Project euler53 #1511

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	/**
	// https://projecteuler.net/problem=53
	There are exactly ten ways of selecting three from five, 12345:
	123, 124, 125, 134, 135, 145, 234, 235, 245, 345
	In combinatorics, we use the notation, 5C3 = 10
	In general, nCr = n!/(r!(n-r)!), where r <= n
	n! = n(n-1)...32*1, and 0! = 1
	It is not until n=23, that a value exceeds one-million: 23C10 = 1144066
	How many, not necessarily distinct, value of nCr for 1 <= n <= 100 are greater than one-million?
	*/
	export const answer = (minVal, maxVal) => {
	/*
	When n is fixed, the maximum value of nCr is when r is the closes to n/2.
	//Since nCr = nC(n-r), loop from the ceil of n/2 and increase by one until
	the value becomes less than or equal to one million. Then, multiply by two
	because of symmetry, but if n is even, then subtract one to avoid overcounting.
	*/
	var factorials = [1];
	var maxR = 0;
	var numWork = 0;
	var totalNumWork = 0;
	for (var i=1;i<=maxVal;i++){
	factorials.push(factorials[factorials.length-1]*i);
	}
	for (var n=minVal;n<=maxVal;n++){
	maxR = Math.ceil(n/2);
	numWork = 0;
	for (var r=maxR;r<=n;r++){
	if (factorials[n]/(factorials[r]*factorials[n-r]) > 1000000){
	numWork++;
	}
	else{
	break;
	}
	}
	if (n%2 == 1){
	numWork = 2*numWork;
	}
	else{
	numWork = Math.max(0, 2*numWork-1);
	}
	totalNumWork += numWork;
	}
	return totalNumWork
	}

10 changes: 10 additions & 0 deletions Project-Euler/test/Problem053.test.js

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	import { answer } from '../Problem053.js'

	describe('Number of values of nCr that exceed 1 million when n is in a certain range', () => {
	test('range is 10 to 100', () => {
	expect(answer(10,100)).toBe(4075)
	})
	test('range is 1 to 150', () => {
	expect(answer(1,150)).toBe(10000)
	})
	})

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