table of Contents
Contest Info
| Solved | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| 2/6 | O | O | - | - | - | - |
- O through the game
- Ø After the game by
- ! I tried but failed
- - No attempt
Solutions
A. Almost Equal
The meaning of problems:
construct a arranged such that it forms a loop, and any three adjacent numbers and by no more than \ (1 \) .
Ideas:
We have found any adjacent three numbers and differ by no more than \ (1 \) , and the assumption is \ (\?) , Lists the following formula:
\ [\ eqnarray the begin {*} A_1 + + A_3 & A_2 ?? = & \\ a_2 + a_3 + a_4 & = & \\ \ cdots \\ a_ {n - 2} + a_ {n - 1}? + a_n & = & \\ a_n + a_1 + a_2 & = &? \ end {eqnarray *} \]
then there is:
\ [\ the begin {the eqnarray *} | A_1 - A_4 | & \ Leq &. 1 \\ | A_2 - A_5 | & \ Leq &. 1 \\ | A_3 - a_6 | & \ Leq &. 1 \\ | a_4 - a_7 | & \
leq & 1 \\ \ end {eqnarray *} \] then obviously there is \ (a_1, a_4 \) is adjacent to two numbers, \ (A_2, A_5 \) is adjacent to two number, \ (A_3, a_6 \) two adjacent numbers.
So this assignment just fine, and then found \ (n \) is not an even number of times.
B. Shortest Cycle
Meaning of the questions:
There \ (n \) points, any two \ ((i, j) \ ) if \ (i \ & j \ neq 0 \) , then \ ((i, j) \ ) between there is an edge.
Now looking for a minimum ring.
Ideas:
Consider each one, then this is a \ (1 \) is the number of connected components will form a strong, if it is a \ (1 \) the number of points greater than or equal \ (3 \) , then there must be a size \ (3 \) ring.
Otherwise direct violence \ (DFS \) to find the ring can be.