Problem:
Exploring Caves

There are many caves deep in mountains found in the countryside. In legend,
each cave has a treasure hidden within the farthest room from the cave's
entrance. The Shogun has ordered his Samurais to explore these caves with
Karakuri dolls (robots) and to find all treasures. These robots move in the
caves and log relative distances and directions between rooms.

Each room in a cave is mapped to a point on an integer grid (x, y >= 0).
For each cave, the robot always starts from its entrance, runs along the grid
and returns to the entrance (which also serves as the exit). The treasure in
each cave is hidden in the farthest room from the entrance, using Euclid
distance for measurement, i.e. the distance of the room at point (x, y) from the
entrance (0, 0) is defined as the square root of (x*x+y*y). If more than one
room has the same farthest distance from the entrance, the treasure is hidden in
the room having the greatest value of x. While the robot explores a cave, it
records how it has moved. Each time it takes a new direction at a room, it notes
the difference (dx, dy) from the last time it changed its direction. For
example, suppose the robot is currently in the room at point (2, 4). If it moves
to room (6, 4), the robot records (4, 0), i.e. dx=6-2 and dy=4-4. The first data
is defined as the difference from the entrance. The following figure shows rooms
in the first cave of the Sample Input. In the figure, the farthest room is the
square root of 61 distant from the entrance.

Based on the records that the robots bring back, your job is to determine the
rooms where treasures are hidden.

Input

In the first line of the input, an integer N showing the number of
caves in the input is given. Integers dxi and
dyi are i-th data showing the differences between
rooms. Note that since the robot moves along the grid, either
dxi or dyi is zero. An integer pair
dxi = dyi = 0 signals the end of one cave's
data which means the robot finished the exploration for the cave and returned
back to the entrance. The coordinates are limited to (0,0)-(1000,1000).

Output

Print the position (x, y) of the treasure room on a line for each cave.

Sample Input

3
1 0
0 1
-1 0
1 0
0 5
-1 0
0 -1
5 0
0 1
0 -1
1 0
0 -4
-3 0
0 3
2 0
0 -2
-1 0
0 1
0 -1
1 0
0 2
-2 0
0 -3
3 0
0 4
-4 0
0 -5
-2 0
0 0
1 0
-1 0
0 0
2 0
0 1
-1 0
0 1
-1 0
0 -2
0 0

Output for the Sample Input

6 5
1 0
2 1

Solution in JAVA (judge verdict: Accepted)

import java.util.*;
import java.lang.Math;
class Main
{
    static int maxX;
    static int maxY;
    static int maxLength;
    final static int startX=0;
    final static int startY=0;
    
    public static void main(String[] args)
    {
	int dx,dy,length;
	int currentX,currentY;
	Scanner sc=new Scanner(System.in);
	int attend=sc.nextInt();
	for(int i=0;i<attend;i++){
	    currentX=startX;
	    currentY=startY;
	    maxLength=0;maxX=0;maxY=0;
	    while(true){
		dx=sc.nextInt();
		dy=sc.nextInt();
		currentX+=dx;
		currentY+=dy;
		if(dx==startX&&dy==startY)break;

		length=currentX*currentX+currentY*currentY;

		if(maxLength==length){
		    if(maxX<currentX){
			maxX=currentX;
			maxY=currentY;
		    }
		}
		else if(maxLength<length){
		    maxLength=length;
		    maxX=currentX;
		    maxY=currentY;
		}
	    }
	    System.out.println(maxX+" "+maxY);
	}
	
    }
    
}