Recursion Program

Write a recursive program to determine and print the Nth line of Pascal's Triangle, as shown below. Each

interior value is the sum of the values above it$.($Hint: Use a $2$D array to store the values on each line.$)$

$1$

$11$

$121$

$1331$

$14641$

$15101051$

$1615201561$

$172135352171$

$18285670562881$

To do this, you will create two classes:

PacalTriangleGenerator and the Driver

PascalTriangleGenerator class:

Instance variable: two integer arrays, row$1$ and row$2$

Methods:

$$ Constructor that instantiates the two arrays$/$ The first array will contain one element and the

other will contain two elements. Set the value of each element to $1.$

$$ computeRow$()$ This is your recursive method that computes the specified row of Pascal$$s

triangle. Accepts an integer that represents a row number and returns an integer array

o There will be two base cases: value passed in is a one, which would only occur if the

original number is a one, and if value passed in is a $2$

o Initially the specified row that is passed in is the bottom of the triangle. With each call of

this method recursively, you will work your way up the triangle until you are on row $2.$

o The general case calls the computeNextRow method and passes into it the result of

calling the computerRow method, decreasing the row number by $1$ each time

$$ computeNextRow$()$ computes the next row of Pascal$$s Triangle given the previous one. It

accepts an integer array that represents the previous row and returns an integer array

Driver class:

This class will only contain one method, in addition to the main method. It will prompt the user

for a total lines, call the method to create a pascal triangle and then prompt the user to indicate

whether a new triangle should be drawn.

Methods:

$$ newTriangle$-$ This method does not receive or return anything. It draws the Pascal

Triangle.

o Prompt and accept the number of rows

o Inside a loop$-$ loop should traverse each row of the triangle

$$ Instantiate a PascalsTriangleGenerator object

$$ Call the computeRow method of PascalsTriangleGenerator

$$ Output the triangle

$$ Main$()$

o Inside a loop$-$ loop should terminate when the user indicates they want to stop

$$ Call the newTriangle

$$ Prompt and accept user input for whether they want another triangle?

Sample output:

How many lines of Pascal's Triangle? $5$

$1$

$11$

$121$

$1331$

$14641$

Another $($y$/$n$)?$ y

How many lines of Pascal's Triangle? $7$

$1$

$11$

$121$

$1331$

$14641$

$15101051$

$1615201561$

Another $($y$/$n$)?$ n