Using Java to design and implement the class PascalTriangle that will generate a Pascal Triangle from a given number of rows. Represent each row in a triangle as a list and the entire triangle as a list of these lists. Please implement the class ArrayList for these lists. Please do not use the binomial coeffiient formula { C(n,k)= n! / (k!*(n-k)!) to create the triangle. The triangle has to be generate using in this way: each row of the triangle begins and ends with 1, value at (x,y) equals to sum of value at (x-1, y-1) & (x-1,y), whereas x is the row number and y is the columm. As seen in this Pascal's Triangle:1111113311441Each row begins and ends with 1. Each interior entry is the sum of the twoentries above it. For example, in the last row given here, 4 is the sum of 1 and3, 6 is the sum of 3 and 3, and 4 is the sum of 3 and 1.If we number both the rows and the entries in each row beginning with 0, theentry in position k of row n is often denoted as C(n, k). For example, the 6 inthe last row is C(4, 2). Given n items, C(n, k) turns out to be the number ofthatyou can select k of the n items. Thus, C(4, 2), which is 6, is thewaysnumber of waysthatyou can selecttwo of four given items. So if A, B, C, and D are the four items, here are thesix possible cho ices:А В, А С, А D, BС, В О, СDNote that the order of the items in each pair is irrelevant. For instance, the choiceAB is the same as the cho ice B A.

Program Approach:- 1. Include header file 2. Create the class PascalProblem 3. Create the default…

Answered: Using Java to design and implement the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Using Java to design and implement the class PascalTriangle that will generate a Pascal
Triangle from a given number of rows. Represent each row in a triangle as a list and the entire
triangle as a list of these lists. Please implement the class ArrayList for these lists.
Please do not use the binomial coeffiient formula { C(n,k)= n! / (k!*(n-k)!) to create the triangle. The triangle has to be generate using in this way: each row of the triangle begins and ends with 1, value at (x,y) equals to sum of value at (x-1, y-1) & (x-1,y), whereas x is the row number and y is the columm.

As seen in this Pascal's Triangle:
1
1
1
1
1
1
3
3
1
1
4
4
1
Each row begins and ends with 1. Each interior entry is the sum of the two
entries above it. For example, in the last row given here, 4 is the sum of 1 and
3, 6 is the sum of 3 and 3, and 4 is the sum of 3 and 1.
If we number both the rows and the entries in each row beginning with 0, the
entry in position k of row n is often denoted as C(n, k). For example, the 6 in
the last row is C(4, 2). Given n items, C(n, k) turns out to be the number of
that
you can select k of the n items. Thus, C(4, 2), which is 6, is the
ways
number of ways
that
you can select
two of four given items. So if A, B, C, and D are the four items, here are the
six possible cho ices:
А В, А С, А D, BС, В О, СD
Note that the order of the items in each pair is irrelevant. For instance, the choice
AB is the same as the cho ice B A.

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