triangle is an arithmetic and geometric figure often associated with the name of Blaise Pascal, but also studied centuries earlier in India, Persia, China and elsewhere. Its first few rows look like this: where each element of each row is either 1 or the sum of the two elements right above it. For example, the next row of the triangle would be: So the triangle now looks like this: Each row   n   (starting with row   0   at the top) shows the coefficients of the binomial expansion of   (x + y)n.

Write a function that prints out the first   n   rows of the triangle   (with   f(1)   yielding the row consisting of only the element 1). This can be done either by summing elements from the previous rows or using a binary coefficient or combination function. Behavior for   n ≤ 0   does not need to be uniform, but should be noted.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pascal's triangle step by step in the Ada programming language

Source code in the ada programming language

package Pascal is
   
   type Row is array (Natural range <>) of Natural;
   
   function Length(R: Row) return Positive;
   
   function First_Row(Max_Length: Positive) return Row;
   
   function Next_Row(R: Row) return Row;
   
end Pascal;


package body Pascal is
   
   function First_Row(Max_Length: Positive) return Row is
      R: Row(0 .. Max_Length) := (0 | 1 => 1, others => 0);
   begin
      return R;
   end First_Row;
   
   function Next_Row(R: Row) return Row is
      S: Row(R'Range);
   begin
      S(0) := Length(R)+1;
      S(Length(S)) := 1;
      for J in reverse 2 .. Length(R) loop
         S(J) := R(J)+R(J-1);
      end loop;
      S(1) := 1;
      return S;
   end Next_Row;
   
   function Length(R: Row) return Positive is
   begin
      return R(0);
   end Length;
   
end Pascal;


with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Command_Line, Pascal; use Pascal;

procedure Triangle is
   
   Number_Of_Rows: Positive := Integer'Value(Ada.Command_Line.Argument(1));
   Row: Pascal.Row := First_Row(Number_Of_Rows);
      
begin
   loop
      -- print one row
      for J in 1 .. Length(Row) loop
	 Ada.Integer_Text_IO.Put(Row(J), 5);
      end loop;
      Ada.Text_IO.New_Line;
      exit when Length(Row) >= Number_Of_Rows;
      Row := Next_Row(Row);
   end loop;
end Triangle;

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