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...


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

Extracted text: 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.

Jun 08, 2022
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