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  • Dawn and the train are both breaking when Ethic and Hedge arrive in the woods.

  • The adventurers have recovered the first artifact

  • the Node of Power

  • and have come to the 198forest in search of the second.

  • Here they're welcomed by the director of the colony, Octavia.

  • She established this treehouse sanctuary

  • after the robots freed everyone from having to work.

  • It was meant to be a haven where people could follow their passions,

  • take up crafts, and find fulfillment.

  • Which they didat first.

  • Some years ago everyone forgot the point.

  • They abandoned arts and crafts

  • and instead just painted and exhibited pictures of themselves

  • over, and over, and over.

  • The location of the second artifact is no secret;

  • it's in a tower, guarded by a garrison of bots,

  • a bottomless ravine, and who knows what other traps.

  • As soon as the tower went up with the node inside,

  • human communication across the land went dark.

  • Octavia's been after it for years,

  • but try as she might, the defenses thwart her.

  • In order to even get to the tower, the team will need a distraction.

  • Octavia has an idea:

  • stir up the people through some well-intentioned vandalism.

  • The residents' paintings are all squares that come in different sizes,

  • all an odd number of pixels across.

  • Helper-bots pick up the finished portraits

  • and hang them in public places for everyone to admire.

  • There's a slim margin of time when Hedge can access the paintings.

  • If he were to deface each one with an X,

  • the people would blame the helper-bots,

  • creating just the distraction the team needs.

  • If only it were so easy.

  • Hedge can't just paint an X—

  • his painting processor requires very specific instructions.

  • Treating the paintings as square grids,

  • he can fill in one pixel, or little square, at a time.

  • He can move forwards and make 90 degree turns over the canvas,

  • but can't move diagonally.

  • How does Ethic program Hedge to paint an X over each portrait?

  • Pause now to figure it out for yourself.

  • Here's a hint.

  • Try drawing a square grid like this,

  • and simulating Hedge's path over it.

  • What patterns can you find to guide him?

  • Pause now to figure it out for yourself.

  • The challenge here is to craft a set of instructions

  • that will work for any square grid.

  • Fortunately, one of the strengths of programming

  • is the flexibility to solve not just one problem,

  • but a whole class of them all at once.

  • It often helps to start with one case, and work towards the general.

  • Let's say we had this square.

  • Hedge can measure the length of its sides and store that number as a variable.

  • Now, what we need is a plan for how Hedge will paint an X,

  • pixel by pixel.

  • There's more than one right answer for how to do this;

  • let's look at two.

  • First, what if Hedge went row by row, like a typewriter?

  • If it's a 9 pixel by 9 pixel painting,

  • in the first row he'd paint, skip 7, and then paint again.

  • In the second row he'd skip the first, paint, skip 5, and paint.

  • And so on.

  • The pattern here is that for each row the pixels skipped at the beginning

  • go up by one,

  • and the pixels skipped in the middle go down by 2.

  • Things get more complicated when Hedge reaches the center.

  • Here there's a row with just one pixel painted.

  • Then the whole thing reverses

  • the number of pixels skipped goes down by one each time on the left,

  • and up by two each time in the middle.

  • Instructing Hedge to do this with a series of loops will work

  • and is a perfectly fine solution.

  • The main drawback is that this requires quite a bit of logic

  • knowing what to do in the middle, when to reverse the process,

  • and exactly how to reverse it.

  • So how might we approach this

  • so that the logic remains consistent from start to finish?

  • The key insight is to look at a grid as a series of concentric squares.

  • Each square follows the same pattern

  • painted pixels in the corners, and unaltered pixels in between.

  • So if we can figure out a way to paint one nested square,

  • transition to the next, and repeat, we can paint them all.

  • Painting the outermost one is easy.

  • Start in a corner and paint that pixel.

  • If we call the length of the painting n,

  • fly forward n minus 1 spaces.

  • Paint another pixel, and turn right.

  • Now do the whole thing againand again.

  • Now move forward one less space, turn right, fly forward once,

  • and Hedge will be in the next concentric square

  • and ready to repeat the whole process.

  • Each square is n minus 2 pixels smaller than the last in length and width,

  • and we can follow this spiral pattern all the way to the center

  • with a loop and a variable that tracks how far Hedge should fly.

  • Is one of these methods better than the other?

  • It really depends on what you value.

  • The strength of the spiral is the simplicity of finding a pattern

  • and reusing the same logic from start to finish.

  • The advantage of the typewriter approach

  • is that it's a more generalized solution,

  • meaning it can be adapted much more simply to fill in any pattern.

  • For Ethic's sake, either will do just fine.

  • So here's what happens.

  • Hedge rapidly defaces all of the portraits.

  • And within moments

  • cries of anguish break out all over the forest.

  • The garrison guarding the tower abandon their posts

  • to calm the agitated people,

  • and Ethic, Hedge, and Octavia slip through

  • and nearly slip into the depths of the gorge

  • standing between them and the tower.

Dawn and the train are both breaking when Ethic and Hedge arrive in the woods.

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B1 US TED-Ed hedge paint square pixel octavia

The Artists | Think Like A Coder, Ep 5

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    ally.chang posted on 2020/02/26
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