nck-pascal

The nck-pascal library is the result of a personal investigation of Pascal's triangle that began in college and lasted for a few years. I was pleased when all the rules defining the criteria for visiting Pascal's triangle were implemented.

This library allows calculating combinations of N variables in arrays of K elements, with the possibility of choosing to start with the elements at the beginning or at the end of the array; since the solution is symmetric.

It started with a recursive implementation, but for N greater than 1500 (For that number of variables, don't supply a Pascal's triangle, otherwise it will burst memory) it gave an error, so an array of states was created that is used in a while loop.

If you like this library, if it helps you solve a problem, you have the possibility, offer a coffee.

You can see a test page at https://pjsr1980.github.io/nck-pascal

To use the library it is necessary to create a nckVisitor with the following functions:

interface nckVisitor {
    onResult(nckd: nckData): void;      // If a new combination is calculated
    goFalse(nckd: nckData): boolean;    // Investigate solutions where the current variable is False
    goTrue(nckd: nckData): boolean;     // Investigate solutions where the current variable is True
}

Where the nckData type is defined as follows:

type nckData = {
    result: BitVec;     // current result vector
    pascal?: Pascal;    // Pascal's Triangle, it's optional
    row?: bigint;       // the solution line number, present only if pascal is given
    tr: number;         // Current line number of Pascal's triangle
    tc: number;         // Current column number of Pascal's triangle
    rv: number;         // Current position of the current variable
    l1: boolean;        // flag that indicates whether the solution starts with the variables on the left
};

As an example, to print all combinations for an N=6 and a K=2, we can write:

import * as nCk from "nck-pascal";

let pascal = new nCk.Pascal();

let visitor = {
    onResult: function(nckd) {
        console.log(nckd.row.toString() + " : " + nckd.result.toString());
	},
    goFalse: function(nckd) {
	    return true;
	},
    goTrue: function(nckd) {
		return true;
	}
}

nCk.VisitL1(visitor, 6, 2, pascal)

And the result will be:

* VisitL1 *         * VisitL0 *      
1  : 110000         1  : 000011
2  : 101000         2  : 000101
3  : 100100         3  : 000110
4  : 100010         4  : 001001
5  : 100001         5  : 001010
6  : 011000         6  : 001100
7  : 010100         7  : 010001
8  : 010010         8  : 010010
9  : 010001         9  : 010100
10 : 001100         10 : 011000
11 : 001010         11 : 100001
12 : 001001         12 : 100010
13 : 000110         13 : 100100
14 : 000101         14 : 101000
15 : 000011         15 : 110000

If you don't need the result row value, simply don't provide a Pascal's Triangle:

...
nCk.VisitL1(visitor, 6, 2)
nCk.VisitL0(visitor, 6, 2)

Having a combination, one can find out the solution line number using one of the following functions:

(If Pascal's Triangle is not given, one is created, as this is needed for the calculation)

function RowL1(vec: BitVec, pascal?: Pascal): bigint;
function RowL0(vec: BitVec, pascal?: Pascal): bigint;

The inverse operation can also be done, that is, having the solution line number, the N and the K, the combination can be calculated using one of the following functions:

(If Pascal's Triangle is not given, one is created, as this is needed for the calculation)

function VecL1(row: bigint, n: number, k: number, pascal?: Pascal): BitVec;
function VecL0(row: bigint, n: number, k: number, pascal?: Pascal): BitVec;

The BitVec solution vector has the following specification:

export declare class BitVec {
    private _nbits;
    private _data;

    constructor(nbits: number);

    clone(): BitVec;

    get nbits(): number;
    get nbytes(): number;
    
    setAll(value: boolean): void;

    get(pos: number): boolean;
    set(pos: number, val: boolean): void;

    countTrue(): number;
    countFalse(): number;

    getTrue(): number[];
    getFalse(): number[];

    toString(): string;

    equal(o: BitVec): boolean;
}