P8477 "GLR-R3" Spring Equinox
The title looks rather fiendish, consider how to mess it up a bit.
First, one of the simplest ideas, with a board for each pair of solution sets, could be to use the\(n^2\) A board solution, you can tell it's not optimal, but you can get a Sub1 score.
Thriftily, we can put it together at this point if we take one side of each plate and use it to correspond to a solution that only needs to be\(2n\) The boards are solved for Sub1,Sub2 scores.
We found that the above approach has a serious flaw: each board has a side that has not been exposed to the solution, and we considered optimizing here.
think over\(X\) What's the use of not having access to the back of the solution, we put the\(X\) Split evenly into two groups, one\(X_1 = \{x_1,x_2,\cdots,x_{\lfloor \frac{n}{2}\rfloor}\}\)The group is\(X_2=\{x_{\lfloor \frac{n}{2}\rfloor+1},x_{\lfloor \frac{n}{2}\rfloor+2},\cdots,x_n\}\)。
We are now offering each\(X_1\) The boards are all the same as the\(Y\) of the split board to do the experiment, at which point a total of\(n+\lceil\frac{n}{2}\rceil\) classifier for individual things or people, general, catch-all classifier
We find that at this point for the remaining portion we can achieve full coverage by combining the boards, so the total required is\(\lceil\frac{n}{2}\rceil+ n\)By doing the math we can find out just how much\(1\)The first is that it is not possible to pass the Sub3.
We therefore need to optimize this algorithm, and find that we actually don't need a separate board at all for the odd case, and that we can let the post-flip experiments before completing the\(x_n\) cap (a poem)\(Y\) group experiments so that an additional divider can be reduced at the end, and therefore optimized to\(\lfloor \frac{n}{2} \rfloor+n\)It is perfectly possible to pass the Sub3.
Considering how to pass Sub4, we found that in Sub3 the clean board was used to touch the unclean board causing the clean board to be contaminated, and that it would have been better to utilize the clean board.
If we first put\(X\) cap (a poem)\(Y\) are equally divided into three parts, and then first use the\(X_1\) cap (a poem)\(Y_{1\sim 3}\) Paste them all at once, at which point we get\(\frac{n}{3} + n\) A board.
Then a diagram like this will form.
We'll take it out at this point.\(Y_3\) Flip to use the undyed side to dye the gray (there is no plate there for the gray), at which point we are in the\(Y_3\) Here's a direct link to the\(X_1\) The contaminated side of the and\(Y_3\) The contaminated side is put together, at which point the two uncontaminated sides are left to proceed directly to the\(X_2\) together with\(Y\) configuration is sufficient.
After dyeing our\(X_1\) Both sides are contaminated, but easy to spot\(Y_1\) cap (a poem)\(Y_2\) Still untainted.
Let's just put\(Y_2\) flip\(X_3\)This gives us a left-hand side\(X_3\) right side\(Y_2\) of the board.
We've taken what was an uncontaminated side of the\(Y_1\) cap (a poem)\(Y_3\) Just put it together. You'll need it.\(\frac{4n}{3}\) A board that passes Sub4.
Taking a look at Sub5, we see that Sub4 has some very suboptimal areas that could be further optimized, and we can see that in Sub4 our thinking was to make sure that a large area was all blank in order to be able to spell.
But we found out that in fact all we needed was a blank slate.
We split the left side into\(4\) and dividing the right-hand side into\(4\) copies, at this point only for the left side of the\(X_1\) Matching boards, for all of the right side.
thence\(X_1\) together with\(Y_{\{1\sim 4\}}\) Reacting all at once, we put\(X_1\) turn upside down\(X_2\), separated by a blank plate, directly and\(Y_{\{i\sim 4\}}\) All react once.
Then just react in a similar way as in the previous step, which requires\(\frac{n}{4}+n+1\) block, which can be passed through Sub5.
At this point we realized something, eh here we are\(X\) cap (a poem)\(Y\) The total number of points is the same, and we split into two parts for the left-hand side\(X_1,X_2\), for the right side is divided into three parts\(Y_1,Y_2,Y_3\)The following is a list of the most important of these\(X_1\) Matching boards, while\(Y_1,Y_2\) Matchboard.
Let's start with the\(X_1\) cap (a poem)\(Y_1,Y_2\) To carry out the experiment, we added a blank spacer after the test to allow\(Y_1\) Turn over, at this point across the blank divider for the\(Y_3\) For the experiment, one side of the blank divider would be the same as the\(Y_1\) Exposure leads to contamination.
At this point we flip\(X_1\) carry out\(X_2\) The experiment of giving the contaminated side of the blank divider to the\(X_1\) The side that was flipped over and then experimented\(X_2\) together with\(Y\) The experiment, due to the\(Y_2\) There's still one side that's not contaminated, so it just about works.
Available through Sub7.