SRM 591 1A 2014.5.26

SRM 591 1A 2014.5.26

DIV1

250

Problem Statement
	Manao is working in the Tree Research Center. It may come as a surprise that the trees they research are not the ones you can see in a park. Instead, they are researching special graphs. (See Notes for definitions of terms related to these trees.) Manao's daily job is reconstructing trees, given some partial information about them. Today Manao faced a difficult task. He needed to find the maximum possible diameter of a tree, given the following information: Some vertex in the tree is called V. The distance between V and the farthest vertex from V is D. For each x between 1 and D, inclusive, Manao knows the number of vertices such that their distance from V is x. You are given a vector <int> cnt containing D strictly positive integers. For each i, the i-th element of cnt is equal to the number of vertices which have distance i+1 from V. Please help Manao with his task. Return the maximum possible diameter of a tree that matches the given information.
Definition
	Class: TheTree Method: maximumDiameter Parameters: vector <int> Returns: int Method signature: int maximumDiameter(vector <int> cnt) (be sure your method is public)
Limits
	Time limit (s): 2.000 Memory limit (MB): 64
Notes
-	A tree is a connected graph with no cycles. Note that each tree with N vertices has precisely N-1 edges.
-	The distance between two vertices of a tree is the smallest number of edges one has to traverse in order to get from one of the vertices to the other one.
-	The diameter of a tree is the maximum of all pairwise distances. In other words, the diameter is the distance between the two vertices that are the farthest away from each other.
Constraints
-	cnt will contain between 1 and 50 elements, inclusive.
-	Each element of cnt will be between 1 and 1000, inclusive.
Examples
0)
	{3} Returns: 2 The only tree that matches the given information is shown below. The vertex V is red.
1)
	{2, 2} Returns: 4 There are two trees which correspond to the given partial information: The tree on the left has diameter 3 and the tree on the right has diameter 4.
2)
	{4, 1, 2, 4} Returns: 5 This is one example of a tree that corresponds to the given constraints and has the largest possible diameter.
3)
	{4, 2, 1, 3, 2, 5, 7, 2, 4, 5, 2, 3, 1, 13, 6} Returns: 21

Code:

#include<iostream>

#include<string>

#include<vector>

using namespace std;

class TheTree

{

public: int maximumDiameter(vector<int> cnt)

{

intans=0;

for(inti=0;i<cnt.size();i++)

{

if(cnt[i]>=1)

{

ans++;

cnt[i]--;

}

elsebreak;

}

for(inti=0;i<cnt.size();i++)

{

if(cnt[i]>=1)

{

ans++;

cnt[i]--;

}

elsebreak;

}

returnans;

}

};