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- Problem 2: Cows on Ice [Jelle van den Hooff, 2010]
- Bessie is ice skating on a large frozen lake modelled as a 2-dimensional
- grid with coordinates in the range -1,000,000,000..1,000,000,000.
- N (1 <= N <= 20,000) of the lake's grid cells contain rocks
- (conveniently numbered 1..N). The other cells contain slippery ice.
- Since Bessie is not a very good skater, she traverses the lake's
- cells by pushing herself away from her current position near a rock
- and sliding continuously in the same direction until she hits another
- rock (stopping in the square before she hits the rock, of course).
- Never good with complicated angles, Bessie can push herself only
- straight north, east, south, or west. She can't push herself through
- the rock, of course, and thus generally has only three possible
- directions to move.
- Sliding is not without risks. Bessie must hit a rock or might end
- up sliding for a very long time. She must aim her pushes carefully.
- Consider the situation depicted below; Bessie wants to get to
- location (x=5,y=1), which is east of her current location (. = ice,
- * = rock, B = Bessie, G = goal). If she slides directly to the east,
- she will slide past the location since she can stop only by
- encountering a rock head on. One way to get to (5,1) is the following:
- (a) (b) (c) (d)
- 4 .....*. .....*. .....*. .....*.
- 3 ..*.... slide ..*.... slide ..*.... slide ..*....
- 2 ......* north ..B...* east .....B* south ......*
- 1 .*B..G. ------> .*...G. ------> .*...G. ------> .*...B.
- 0 *....*. *....*. *....*. *....*.
- 0123456
- Bessie could slide north, east, or south in situation (a), but only
- north has a rock for stopping. For situation (b), she can slide
- only east for the same reason.
- For the input, rock i is located at cell X_i,Y_i (-1,000,000,000
- <= X_i <= 1,000,000,000; -1,000,000,000 <= Y_i <= 1,000,000,000),
- and no two rocks occupy the same position. Bessie starts at Bx,By
- (which is next to a rock) (-1,000,000,000 <= Bx <= 1,000,000,000;
- -1,000,000,000 <= By <= 1,000,000,000). Bessie's goal is Gx,Gy
- (-1,000,000,000 <= Gx <= 1,000,000,000; -1,000,000,000 <= Gy <=
- 1,000,000,000). Bessie can always reach the goal one way or another.
- Bessie doesn't mind sliding. However, pushing herself away from a
- rock is very tiring. To prepare her, FJ would like to know the
- minimum number of pushes Bessie needs to do.
- PROBLEM NAME: ice
- INPUT FORMAT:
- * Line 1: Five space separated integers: N, Bx, By, Gx, and Gy
- * Lines 2..N+1: Line i+1 describes a rock location with space
- separated integers: X_i and Y_i
- SAMPLE INPUT (file ice.in):
- 6 2 1 5 1
- 5 4
- 2 3
- 1 1
- 6 2
- 5 0
- 0 0
- OUTPUT FORMAT:
- * Line 1: A single integer that is the minimum number of pushes for
- Bessie to get to her goal
- SAMPLE OUTPUT (file ice.out):
- 3
- **********************************************************************

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