EDITORIAL: In order to protect copyright is Rui topic, here and hold surface title, write only problem solution.
"This should be the first time in history, OI is Rui Poor Pobai game."
"This shows positive Core training to people more and more."
"I can not understand the negative feedback, because before the race there were more than \ (40 \) a bad review of."
Tianqi pigeon pigeon nb!
- A
"This problem of standard process is linear, but why not have a \ (5 \ times 10 ^ 6 \) ? Because spj to take a \ (\ log \) , so that the T."
\(100pts:\)
By meterObserved that the solution if and only if \ (\ SUM K ^ {-} a_i \ GEQ. 1 \) .
Without loss of generality, we can prove that \ (\ sum k ^ {- a_i} = 1 \) solvable time.
In order for \ (\ SUM K ^ {-} = a_i. 1 \) , we found that the final sorted \ (K \) number must be equal (extra number can be deleted, without affecting the result).
\ (K \ K ^ CDOT {-} = K ^ {a_i - (a_i-1)} \) , so the \ (K \) a \ (a_i \) into \ (1 \) a \ (a_i- 1 \) total contribution unchanged.
When implemented, can be \ (K \) a \ (I \) is converted into \ (1 \) a \ (I-1 \) , to give a final \ (0 \) is solvable.
Greedy can, after ordering achieve excellent output linear program can do.
- B
\(42pts:\)
Because of \ ([l_2, r_2] \ ) disjoint, and discovery interval length does not exceed \ (n-\) , to violent disjoint-set.
Complexity \ (O (n-\ CDOT \ n-Alpha) \) .
\(100pts:\)
Still due to \ ([l_2, r_2] \) disjoint, for each \ ([l_2, r_2] \) to \ ([l_1, r_1] \ ) even edge, found that each \ ([l_2, r_2 ] \) only have one father, the formation of a natural tree.
For each insertion and asked his father to jump all violence in the trees, you can jump to the root node with the process.
The only problem is that if \ ([l_1, r_1] \ ) and \ ([l_2, r_2] \ ) intersect, you may need to skip the entire range of violence.
If more than half of the intersection of two sections, the section must be circular, it can be of circular section modulus.
Complexity \ (O (m ^ 2) \) .I learned silly disjoint-set
- C
Obviously FIG Each communication block should have an even number of sides, and each point is odd degrees.
Problem is equivalent to find \ (\ frac {n} 2 \) chains to cover all edges, endpoints are required to cover each edge point and do not intersect. Also each strand are even required.
Consider how the restrictions do not have an even number, apparently to build a virtual point you can run Euler tour.
\(10pts:\)
For the complete graph, found that only \ (4 | n \) when solvable.
Consider each addition \ (4 \) points, the internal structure is clear, and before the \ (4n \) points are even side is a degree even number of bipartite graph, well done.
\(65pts:\)
Explosive search,I do not know why run so fast。
\(100pts:\)
Consider obtaining a \ (\ frac m2 \) chain covering both strands. Assumed to have been obtained, we built a new map, if there is a chain connected directly \ ((x, y) \ ) , then even the new figure in a \ ((x, y) \ ) side. Apparently the new figure does not change the degree of parity, running Euler tour in a new figure, finally open to each chain.
Consider how to find the chain cover.
Build a dfs tree in Ituri, the non-tree edge must be atavistic side.
For each edge point in a shallow depth consideration, when such a node to the remaining edges associated with it must contain only: its son and the edge between it and its subtree connected back to its Zu side, it is connected to his father's side. For the first two categories edge matching, if there are remaining on the match fell to the father's side. Since an even number of sides, the root node will be able to match.
Written on the back:
This is also the most volatile evaluate the game is Rui history. While some people manipulate eventually turned into a negative, but still in the middle reaches \ (+ 30 \) , and I am honored to record this moment.
The reason is very interesting, and very sad.
"Due to the small K injuries , so many friends to comfort him."
"Little K was busy recovery server a data loss."
"I have a small K \ (n-\) a working chamber , which \ (n-\) with studio between \ (m \) path connected to one another."
What little K represent? I believe we already know.
This is my first time on this question generated heartfelt tribute to the topic and people.