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  • Ethic and Hedge are on the ground floor of a massive tower.

  • Barriers of energy separate them from their quest’s second goal:

  • the Node of Creation.

  • To reach it, Ethic must use three energy streams to climb the tower.

  • As soon as she steps forward a timer will begin counting down from 60 seconds.

  • At the back of the room there’s a basin made of invisible towers

  • that can hold energy between them.

  • After one minute, a torrent of energy will pour down from above,

  • filling one unit at a time,

  • with a force field preventing it from spilling out the front or back.

  • During the 60 calm seconds,

  • Ethic and Hedge must decide exactly how many units of energy will fall.

  • For each of the three challenges,

  • they must choose the amount that will fill the basin exactly.

  • If they do so, the energy will propel them further upwards.

  • But if they get the amount at all wrong, the energy lift will fail,

  • dropping them.

  • Diagrams on the walls illustrate some examples.

  • This configuration will capture exactly 2 units of energy.

  • This configuration will capture 4— 3 here, and 1 here.

  • And this one will also capture 4,

  • because any energy on the right would spill out.

  • The energy will rain down in such a way

  • that itll only overflow if there’s no space that could hold it.

  • Hedge can make one tower of blocks visible at a time and count how tall it is,

  • but he can’t look at the whole structure all at once.

  • How does Ethic program Hedge to figure out

  • exactly how much energy each basin can hold?

  • Pause now to figure it out for yourself.

  • Here’s one way of thinking about what’s happening:

  • each unoccupied cell will hold energy

  • if and only if there is a wall eventually to its left,

  • and a wall eventually to its right.

  • But it would take a long time for Hedge to check this for each individual cell.

  • So what if he were to consider a whole column of blocks at a time?

  • How many units of energy can this hold, for instance?

  • Pause now to figure it out for yourself.

  • Let’s analyze the problem by looking at our example.

  • There are 5 columns of blocks here.

  • The leftmost one can’t hold any energy, because there’s nothing higher than it.

  • The 2nd stack can have 3 units above it,

  • as they would be trapped between these two 4 block stacks.

  • We get 3 units by taking the height where the energy would level off— 4,

  • and subtracting the height of the stackso that’s 4 minus 1.

  • The 3rd stack is similar— 4 to the left, 4 to the right, and it’s 3 high,

  • so itll hold 4 minus 3 equals 1 unit.

  • The 4th stack and 5th stacks have nothing higher than them to the right,

  • so they can’t hold any energy.

  • We can adapt this idea into an algorithm.

  • Considering one column at a time as the point of reference,

  • Hedge can look to the left stack by stack to find the height of the tallest one,

  • look to the right to find the height of the tallest one,

  • and take the smaller of the two as the height the energy can fill up to.

  • If the result is higher than the column in question,

  • subtract the height of the original column,

  • and the result will be the number of units that column can hold.

  • If it's equal to or below the level of the column in question,

  • the energy would spill off.

  • Hedge can apply that to an entire basin with a loop

  • that starts on the left-most column and moves right, one column at a time.

  • For each column, hell run the same stepslook all the way left for the tallest,

  • do the same to the right, take the lower height of the two,

  • subtract the original column height,

  • and increase the grand total if that number is positive.

  • His loop will repeat as many times as there are columns.

  • That will work, but itll take a long time for a large basin.

  • At every step Hedge repeats the action of looking left and looking right.

  • If there are N stacks, hell look at all N stacks N times.

  • Is there a faster way?

  • Here’s one time saver: before doing anything else,

  • Hedge can start on the left,

  • and keep a running tally of what the highest stack is.

  • Here that would be 2, 2 again, since the first was higher,

  • then 4, 4, 4.

  • He can then find the highest right-most stacks

  • by doing the same going right-to-left: 1, 3, 4, 4, 4.

  • In the end hell have a table like this in his memory.

  • Now, Hedge can take one more pass to calculate how much energy there will be

  • above every stack with the same equation from before:

  • take the smaller of the stored left and right values,

  • and subtract the height of the current tower.

  • Instead of looking at N stacks N times, hell look at N stacks just 3 times

  • which is what’s called linear time.

  • There are ways to optimize the solution even further,

  • but this is good enough for our heroes.

  • Ethic and Hedge work as one.

  • The first cascade is a breeze, and they rise up the tower.

  • The second is a little tougher.

  • The third is huge, with dozens of stacks of blocks.

  • The timer ticks down towards zero, but Ethic’s program is fast.

  • She gets the wheel in position just in time,

  • and the energy lifts them to the Node of Creation.

  • Like the first, it reveals a vision: memories of years gone by.

  • The world machine changed everything,

  • and Ethic, in her position as chief robotics engineer,

  • grew troubled by what she saw.

  • When the Bradbarrier went up to keep the people in,

  • she knew something was seriously wrong.

  • So she created three artifacts

  • with the ability to restore people’s power, creativity, and memory,

  • and smuggled them to three communities.

  • Before she could tell people how to use them,

  • the government discovered her efforts and sent bots to arrest her

  • and the other programmers.

  • The last thing Ethic used the world machine to create

  • was a robot that would protect the ancient device

  • from the forces of ignorance by enclosing it in a giant maze.

  • She named her creation Hedge.

  • Without warning, the energy lift flickers, then fizzles out.

Ethic and Hedge are on the ground floor of a massive tower.

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Epiphanyの塔|Think Like A Coder, Ep 7 (The Tower of Epiphany | Think Like A Coder, Ep 7)

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    林宜悉 に公開 2021 年 01 月 14 日
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