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  • Their fall from the tower sends Ethic and Hedge

  • spinning into the rapids of a river of pure energy.

  • This torrent flows from the Bradbarrier all the way to Huxenborg.

  • There an entire city's worth of factories

  • build the robots and house the Node of Memory,

  • the last of the three powerful artifacts Ethic needs to collect.

  • After a long day and a longer night

  • they find themselves in a canyon of brick and steel.

  • Just when they're about to reach the end of the line,

  • a rope catches them.

  • Their savior, Lemma, has been waiting for them.

  • When Ethic claimed the Node of Creation from the forest tower,

  • radios all across the land came back to life.

  • Adila, the resistance leader, immediately started contacting her allies,

  • none more important than Lemma,

  • a brilliant scientist working from within Huxenborg to bring down the machines.

  • Unfortunately, the radios also tipped off the robots.

  • So they've taken defensive measures

  • to protect the final artifact in its home in the very heart of the city.

  • There's only one way to get there: the gauntlet of forking paths.

  • It's a deadly series of luminous conveyors that wind underneath Huxenborg.

  • Starting from the current position,

  • each section runs for a distance, then splits in two.

  • Every branch does the same thing, again and again.

  • There are thousands of branches.

  • Only one path leads to the artifact; all the others to destruction.

  • Fortunately, the Node of Creation has granted Hedge a strange power:

  • he can produce slightly smaller versions of himself.

  • Each version can do only two things: radio information back to its parent,

  • and produce slightly smaller versions of itself

  • which can do the same two things, as can their children,

  • for as many generations as needed.

  • A patrol is closing in on their position, so Ethic's time is limited.

  • What instructions should she give Hedge to find the one safe path?

  • Pause the video to figure it out yourself.

  • Hint in 3

  • Hint in 2

  • Hint in 1

  • Programmers have an elegant tool in their arsenal called recursion.

  • Recursion is when you have a set of instructions that refers back to itself.

  • It's like using a word in its own definition,

  • except where that's frowned upon, this is incredibly effective.

  • Recursion involves repetition, but in a different way than loops.

  • Where a loop takes one action and repeats it again and again,

  • recursion will start an action, and before it's finished, use it again,

  • and before that's finished, use it again, and so on.

  • It keeps doing this until some end state is reached.

  • It then passes the information back up, layer after layer,

  • until it reaches the top and ends the cycle.

  • Recursion is ideal for problems that involve self-similarity,

  • where each part resembles the larger whole.

  • Like, for example, a deadly defense system designed to end any person or thing

  • who dares tread upon it.

  • Pause the video to figure it out yourself.

  • Solution in 3

  • Solution in 2

  • Solution in 1

  • Ethic's conundrum seems sprawling on the surface,

  • but there's a remarkably simple solution to it using recursion.

  • In order to find it, let's first look at the simplest version of this puzzle:

  • what if the entire maze were just two paths?

  • If Hedge copies himself, the copy that goes the wrong way will be destroyed.

  • So the other one, which will reach the artifact,

  • can radio back the path it took, and then no matter which way is correct,

  • that's the answer Hedge will receive.

  • This is called the "base case" of the recursion.

  • Now, suppose the maze branches twice from the starting point,

  • and at every intersection, Hedge's copies

  • let's call them Twig 1 and Twig 2—

  • make more copieslet's call them Leaves 1 through 4.

  • Three Leaves will be destroyed.

  • The one that reaches the artifact will radio back the right answer,

  • but only to its parent.

  • So if Twig 1 or 2 is waiting at an intersection

  • and hears something over the radio,

  • that's the right way to go to the artifact from where it is.

  • To tell Hedge the right answer from his perspective,

  • the Twig should say which way it went,

  • and then the route it just heard over the radio.

  • This same process will work no matter how many times the maze branches.

  • Any answer a copy hears on the radio

  • must be the way to the control room from its location,

  • and if it then adds the branch it took,

  • it can tell its parent how to get there as well.

  • We can sum up the instructions in an action called Pathfinder

  • that every version of Hedge will follow:

  • 1. If you've reached the artifact,

  • radio to your parent whether you got there by going left or right.

  • 2. When you reach an intersection, move off the conveyor

  • and send new copies down the left and right paths.

  • Have them each run Pathfinder.

  • This is where recursion comes in,

  • and this may happen many times before the last instruction triggers, which is:

  • 3. If you hear anything over the radio, you should radio to your parent

  • whether you got to your spot by going left or right,

  • then repeat everything you just heard.

  • Pathfinder is an example of what programmers call functions,

  • subroutines, or procedures.

  • No matter the terminology, the idea is the same

  • it's a set of instructions given a label so that it can be easily reused

  • perhaps even by itself.

  • And in our case that'll work perfectly

  • an entire network of paths mapped using just three instructions.

  • So here's what happens.

  • By the time the patrol rounds the corner, Ethic and Lemma have improvised disguises.

  • They try to confuse the bots long enough to buy Hedge time.

  • Finally, Hedge's radio crackles to life with a series of directions.

  • The three dive onto the conveyor and flee for their lives,

  • with a squadron of enforcer bots in hot pursuit.

Their fall from the tower sends Ethic and Hedge

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B1 TED-Ed hedge recursion radio artifact ethic

The Gauntlet | Think Like A Coder, Ep 8

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    林宜悉 posted on 2020/07/03
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