DMOPC '15 Contest 7 P4 - Magic - Olympiads Online Judge

DMOPC '15 Contest 7 P4 - Magic

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Points: 10 (partial)

Time limit: 0.6s

Memory limit: 64M

Author:

WallE256

Problem types

Two magicians named Alice and Bob participate in a challenge. The two participate in a race on a circular track split into $K$ $K$ equal-length sectors, determined by the points $P_0, P_1, \dots, P_{K-1}$ $P_{0}, P_{1}, \dots, P_{K - 1}$ .

Alice starts at point $P_a$ $P_{a}$ and runs through $S_a$ $S_{a}$ sectors per second.
Bob starts at point $P_b$ $P_{b}$ and runs through $S_b$ $S_{b}$ sectors per second.

If at any point in the race the distance between the two is less than $D$ $D$ , Alice will use her magic to instantly push Bob a minimum distance such that the two magicians remain at a distance greater or equal to $D$ $D$ . The winning conditions are as follows:

Alice wins if it is possible that sometime during the race, the sum of the shortest distance (running on the circular track) between herself to $P_0$ $P_{0}$ and Bob to $P_0$ $P_{0}$ is prime.
Bob wins if Alice cannot.

In a given scenario, who wins?

Input Specification

The first line of input will contain the integers $K$ $K$ $(0 < K \le 1000)$ $(0 < K \leq 1000)$ and $D$ $D$ $(0 \le D < \dfrac{K}{2})$ $(0 \leq D < \frac{K}{2})$ .
The second line of input will contain the integers $S_a$ $S_{a}$ and $S_b$ $S_{b}$ .
The third line of input will contain the integers $P_a$ $P_{a}$ and $P_b$ $P_{b}$ .

Output Specification

Either Alice or Bob, identifying the winner.

Constraints

$S_a, S_b, P_a, P_b < K$ $S_{a}, S_{b}, P_{a}, P_{b} < K$ .
At least a turn is executed.
In case Alice and Bob are on the same segment, Bob is pushed behind Alice.

Sample Input

Copy

6 2
2 3
0 1

Sample Output

Copy

Alice

Explanation

At the start, the positions of $(\text{Alice}, \text{Bob})$ $(Alice, Bob)$ are $(0,1)$ $(0, 1)$ , but immediately this changes to $(0, 2)$ $(0, 2)$ as Alice pushes Bob. In the second instant, we have the positions $(0+2=2, 2+3=5)$ $(0 + 2 = 2, 2 + 3 = 5)$ , such that the sum of distances to $P_0$ $P_{0}$ is $(6-2)+(6-5)=5$ $(6 - 2) + (6 - 5) = 5$ . Since $5$ $5$ is a prime number, Alice wins.

Comments

0

kobortor commented on April 14, 2016, 12:47 a.m. ← edited →

When the position is $(0, 2)$ $(0, 2)$ , why doesn't she win?

0

bobbotboy commented on April 14, 2016, 12:57 a.m. ← edited →

Constraints: At least a turn is executed.

I think this means that each person must move once (by $S_a$ $S_{a}$ and $S_b$ $S_{b}$ units) before calculamatating whether prime or not.

1

kobortor commented on April 14, 2016, 1:06 a.m.

Then the testcase is weak, I submitted without checking if its the first run and got AC.

1
d commented on April 12, 2016, 9:11 p.m. ← edited →
Copy
100 2 35 2 0 10

Edit: Alice and Bob don't really run in a continuous motion, they teleport $S$ $S$ sectors every second.