Step by Step solution about How to resolve the algorithm Kaprekar numbers step by step in the JavaScript programming language

The provided JavaScript code defines a function, isKaprekar, that checks whether a given number is a Kaprekar number and then uses it in another function, kaprekar, to find and print Kaprekar numbers within a specified range and in different number bases. Here's a detailed explanation:

• isKaprekar(n, bs) function:

  • This function checks whether a given positive integer n is a Kaprekar number in the specified base bs (defaulting to base 10 if not provided).

  • It calculates the square of n and converts it to a string in the specified base.

  • It then iterates over each split point in the squared string and checks if the string can be split into two positive integers a and b such that a + b equals the original number n. If such a split is found, it returns true, indicating that n is a Kaprekar number in the given base.

• kaprekar(s, e, bs, pbs) function:

  • This function finds and prints Kaprekar numbers within a specified range [s, e], in the specified base bs (defaulting to base 10), and prints them in a different base pbs (defaulting to base 10).

  • It iterates over each number n in the range [s, e] and checks if n is a Kaprekar number using the isKaprekar function.

  • If n is a Kaprekar number, it prints the string representation of n in the specified print base pbs.

• Usage of the functions:

  • The code uses the kaprekar function to find and print Kaprekar numbers in different ranges and bases:

    • kaprekar(1, 99): Finds and prints Kaprekar numbers between 1 and 99 in base 10 and prints them in uppercase base 10.

    • kaprekar(1, 255, 16): Finds and prints Kaprekar numbers between 1 and 255 in base 16 and prints them in uppercase base 10.

    • kaprekar(1, 255, 16, 16): Finds and prints Kaprekar numbers between 1 and 255 in base 16 and prints them in uppercase base 16.

    • kaprekar(1, 288, 17, 17): Finds and prints Kaprekar numbers between 1 and 288 in base 17 and prints them in uppercase base 17.

function isKaprekar( n, bs ) {
	if ( n < 1 ) return false
	if ( n == 1 ) return true
	bs = bs || 10
	var s = (n * n).toString(bs)
	for (var i=1, e=s.length; i<e; i+=1) {
		var a = parseInt(s.substr(0, i), bs)
		var b = parseInt(s.substr(i), bs)
		if (b && a + b == n) return true
	}
	return false
}


function isKaprekar( n, bs ) {
	if ( n < 1 ) return false
	if ( n == 1 ) return true
	bs = bs || 10
	for (var a=n*n, b=0, s=1; a; s*=bs) {
		b += a%bs*s
		a = Math.floor(a/bs)
		if (b && a + b == n) return true
	}
	return false
}


function kaprekar( s, e, bs, pbs ) {
	bs = bs || 10; pbs = pbs || 10
	const toString = n => n.toString(pbs).toUpperCase()
	document.write('start:',toString(s), ' end:',toString(e), ' base:',bs, ' printBase:',pbs, '<br>' )
	for (var k=0, n=s; n<=e; n+=1) if (isKaprekar(n, bs)) k+=1, document.write(toString(n), ' ') 
	document.write('<br>found ', k, ' numbers<br><br>')
}

kaprekar( 1, 99 )
kaprekar( 1, 255, 16)
kaprekar( 1, 255, 16, 16)
kaprekar( 1, 288, 17, 17)