OneMorePoint | Topcoder Archive

Problem Statement

There are some rectangles on a plane. Determine whether a point exists such that above, below, to the left, and to the right of the point lies an interior point of a rectangle. This point must not lie inside or on the boundary of any of the given rectangles.

You are given a String[] rectangles, each element of which is formatted as "X1 Y1 X2 Y2", where X1 and Y1 are the coordinates of the lower left corner of a rectangle, and X2 and Y2 are the coordinates of the upper right corner. You are to return a String, "YES" if such a point exists and "NO" otherwise.

Definition

Class:: OneMorePoint
Method:: interiorPoint
Parameters:: String[]
Returns:: String
Method signature:: String interiorPoint(String[] rectangles)
(be sure your method is public)

Notes

Point A(xa, ya) is above point B(xb, yb) if xa = xb and ya > yb.
Point A(xa, ya) is below point B(xb, yb) if xa = xb and ya < yb.
Point A(xa, ya) is to the left of point B(xb, yb) if xa < xb and ya = yb.
Point A(xa, ya) is to the right of point B(xb, yb) if xa > xb and ya = yb.

Constraints

rectangles will contain between 0 and 50 elements, inclusive.
Each element of rectangles will be formatted as "X1 Y1 X2 Y2".
X1, Y1, X2, and Y2 will each be an integer between 0 and 10000, inclusive, with no extra leading zeros.
X2 will be greater than X1, and Y2 will be greater than Y1.

Examples

```
{"0 0 2 1", "2 0 3 2", "1 2 3 3", "0 1 1 3"}
```
```
Returns: "YES"
```
The given rectangles are shown in grey in this figure. Any white point will meet our requirements.

{"0 0 2 1", "2 0 3 2", "1 2 3 3", "0 1 1 3", "1 1 2 2"}

Returns: "NO"

{"0 0 2 1", "3 0 4 2", "2 3 4 4", "0 2 1 3"}

Returns: "NO"

{"0 0 100 1", "100 1 200 2", "0 0 1 100", "50 50 51 51"}

Returns: "YES"

```
{"1 1 1000 1000"}
```
```
Returns: "NO"
```

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