# CtCI - Grade School Algorithm

A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are in use. Efficient multiplication algorithms have existed since the advent of the decimal system.

We usually learn this in 1st-2nd grade as the easiest method to multiply two big numbers apparently because it is easier to visualize the values for the subsequent operation (which is a sum) to get to the desired results.

For a multi-digit number `5678` we want to visualize the grade-school algorithm when it is multiplied by `1234` including the raised numbers and the middle sums before we print the result to the user.

``````# Input
5678x1234
``````
``````# Output
5678
1234 *
-------
22712 +
17034~
11356~~
5678~~~
-------
7006652
``````

### Solution

``````package main

import (
"fmt"
"strconv"
"strings"
)

func padleft(text string, length int) string {
var total = len(text)

if total < length {
text = strings.Repeat("\x20", length-total) + text
}

return text
}

func main() {
var line string
var sections []string

fmt.Scanf("%s", &line)

parts := strings.Split(line, "x")

if len(parts) < 2 {
fmt.Println("Usage: echo \"5678x1234\" | solution")
return
}

step := 0
total := 0
longest := 0
base := parts
multiplier := parts
blength := len(base)
mlength := len(multiplier)

sections = append(sections, base)
sections = append(sections, multiplier)
sections = append(sections, "") /* separator */

for m := mlength - 1; m >= 0; m-- {
remain := 0
subtotal := ""
num := int(multiplier[m] - '0')

for n := blength - 1; n >= 0; n-- {
baseint := int(base[n] - '0')
result := (baseint * num) + remain
resultstr := strconv.Itoa(result)

if result > 9 {
subtotal = string(resultstr) + subtotal
remain = int(resultstr - '0')
} else {
subtotal = resultstr + subtotal
remain = 0
}
}

if remain > 0 {
subtotal = strconv.Itoa(remain) + subtotal
}

submult := subtotal + strings.Repeat("~", step)
submultstr := subtotal + strings.Repeat("0", step)
submultint, _ := strconv.Atoi(submultstr)

total += submultint

if len(submult) > longest {
longest = len(submult)
}

sections = append(sections, submult)
step++
}

for key, text := range sections {