# Make a Number Expression

Few years ago, an esoteric programming language named 아희(Aheui) was created. Well, actually you don't need to know about this language or Korean characters.

Aheui uses stacks and a queue, but this time we use one stack and ignore other stacks and queue. You can push a number between 2 and 9 into a stack. You can do arithmetic operations by popping two numbers and pushing result. And you can duplicate a top number.

So, when I need a big number in Aheui, making a number was not an easy work. Push, push, multiply, duplicate, push, multiply, push, add…. It takes too much time and sometimes waste of bytes. I need a shortest expressions.

## Summary

Your task is to write a function or a program which takes a number n (0 <= n <= 1000000) and returns concatenation of tokens.

Tokens are basically a postfix notation. Tokens are consisted of

• Number between 2 and 9, which means "push number into stack"
• +, -, /, *, which means "pop two numbers from stack, do arithmetic operation, push the result into stack". All calculations are in integer.
• >, which means "duplicate a top number"

Tokens will be concatenated with empty string, so 5 5 + will be 55+.

After calculations, n must be on the top of the stack.

### Sample input and output

INPUT = 0
OUTPUT = 22-
(or 33-, 44-, whatever)

INPUT = 1
OUTPUT = 22/
(or 32-, 33/, whatever)

INPUT = 5
OUTPUT = 5
(We don't need calculations, just push)

INPUT = 64
OUTPUT = 88*
(or 8>*)

INPUT = 1337
OUTPUT = 75*2+>*48*-
(This may not be a shortest solution)


## Scoring

This is a list of test cases. Test cases are seperated by a new line character. You may write a test script which converts those bunch of numbers to string of tokens, or you can do it by your hand.

Let

• S = size of complete function or program
• O = length of converted strings
• I = size of test cases (In this case, I = 526)

Then your score will be S * (O / I). Sizes are in bytes.

S includes function declarations, #includes, imports, whatever. Test script is not counted.

## Scoring example

Let S is 150.

### Sample Test cases

0
1
5
64
1337


### Sample Output

22-22/588*75*2+>*48*-


In this case, I = 9, and O = 21. So your score is 150 * (21 / 9) = 350.

## Rules

• Standard "loopholes" are forbidden.
• Lowest score wins.
• If there is a tie, smaller code size wins.
• Winner will be selected after three weeks (2014-08-04).

I wrote a validator in Node.js. Put input.txt and output.txt in same directory, and run node validator.js.

And I found two-year-old similar question. But scoring is different (this question includes code size in score), and this question can't use 1. So I hope it's not a duplicate.

• Clarification needed. 1.The requested number must be on top of stack? What if the stack is not empty after popping the result? 2.Division is integer or floating point? – edc65 Jul 14 '14 at 15:24
• @edc65 1. Yes. It must be on the top of the stack. 2. Integer, floor. 53/ = 1, not 2. – Snack Jul 15 '14 at 2:25

function X($){S=Math.sqrt;function J(A){return A.join("")}function M(A,B){return A.length<B.length?A:B}function D(q){var w="",e,r,t,y;for(e=9;e>1;e--){r=~~(q/e);t=r*e-q;if(t==0)y=J([G(r),e,"*"]);else y=J([G(r),e,"*",G(-t),"+"]);if(w=="")w=y;w=M(w,y)}return w}function Q(a){var s=~~S(a),d=a-s*s,f=J([G(s),">*",G(d),"+"]),g;s=Math.ceil(S(a));d=s*s-a;g=J([G(s),">*",G(d),"-"]);return M(f,g)}function G(z){var x,c,v,b,n,m;if(z==0)return"22-";if(z==1)return"22/";if(z>1&&z<10)return""+z;if(z>9&&z<19){x=~~(z/2);c=z-x;return J([x,c,"+"])}for(v=9;v>1;v--){b=~~(z/v);if(b>1&&b<10&&b*v==z)return J([v,b,"*"])}n=S(z);if(~~n==n)return J([G(n),">*"]);return M(D(z),Q(z))}return G($)}

• If you can transform your functions (or some of them) to functional form, meaning that you can transform them such that a function like function F(a){return <lots of code>} becomes possible, you can use the ECMAscript 6 syntax F=(a)=><lots of code>. Furthermore, you have if(z==0)return"22-";if(z==1)return"22/";. I think you can compress that to if(z<2)return["22-","22/"][z];. (If z can be negative, add a &&z>=0.) – tomsmeding Jul 14 '14 at 6:27
• +1 Great job! Golfed a little more and rewrited for EcmaScript 6 your code size is 406. X=$=>(S=Math.sqrt,M=(A,B)=>A.length<B.length?A:B,D=(q,w="",e,r,t,y)=>{for(e=9;e>1;e--)r=~~(q/e),t=q-r*e,y=t?G(r)+e+"*"+G(t)+"+":G(r)+e+"*",w=M(w||y,y);return w}, Q=(a,s=~~S(a))=>M(G(s)+">*"+G(a-s*s)+"+",G(++s)+">*"+G(s*s-a)+"-"), G=(z,v,b)=>{if(z<18)return z<2?"22"+"-/"[z]:z<10?z:"8"+(z-8)+"+";for(v=9;v>1;v--)if((b=~~(z/v))>1&b<10&b*v==z)return""+v+b+"*";return ~~(v=S(z))-v?M(D(z),Q(z)):G(v)+">*"},G($)) – edc65 Jul 15 '14 at 16:10