Pascal's triangle
Pascal's triangle is an interesting math concept. Its first few rows look like this:
You are encouraged to solve this task according to the task description, using any language you may know.
1 1 1 1 2 1 1 3 3 1
where each element of each row is either 1 or the sum of the two elements right above it. For example, the next row would be 1 (since the first element of each row doesn't have two elements above it), 4 (1 + 3), 6 (3 + 3), 4 (3 + 1), and 1 (since the last element of each row doesn't have two elements above it). 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.
Ada
<ada> -- Pascals triangle
with Ada.Integer_Text_Io; use Ada.Integer_Text_Io; with Ada.Text_Io; use Ada.Text_Io;
procedure Pascals_Triangle is
type Row is array(Positive range <>) of Integer;
type Row_Access is access Row;
type Triangle is array(Positive range <>) of Row_Access;
function General_Triangle(Depth : Positive) return Triangle is
Result : Triangle(1..Depth);
begin
for I in Result'range loop
Result(I) := new Row(1..I);
for J in 1..I loop
if J = Result(I)'First or else J = Result(I)'Last then
Result(I)(J) := 1;
else
Result(I)(J) := Result(I - 1)(J - 1) + Result(I - 1)(J);
end if;
end loop;
end loop;
return Result;
end General_Triangle;
procedure Print(Item : Triangle) is
begin
for I in Item'range loop
for J in 1..I loop
Put(Item => Item(I)(J), Width => 3);
end loop;
New_Line;
end loop;
end Print;
begin
Print(General_Triangle(7));
end Pascals_Triangle; </ada>
Java
Summing from Previous Rows
This implementation prints nothing for n <= 0. <java>import java.util.LinkedList; ...//class definition, etc. public static void genPyrN(int rows){ if(rows <= 0) return; //save the last row here LinkedList<Integer> last= new LinkedList<Integer>(); last.add(1);//it's row 0...it starts with 1 for(int i= 0;i <= rows;++i){ //work on the next row LinkedList<Integer> thisRow= new LinkedList<Integer>(); for(int j= 0;j < i;++j){//loop the number of elements in this row if(j == last.size() || j == 0){//if we're on the ends thisRow.add(1); }else{//otherwise, sum from the last row thisRow.add(last.get(j - 1) + last.get(j)); } } thisRow.add(1); last= thisRow;//save this row System.out.println(thisRow); } }</java>