(49g 50g) Fast Pascal's triangle and its relatives

08192018, 02:14 PM
(This post was last modified: 08192018 07:10 PM by John Keith.)
Post: #4




RE: (49g 50g) Fast Pascal's triangle and its relatives
By definition, each entry in Pascal's triangle is the sum of the two numbers above it. This leads to a very fast method of computing a row of Pascal's triangle given the previous row (as a list) on the stack:
Code:
The following program returns rows 0 through n of Pascal's triangle as a list of lists. It calculates the first 100 rows (a 63K byte object) in less than 20 seconds. No external libraries are required. Code:
While generating Pascal's triangle is not very useful in general, the entries of Pascal's triangle are the binomial coefficients, which can be useful themselves. As an example, here is a program, based on the one above, which returns the ordered Bell numbers from 0 through n: Code:
This program should be used in exact mode as the numbers involved are very large. However, all three programs in this post will work on the HP48g/gx. 

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Messages In This Thread 
(49g 50g) Fast Pascal's triangle and its relatives  John Keith  08112018, 04:58 PM
RE: (49g 50g) Fast Pascal's triangle and its relatives  Joe Horn  08122018, 12:41 AM
RE: (49g 50g) Fast Pascal's triangle and its relatives  John Keith  08122018, 02:12 PM
RE: (49g 50g) Fast Pascal's triangle and its relatives  John Keith  08192018 02:14 PM
RE: (49g 50g) Fast Pascal's triangle and its relatives  Joe Horn  08202018, 12:43 AM
RE: (49g 50g) Fast Pascal's triangle and its relatives  John Keith  08202018, 12:15 PM
RE: (49g 50g) Fast Pascal's triangle and its relatives  Thomas Klemm  03022019, 07:12 PM
RE: (49g 50g) Fast Pascal's triangle and its relatives  John Keith  01282020, 06:12 PM
RE: (49g 50g) Fast Pascal's triangle and its relatives  John Keith  12152021, 07:31 PM

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