Big Christmas Tree-优快云博客

本文探讨了在KCM城市中构建大型圣诞树的问题，通过分析树的结构、节点权重和边的价格，提出了一种算法来最小化整体成本。

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Description

Christmas is coming to KCM city. Suby the loyal civilian in KCM city is preparing a big neat Christmas tree. The simple structure of the tree is shown in right picture.

The tree can be represented as a collection of numbered nodes and some edges. The nodes are numbered 1 through n. The root is always numbered 1. Every node in the tree has its weight. The weights can be different from each other. Also the shape of every available edge between two nodes is different, so the unit price of each edge is different. Because of a technical difficulty, price of an edge will be (sum of weights of all descendant nodes) × (unit price of the edge).

Suby wants to minimize the cost of whole tree among all possible choices. Also he wants to use all nodes because he wants a large tree. So he decided to ask you for helping solve this task by find the minimum cost.

Input

The input consists of T test cases. The number of test cases T is given in the first line of the input file. Each test case consists of several lines. Two numbers v, e (0 ≤ v, e ≤ 50000) are given in the first line of each test case. On the next line, v positive integers w_i indicating the weights of v nodes are given in one line. On the following e lines, each line contain three positive integers a, b, c indicating the edge which is able to connect two nodes a and b, and unit price c.

All numbers in input are less than 2¹⁶.

Output

For each test case, output an integer indicating the minimum possible cost for the tree in one line. If there is no way to build a Christmas tree, print “No Answer” in one line.

Sample Input

2
2 1
1 1
1 2 15
7 7
200 10 20 30 40 50 60
1 2 1
2 3 3
2 4 2
3 5 4
3 7 2
3 6 3
1 5 9

Sample Output

15
1210

题解：其实就是求最短路径，反正我是没读懂，看来别人的感觉和题目说的完全不同。

SPFA（数组邻接表）：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>

using namespace std; 

const long long INF = 0x3ffffffffffff;

struct Node
{
	int to;
	int cost;
	Node(){
	}
	Node(int a,int b)
	{
		to = a;
		cost = b;
	}
};

int first[50005];
int next[100005];
Node e[100005];
bool visited[50005];
long long d[50005];
long long w[50005];

void spfa(int n)
{
	memset(visited,false,sizeof(visited));
	for(int i = 1;i <= n;i++)
	{
		d[i] = INF;
	}
	d[1] = 0;
	queue<int> q;
	q.push(1);
	visited[1] = true;
	while(!q.empty())
	{
		int x = q.front();
		q.pop();
		visited[x] = false;
		for(int i = first[x];i != -1;i = next[i])
		{
			int t = e[i].to;
			if(d[t] > d[x] + e[i].cost)
			{
				d[t] = d[x] + e[i].cost;
				if(!visited[t])
				{
					q.push(t);
					visited[t] = true;
				}
			}
		}
	}
}

int main()
{
	int ncase;
	cin>>ncase;
	while(ncase--)
	{
		int n,m;
		scanf("%d%d",&n,&m);
		for(int i = 1;i <= n;i++)
		{
			first[i] = -1;
			scanf("%lld",w + i);
		}
		int k = 0;
		for(int i = 0;i < m;i++)
		{
			int u,v,c;
			scanf("%d%d%d",&u,&v,&c);
			e[k].to = v;
			e[k].cost = c;
			next[k] = first[u];
			first[u] = k++;
			e[k].to = u;
			e[k].cost = c;
			next[k] = first[v];
			first[v] = k++;
		}
		
		if(n == 0 || m == 0)
		{
			printf("0\n");
			continue;
		}
		spfa(n);
		bool flag = true;
		long long ans = 0;
		for(int i = 1;i <= n;i++)
		{
			if(d[i] == INF)
			{
				flag = false;
				break;
			}
			ans += d[i] * w[i];
		}
		if(flag)
		{
			printf("%lld\n",ans);
		}
		else
		{
			printf("No Answer\n");
		}
	}
		
	return 0;
}

djistra（数组邻接表）：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>

using namespace std; 

const __int64 INF = 10000000000;

struct Node
{
	int to;
	__int64 cost;
	Node(){
	}
	Node(int a,__int64 b)
	{
		to = a;
		cost = b;
	}
	bool operator< (Node t) const
	{
		return cost > t.cost;
	}
};
int first[50005];
int next[100005];
Node e[100005];
bool visited[50005];
__int64 d[50005];
__int64 w[50005];
__int64 ans = 0;

void djistra(int n)
{
	memset(visited,false,sizeof(visited));
	for(int i = 1;i <= n;i++)
	{
		d[i] = INF;
	}
	d[1] = 0;
	priority_queue<Node> q;
	q.push(Node(1,0));
	ans = 0;
	int cnt = 0;
	while(!q.empty())
	{
		Node p = q.top();
		q.pop();
		if(visited[p.to])
		{
			continue;
		}
		cnt++;
		ans += d[p.to] * w[p.to];
		visited[p.to] = true;
		for(int i = first[p.to];i != -1;i = next[i])
		{
			int x = e[i].to;
			if(!visited[x] && d[x] > d[p.to] + e[i].cost)
			{
				d[x] = d[p.to] + e[i].cost;
				q.push(Node(x,d[x]));
			}
		}
	}
	if(cnt != n)
	{
		ans = -1;
	}
}

int main()
{
	int ncase;
	cin>>ncase;
	while(ncase--)
	{
		int n,m;
		scanf("%d%d",&n,&m);
		for(int i = 1;i <= n;i++)
		{
			first[i] = -1;
			scanf("%I64d",w + i);
		}
		int k = 0;
		for(int i = 0;i < m;i++)
		{
			int u,v;
			__int64 c;
			scanf("%d%d%I64d",&u,&v,&c);
		    e[k].to = v;
			e[k].cost = c;
			next[k] = first[u];
			first[u] = k++;
			e[k].to = u;
			e[k].cost = c;
			next[k] = first[v];
			first[v] = k++;
		}
		if(n == 0 || n == 1)
		{
			printf("0\n");
			continue;
		}
		djistra(n);
		if(ans != -1)
		{
			printf("%I64d\n",ans);
		}
		else
		{
			printf("No Answer\n");
		}
	}
	
	return 0;
}

超时vector：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>
#include <utility>

using namespace std; 

const __int64 INF = 0x3fffffffffff;

struct Node
{
	int to;
	int cost;
	Node(){
	}
	Node(int a,int b)
	{
		to = a;
		cost = b;
	}
	bool operator< (Node t) const
	{
		return cost > t.cost;
	}
};
typedef pair<__int64,int>plli;
priority_queue<plli , vector<plli> , greater<plli> > q;

vector<Node> vec[50005];
bool visited[50005];
__int64 d[50005];
int w[50005];
__int64 ans;


void djistra(int n)
{
	memset(visited,false,sizeof(visited));
	for(int i = 1;i <= n;i++)
	{
		d[i] = INF;
	}
	d[1] = 0;
	ans = 0;
	priority_queue<Node> q;
	q.push(Node(1,0));
	int cnt = 0;
	while(!q.empty())
	{
		Node p = q.top();
		q.pop();
		if(visited[p.to])
		{
			continue;
		}
		ans += w[p.to] * d[p.to];
		cnt++;
		visited[p.to] = true;
		for(int i = 0;i < vec[p.to].size();i++)
		{
			int x = vec[p.to][i].to;
			if(!visited[x] && d[x] > d[p.to] + vec[p.to][i].cost)
			{
				d[x] = d[p.to] + vec[p.to][i].cost;
				q.push(Node(x,d[x]));
			}
		}
	}
	if(cnt != n)
	{
		ans = -1;
	}
}

int main()
{
	int ncase;
	cin>>ncase;
	while(ncase--)
	{
		int n,m;
		scanf("%d%d",&n,&m);
		for(int i = 1;i <= n;i++)
		{
			scanf("%d",w + i);
		}
		for(int i = 0;i < m;i++)
		{
			int u,v,c;
			scanf("%d%d%d",&u,&v,&c);
			vec[u].push_back(Node(v,c));
			vec[v].push_back(Node(u,c));
		}
		if(n == 0 || m == 0)
		{
			printf("0\n");
			continue;
		}
		djistra(n);
		if(ans != -1)
		{
			printf("%I64d\n",ans);
		}
		else
		{
			printf("No Answer\n");
		}
		
		for(int i = 1;i <= n;i++)
		{
			vec[i].clear();
		}
		
	}
	
	return 0;
}