HBC24005HappyTriangle[USACO 2016 Jan B]Angry Cows题解

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Bessie the cow has designed what she thinks will be the next big hit video game: "Angry Cows". The premise, which she believes is completely original, is that the player shoots a cow with a slingshot into a one-dimensional scene consisting of a set of hay bales located at various points on a number line; the cow lands on a hay bale with sufficient force to cause the bale to explode, which in turn might set of a chain reaction that causes additional nearby hay bales to explode. The goal is to use a single cow to start a chain reaction that detonates as many hay bales as possible.There are N hay bales located at distinct integer positions x1,x2,…Please determine the maximum number of hay bales that can explode if a single cow is launched onto the best possible hay bale to start a chain reaction.

Bessie the cow has designed what she thinks will be the next big hit video game: "Angry Cows". The premise, which she believes is completely original, is that the player shoots a cow with a slingshot into a one-dimensional scene consisting of a set of hay bales located at various points on a number line; the cow lands on a hay bale with sufficient force to cause the bale to explode, which in turn might set of a chain reaction that causes additional nearby hay bales to explode. The goal is to use a single cow to start a chain reaction that detonates as many hay bales as possible. There are N hay bales located at distinct integer positions x1,x2,…,xN on the number line. If a cow is launched onto a hay bale at position x, this hay bale explodes with a "blast radius" of 1, meaning that any other hay bales within 1 unit of distance are also engulfed by the explosion. These neighboring bales then themselves explode (all simultaneously), each with a blast radius of 2, so these explosions may engulf additional yet-unexploded bales up to 2 units of distance away. In the next time step, these bales also explode (all simultaneously) with blast radius 3. In general, at time t a set of hay bales will explode, each with blast radius t. Bales engulfed by these explosions will themselves explode at time t+1 with blast radius t+1, and so on. Please determine the maximum number of hay bales that can explode if a single cow is launched onto the best possible hay bale to start a chain reaction.

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标签： HBC24005HappyTriangle[USACO 2016 Jan B]Angry Cows题解