| ||You want to cross a river 10 feet wide and there are 2 stones in the water you can jump on. A few jumps are needed, but your only concern is the longest one. This is obviously the most problematic, so you wish to choose a path that makes this jump as small as possible.
The length of a jump between two stones of coordinates (x1,y1) and (x2,y2) is defined as the Euclidian distance:
sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2))
You will be given a int x and a int y with exactly 2 elements each, representing the coordinates of the stones: (x[i],y[i]) is the location of the i-th stone. The edge of the shore on which you initially stand has an x-value of 0 and could take any y-value. Thus, the minimal distance between the shore and the first stone you jump on is the x-value in the location of that stone. The edge of the other shore has an x-value of 10 and could take any y-value as well.
Return the distance of the longest jump you need to make, rounded to the nearest integer.
|Method signature:||int longestJump(int x, int y)|
|(be sure your method is public)|
|-||You may jump on the 2 stones in any order, or just on one stone.|
|-||x and y will each contain 2 elements.|
|-||All values in x are between 1 and 9, inclusive.|
|-||All values in y are between 0 and 10, inclusive.|
|-||The two stones are not in the same location.|
|-||No actual distance will be more than 1e-4 close to some integer + 0.5.|
|The three stones are arranged in a line, so the strategy is quite simple here: you first jump on the stone at (3,5), then on the stone at (7,5) and you finally reach the other shore at (10,5). The longest jump has a length of 4 feet: from (3,5) to (7,5). |
If you like to play around, you can follow the path (0,5) - (7,5) - (3,5) - (10,5), but this is not optimal since you have to make a jump of 7 feet!
Thus, the correct answer is 4.
|The path you should take is (0,5) - (3,5) - (6,2) - (10,2). Between (3,5) and (6,2) there is a distance of sqrt(3*3 + 3*3) = 4.2426. There are no jumps longer than this and because the answer is rounded to the nearest integer, you should return 4.|
|If you can jump 9 feet at once, chances are you are also a good swimmer ...|
|Only the stone at (3,0) is used in this case. The stone at (8,10) is more than 7 feet away from both the shore and the stone at (3,0). |
|The river can be a good initiation in the triple-jump technique. But you can also skip the stone at (2,5), as you need to take a 6 feet jump anyway.|