Display
SRM 189 · 2004-03-31 · by lars2520
SRM 189 · 2004-03-31 · by lars2520 · Math
Problem Statement
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.
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)
{-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" }
35)
{0,1001,2000}
{0,999,2000}
Returns: { "0 0", "501 500", "1000 1000" }
Be sure to round up when the fractional part is .5.
Submissions are judged against all 56 archived test cases, of which 6 are shown here. Case numbers match the judge’s.
Coding Area
Language: C++17 · define a public class Display with a public method vector<string> transform(vector<int> x, vector<int> y) · 56 test cases · 2 s / 256 MB per case