### Problem Statement

We want to display a scatterplot in a 1000x1000 window. However, our points may have x and y values anywhere between -1,000,000,000 and 1,000,000,000. So, in order to display our data in a reasonable fashion, we want to make it fit in the window. Your task is, given the x and y values of the data, scale and translate the data so that the lowest x value is 0, and the highest is 1000. Do the same thing for the y values, being careful to preserve the relative distances in both the x and y directions. For example, if x = {-100, 0, 50, 100}, then it should be changed to {0,500,750,1000}. Note that changing the points may result in non-integral values, which should be rounded to the nearest integer (.5 rounds up). The return value should be a String[], each of whose elements is formatted as "<x> <y>", where <x> and <y> are the scaled and translated values of the corresponding elements of the input. <x> and <y> should be separated by exactly one space and have no extra leading zeros.

### Definition

 Class: Display Method: transform Parameters: int[], int[] Returns: String[] Method signature: String[] transform(int[] x, int[] y) (be sure your method is public)

### Constraints

-Each element of x and y will be between -1,000,000,000 and 1,000,000,000, inclusive.
-x will contain at least two distinct values.
-y will contain at least two distinct values.
-x and y will contain the same number of elements.
-x and y will each contain between 2 and 50 elements, inclusive.

### Examples

0)

 `{-100, 0, 50, 100}` `{-100, 0, 50, 100}`
`Returns: { "0 0",  "500 500",  "750 750",  "1000 1000" }`
 If we translate all the points +100 in both the x and y directions, and then scale all the coordinates up by a factor of 5, we find that they meet our requirements.
1)

 `{0,2000,1}` `{0,2001,1}`
`Returns: { "0 0",  "1000 1000",  "1 0" }`
2)

 `{-1000000000,1000000000,500000,499999}` `{-1000000000,1000000000,500000,499999}`
`Returns: { "0 0",  "1000 1000",  "500 500",  "500 500" }`
3)

 `{-53,652,-6132,673,74,-473,373,736363,234,234,234}` `{-6464,36464,-43,373,363,-37633,2022,-644,2520,2520,2520}`
```Returns:
{ "8 421",
"9 1000",
"0 507",
"9 513",
"8 513",
"8 0",
"9 535",
"1000 499",
"9 542",
"9 542",
"9 542" }```
4)

 `{0,1001,2000}` `{0,999,2000}`
`Returns: { "0 0",  "501 500",  "1000 1000" }`
 Be sure to round up when the fractional part is .5.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2295

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4765&pm=2295

lars2520

Math