P2058 - [USACO 2022 February Contest Silver] Problem 2. Robot Instructions

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提交：1 解决：1

Bessie is learning how to control a robot she has recently received as a gift.

The robot begins at point on the coordinate plane and Bessie wants the robot to end at point . Bessie initially has a list of () instructions to give to the robot, the -th of which will move the robot units right and units up (or left or down when and are negative, respectively).

For each from to , help Bessie count the number of ways she can select instructions from the original such that after the instructions are executed, the robot will end at point .

The first line contains

N

. The next line contains

x_{g}

and

y_{g}

, each in the range

- 10^{9} \dots 10^{9}

. The final

N

lines describe the instructions. Each line has two integers

x_{i}

and

y_{i}

, also in the range

- 10^{9} \dots 10^{9}

It is guaranteed that and for all .

N

lines, the number of ways Bessie can select

K

instructions from the original

N

for each

K

from

1

N

In this example, there are six ways Bessie can select the instructions:

(-2,0) (3,0) (4,0) (0,10) (0,-10) (0,10) (1 2 3 5 6 7)
(-2,0) (3,0) (4,0) (0,10) (1 2 3 5)
(-2,0) (3,0) (4,0) (0,10) (1 2 3 7)
(5,0) (0,10) (0,-10) (0,10) (4 5 6 7)
(5,0) (0,10) (4 5)
(5,0) (0,10) (4 7)

For the first way, the robot's path looks as follows:

(0,0) -> (-2,0) -> (1,0) -> (5,0) -> (5,10) -> (5,0) -> (5,10)

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2058: [USACO 2022 February Contest Silver] Problem 2. Robot Instructions

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