Codeforces Round #242 (Div. 2)

11 years ago, # ^ |

+31

Also there is a formula for prefix xors 0 ^ 1 ^ .... ^ k:

int xorUpToK(int k) {
	switch (k % 4) {
		case 0: return k;
		case 1: return 1;
		case 2: return k + 1;
		case 3: return 0;
	}
}

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caioaao

11 years ago, # ^ |

can you explain this formula?

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11 years ago, # ^ |

This is a nice formula for long values of k . To prove it you take

F(3) = 0 ^ 1 ^ 2 ^ 3 = 0

because in binary

0000 ^ 0001 ^ 0010 ^ 0011 = 0000

and operating BIT for BIT

F( 7 ) = F( 3 ) ^ 0100 ^ 0101 ^0110 ^ 0111 = 0000

F( 7 ) = F( 3 ) ^ (01)00 ^ (01)01 ^(01)10 ^ (01)11 = 0000

We can note that () repeats four times , and four is even then (x)^(x)^(x)^(x) = 0 is ever zero

But in this problem is not necesarry because we can precalculate al values <= 10^6

A problem that you really need this formula.

Link to problem

PSDATA: you need know nim numbers before solve Industrial Nim.

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caioaao

11 years ago, # ^ |

Awesome, thanks! I know this problem just needed a simple precomputation, but it's still nice to understand this formula.

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pachon

11 years ago, # ^ |

I think that most coders have checked this post

But without this, you can also do a precomputation :D

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DieAnderen

11 years ago, # ^ |

could you please format your comment to make it more readable. thanks!

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11 years ago, # ^ |

We know that xor is asociative then we can reagrup de expression as p1 xor p2 .... xor p3 * E where E is a new expression and again reagruping :

E = (1 mod 1 xor 2 mod2 ... n mod1 ) xor (1 mod 2 xor 2 mod 2 ... n mod2 ) ....

Then we can get F = 1 mod i xor 2 mod i xor .... n mod i efficiently

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xennygrimmato

11 years ago, # ^ |

Exactly, but what after that? I understood that part, but I could not form a relation afterwards.

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http://codeforces.net/contest/424/submission/6467778

11 years ago, # ^ |

+11

We can get

F = 1 mod i xor 2 mod i xor .... n mod i

if we take every package of size i then we have

F = [ 1 mod i xor 2 mod i xor .... i mod i ]

xor [ (i + 1) mod i xor (i+2) mod i .. (2*i) mod i ] ...

then

F = [ 1 mod i xor 2 mod i xor .... i mod i ] xor [ 1 mod i xor 2 mod i xor .... i mod i ]......

Finally [ ] repeats q = n/i and if q is even there [ ] = 0 else [] = [ 1 mod i xor 2 mod i xor .... i mod i ] and we can consider r = n%i too.

for solve G = [ 1 mod i xor 2 mod i xor .... i mod i ] we can see that is equal to

G = [ 1 xor 2 xor .... i ]

And everthing depends only of G we can precalcalculate with a array.

My Solution

Sorry for my bad english.

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pachon

11 years ago, # ^ |

← Rev. 3 →

I have formed an matrix on a paper of n x n rows represent n and cols mod i

- 0 1 1 1 1 ... 1
- 0 0 2 2 2 ... 2
- 0 1 0 3 3 ... 3
- 0 0 1 0 4 ... 4

as you can see, every column is a cycle of length i, and you can cancel (n/i)/2 cycles, because x ^ x = 0, obviously you will not always have cycles that pairs, so you need the xor of the parts that can't be paired, lets call it rest[i] finally with a for i do ans ^= p[i] ^ rest[i]

my submission 6467752

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Kianoosh

11 years ago, # |

-12

A contest with no successful hacking attempt!

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ivplay

11 years ago, # ^ |

may be there was hack in E. :p

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fyflwc779

11 years ago, # ^ |

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TangSiLoveDingYing

11 years ago, # |

Am I the only person who are confused with problem E's sample case?

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kavishrox

11 years ago, # |

Can anyone tell me why my solution gave WA ? I did precomputation of XORs and my complexity is also good. 6468572

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pachon

11 years ago, # ^ |

← Rev. 3 →

can you at least explain a bit your idea? and ull was not necessary

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HellKitsune

11 years ago, # ^ |

You had the right idea of precalculating xors, but what you're doing on each iteration is not right. Try this simple test:

4
0 0 0 0

The answer should be 2.

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kavishrox

11 years ago, # ^ |

Yeah . Silly mistake on my part , I took mod as simply the difference and it failed on indices like 4%2 and 4%4. .

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ivplay

11 years ago, # |

what was the idea of D?

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11 years ago, # ^ |

Bruteforce and TernarySearch , my friend.

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6467987 6468437 6468850 6467987

11 years ago, # ^ |

Integer ternary search Oo

You crazy person...

P.S. I thought, we can't avoid using set in this problem. Such a surprise.

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mc_mosa

11 years ago, # ^ |

← Rev. 2 →

Actually the $\text{[math]}$ solution passes in time! >.>

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11 years ago, # ^ |

This solution is wrong. Ternary search doesn't work here.

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11 years ago, # ^ |

6469423

Well, but his solution is AC.

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11 years ago, # ^ |

And how do you think what does it mean? :)

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11 years ago, # ^ |

-6

Weak tests, round should be unrated :Ъ

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mc_mosa

11 years ago, # ^ |

Not really, I believe his solution is correct.

His ternary search function is a function of the absolute difference between both times, which is clearly a bitonic function in this problem.

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11 years ago, # ^ |

Hey man i think that you are wrong , Ternary search works because my function f is crecient then g = abs( f — t ) is like a parabola then i need to calculate the minimum.

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11 years ago, # ^ |

You fix left, right and top borders of the track and then find the bottom border by binary search. Let's see what bottom borders we can create.
What happens if all odd rows are decreasing (a[i][j] > a[i][j+1]) and all even rows are increasing (a[i][j] < a[i][j+1])?

If we consider the times needed to go through the parts of track built at these rows, they will be like {d*tUp, d*tDown, d*tUp, d*tDown, ...} where d is the width of the track and tUp and tDown are numbers from the input. It's not a crescent sequence, is it? Of course we also have increasing left and right parts, but they cannot affect so much as the bottom part affects the function (e.g. if the width is very large).

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11 years ago, # ^ |

Oh nice counterExample , maybe in random cases my solution works well:)

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alv-r-

11 years ago, # ^ |

I thought this during the contest, so I went for the O(N^4) solution :(

Still, in the editorial (http://codeforces.net/blog/entry/11944) the author says his solution is O(N^3 * logN).

As far as I've seen, people have used n-ary search to do this, but there are a lot of cases where that would fail, cause you can't guarantee that it's increasing or decreasing at any point.

Take dalex' example with odd decreasing/even increasing rows, you can actually have any random configuration of rows that are all increasing or decreasing and this would make any n-ary search solution fail, as far as I can understand.

So, any ideas of how to achieve the O(N^3 * log N) solution with any other method? (Or is there something that I'm missing and a n-ary search actually works?)

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choke

11 years ago, # ^ |

← Rev. 2 →

champero detected !! :P, Nice problem.

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afrizal

11 years ago, # |

Any editorial?

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JuanMata

11 years ago, # ^ |

here it is.

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Lazzaro

11 years ago, # |

Could anyone help figure out what the wrong is in my two solution of Problem C? 6466959 and 6468449

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xennygrimmato

11 years ago, # |

In Problem C, upper limit of 'p' was 2 x 10**9. However, solutions that took 'p' as int passed.

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JuanMata

11 years ago, # ^ |

the upper limit of int is 2147483647, which is more than 2e9. so ofcourse it will pass!

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OpalDshawn

11 years ago, # |

I am wondering if this algorithm is correct or not. http://codeforces.net/contest/424/submission/6470517 He enums all the point on the top-left , and use trinary-search twice to find the point on the bottom-right. In my view , this solution is incorrect. Just can not find a data challenge this code ? Thanks

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DarkZero

11 years ago, # |

Could anyone share your idea of problem D? I was confused with the problem for more than one hour, sticking to the O(n^4) algorithm and cannot find a way to optimize it....

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cristb

11 years ago, # |

Hello.

Can anyone tell me why submission 6465131 gets Compilation Error on Codeforces, as it compiled perfectly on my local machine ( Linux GCC 4.8.2, though I doubt there are any great differences between this and 4.7) ? Link: http://codeforces.net/contest/424/submission/6465131

Thanks.

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