package multiplystrings

func addDigits(a, b byte) (byte, byte) {
	abInt := int(a-'0') + int(b-'0')
	return byte(abInt/10) + '0', byte(abInt%10) + '0'
}

func addByDigit(dst *[]byte, src byte) {
	for i, b := range *dst {
		if src == '0' {
			return
		}

		src, (*dst)[i] = addDigits(b, src)
	}

	if src != '0' {
		*dst = append(*dst, src)
	}
}

func add(dst *[]byte, src []byte) {
	carry := byte('0')

	for i := range max(len(*dst), len(src)) {
		d, s := byte('0'), byte('0')
		if len(*dst) > i {
			d = (*dst)[i]
		}
		if len(src) > i {
			s = src[i]
		}

		hi, lo := addDigits(d, s)
		total := []byte{lo, hi}
		addByDigit(&total, carry)
		(*dst)[i], carry = total[0], total[1]
	}

	if carry != '0' {
		*dst = append(*dst, carry)
	}
}

func multiplyDigits(a, b byte) (byte, byte) {
	abInt := int(a-'0') * int(b-'0')
	return byte(abInt/10) + '0', byte(abInt%10) + '0'
}

func multiplyByDigit(and []byte, ier byte) []byte {
	result, carry := []byte{}, byte('0')
	for _, b := range and {
		hi, lo := multiplyDigits(b, ier)

		// Fold the incoming carry into the low digit; any overflow rolls
		// into hi, which is small enough that it never overflows again.
		c, lo := addDigits(lo, carry)
		_, carry = addDigits(hi, c)

		result = append(result, lo)
	}

	if carry != '0' {
		result = append(result, carry)
	}

	return result
}

func reverse(s string) []byte {
	digits := make([]byte, len(s))
	for i := range s {
		digits[len(s)-1-i] = s[i]
	}

	return digits
}

func multiply(a, b string) string {
	if a == "0" || b == "0" {
		return "0"
	}

	and := reverse(a)
	result := make([]byte, len(a)+len(b))
	for i := range result {
		result[i] = '0'
	}

	for i := range len(b) {
		ier := b[len(b)-1-i]
		partial := multiplyByDigit(and, ier)

		// Shift left by i places (little-endian: i leading zeros).
		shifted := make([]byte, i+len(partial))
		for j := range i {
			shifted[j] = '0'
		}
		copy(shifted[i:], partial)

		add(&result, shifted)
	}

	end := len(result)
	for end > 1 && result[end-1] == '0' {
		end--
	}

	out := make([]byte, end)
	for i := range end {
		out[i] = result[end-1-i]
	}

	return string(out)
}