NAME

Math::PascalTriangle — Pascal’s triangle binomial coefficients

SYNOPSIS

use Math::PascalTriangle;
say Math::PascalTriangle.get(:line(4), :col(2)); # 6

# build a row (0-based indexing)
my $n = 6;
say (0..$n).map({ Math::PascalTriangle.get(:line($n), :col($_)) }).join(' ');

OVERVIEW

Pascal’s triangle is a triangular arrangement of numbers where each entry is a binomial coefficient. The outer edges are 1. Interior values are the sum of the two entries directly above: T(n, k) = T(n-1, k) + T(n-1, k-1).

• Symmetry: T(n, k) = T(n, n-k).

• Polynomial coefficients: row `n` gives coefficients of (a + b)^n.

• Combinatorics: T(n, k) = C(n, k) counts ways to choose k elements from n.

Indexing in this module is 0-based: the first row/line is line = 0, and the first column is col = 0. Therefore get(:line(n), :col(k)) returns C(n, k).

USAGE

This module exposes a single class method `get` to retrieve entries.

• Call as Math::PascalTriangle.get(:line($n), :col($k)).

• Valid inputs: UInt values with C<<0 <= k <= n>>.

• Returns big integers when values grow large.

• Throws when <col > line> (no triangle entry).

DESCRIPTION

Internally, values are computed via the recursive identity C(n, k) = C(n-1, k) + C(n-1, k-1) and memoized. A simple LRU policy bounds the cache to 9999 entries to avoid unbounded memory growth.

METHODS

method get(UInt:D() :$line!, UInt:D() :$col!) Returns the binomial coefficient C(line, col).

• Base cases: col == 0 and col == line return 1.

• Recursive case: for C<<0 < col < line>>, computes C(line - 1, col) + C(line - 1, col - 1).

• Error case: when <col > line>, no candidate matches and an exception is thrown (see t/02-triangle.t).

CACHING

Results are cached in %cache keyed by the capture ($line, $col). Each access bumps a count in %LRU. When %LRU.elems exceeds 9999, the least-recently used key (lowest count) is evicted from both %LRU and %cache.

EXAMPLES

Single entries

Math::PascalTriangle.get(:line(9), :col(4))   # 126
Math::PascalTriangle.get(:line(99), :col(49)) # 50445672272782096667406248628

# Generate a row
auto $row = 9;
(0..$row).map({ Math::PascalTriangle.get(:line($row), :col($_)) }).say;

# Symmetry example (true)
Math::PascalTriangle.get(:line(9), :col(2)) == Math::PascalTriangle.get(:line(9), :col(7))

AUTHOR

See META6.json for authorship information.

LICENSE

Same license as this distribution; see META6.json.