TC716D2T3

墨蓝 2022-06-13 04:57 157阅读 0赞

# 题目 #

Problem Statement

Treeland is a country with n cities, numbered 0 through n-1. Obviously, the topology of Treeland is a tree: there are exactly n-1 bidirectional roads, each connecting two cities in such a way that it is possible to travel from any city to any other city. You are given the description of the road network: the vector p with n-1 elements. For each valid index i, there is a road that connects the cities i+1 and p\[i\]. The distance between two cities is the smallest number of roads you need to use in order to travel from one city to the other. Rabbit Hanako had a trip in Treeland. She started her trip on day 0 in the city x\[0\] = 0. On each of the following m days she chose a city x\[i\] (possibly the same as her current city) and traveled there by using the only direct route. Each day she wrote down the distance she traveled - i.e., on day i she wrote down the distance d\[i\] between the cities x\[i-1\] and x\[i\]. After the trip was over, she constructed a set D that contained all values d\[i\] she wrote down. For example, if d\[1\], d\[2\], …, d\[m\] are \{1, 0, 0, 1, 3, 5, 0\} then the set D will be \{0, 1, 3, 5\}. You know that Hanako’s trip had the form described above, but you don’t know the value m and the values x\[i\]. You are given a vector < int> S. Check whether it is possible that S = D. In other words, check whether there are values m and x\[1\] … x\[m\] such that the set of distances D will contain exactly the same elements as the given vector < int> S. Return “Possible” if such a trip exists and “Impossible” if it does not.  
Definition

Class:  
JumpDistancesOnTreeEasy  
Method:  
isPossible  
Parameters:  
vector , vector  
Returns:  
string  
Method signature:  
string isPossible(vector p, vector S)  
(be sure your method is public)  
Limits

Time limit (s):  
2.000  
Memory limit (MB):  
256  
Stack limit (MB):  
256  
Constraints

p will contain between 1 and 50 elements, inclusive.

For each i, 0 <= p\[i\] <= i.

S will contain between 1 and 50 elements, inclusive.

Each element in S will be between 0 and |p|, inclusive.

For each i, S\[i\] < S\[i+1\].  
Examples  
0)

\{0,1,1,0,4,4\}  
\{2,4\}  
Returns: “Possible”  
The tree is like:

0 
       /   \   1     4
     / \   / \ 2  3  5   6

One of the possible route is: 0, 2, 3, 6, 5. The distance for each day is \{2, 2, 4, 2\} so S = \{2, 4\}.  
1)

\{0,1,1,0,4,4\}  
\{1,2,3,4,5\}  
Returns: “Impossible”  
The maximal possible distance between any two cities is 4, so you will never have 5 in D.  
2)

\{0,1,1,0,4,4\}  
\{3,4\}  
Returns: “Impossible”

\{0,1,2,3,4,0,6,7,8,9\}  
\{2,4,6,8,10\}  
Returns: “Impossible”

4)  
\{0\}  
\{1\}  
Returns: “Possible”

# 题意: #

给你一棵树，所有的边距离为1，让你从根节点出发，经过若干个节点。将每次行走的距离记录下来记为集合D(去重)。现在给出集合S，问是否存在合法的路径使得D=S。

# 思路: #

先跑一遍Floyd得出每个点之间的距离。如果存在某个点能到达的最大距离>=S的最大值，则显然只要到达该点就能满足题意，相反的，如果从根节点出发无法到达这种点，则无解。

# 代码： #

![5952ff225bb98.png][]  
![5952ff2350e00.png][]  
![5952ff8d47f73.png][]

[5952ff225bb98.png]: https://ooo.0o0.ooo/2017/06/28/5952ff225bb98.png
[5952ff2350e00.png]: https://ooo.0o0.ooo/2017/06/28/5952ff2350e00.png
[5952ff8d47f73.png]: https://ooo.0o0.ooo/2017/06/28/5952ff8d47f73.png