hdu 6201 树形DP

transaction transaction transaction

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 132768/132768 K (Java/Others)

Problem Description

Kelukin is a businessman. Every day, he travels around cities to do some business. On August 17th, in memory of a great man, citizens will read a book named "the Man Who Changed China". Of course, Kelukin wouldn't miss this chance to make money, but he doesn't have this book. So he has to choose two city to buy and sell. 
As we know, the price of this book was different in each city. It is  ai   yuan  in  i t  city. Kelukin will take taxi, whose price is  1 yuan  per km and this fare cannot be ignored.
There are  n−1  roads connecting  n  cities. Kelukin can choose any city to start his travel. He want to know the maximum money he can get.

 

Input

The first line contains an integer  T  ( 1≤T≤10 ) , the number of test cases. 
For each test case:
first line contains an integer  n  ( 2≤n≤100000 ) means the number of cities;
second line contains  n  numbers, the  i th  number means the prices in  i th  city;  (1≤Price≤10000)  
then follows  n−1  lines, each contains three numbers  x ,  y  and  z  which means there exists a road between  x  and  y , the distance is  z km   (1≤z≤1000) . 

 

Output

For each test case, output a single number in a line: the maximum money he can get.

 

Sample Input

  

   1  
4  
10 40 15 30  
1 2 30
1 3 2
3 4 10
  

 

Sample Output

  

   8
  

 

Source

2017 ACM/ICPC Asia Regional Shenyang Online

题意：树，给出n个点，点权val[i]，n-1条边，边权w，求 最长的S->T权重 = val[s] - val[T] -  dist[S->T]

典型的树形DP，对于U，  子树V ,  保存到V的起点maxStart，终点路径和maxEnd，在U处贪心归并，选最大的maxStart ， maxEnd 。

 

import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;
  
  
public class Main {  
      
    public static void main(String[] args) {  
        new Task().solve();  
    }  
}  
  
  
  
class Task {  
    InputReader in = new InputReader(System.in) ;  
    PrintWriter out = new PrintWriter(System.out) ;  
    
    class Edge{
    	int v , w , next ;
    	Edge(int v , int w ,  int next){
    		this.v = v ;
    		this.w = w ;
    		this.next = next ;
    	}
    }
    int[] head ;
    Edge[] e ;
    int eid ;
    void add(int u , int v , int w){
    	e[eid] = new Edge(v , w , head[u]) ;
    	head[u] = eid++ ;
    }
    int[] val ;
    class Node{
    	int start ;
    	int end ;
    	Node(int start , int end){
    		this.start = start ;
    		this.end = end ;
    	}
    }
    
    int reslut ; 
    Node dfs(int u , int father){
    	int maxStart = val[u] ;
    	int maxEnd = -val[u] ;
    	for(int i = head[u] ; i != -1 ; i = e[i].next){
    		int v = e[i].v ;
    		if(v == father){
    			continue ;
    		}
    		Node sonV = dfs(v , u) ;
    		maxStart = Math.max(maxStart  , sonV.start - e[i].w ) ;
    		maxEnd = Math.max(maxEnd  , sonV.end - e[i].w ) ;
    	}
    	reslut = Math.max(reslut , maxStart + maxEnd) ;
    	return new Node(maxStart , maxEnd) ;
    }
      
    void solve(){  
    	int t = in.nextInt() ;
    	while(t-- > 0){
    		int n = in.nextInt() ;
    		val = new int[n+1] ;
    		head = new int[n+1] ;
    		Arrays.fill(head , -1) ;
    		for(int i = 1 ; i <= n ; i++){
    			val[i] = in.nextInt() ;
    		}
    		e = new Edge[n*2+8] ;
    		eid = 0 ;
    		for(int i = 1 ; i < n ; i++){
    			int u = in.nextInt() ;
    			int v = in.nextInt() ;
    			int w = in.nextInt() ;
    			add(u , v , w) ;
    			add(v , u , w) ;
    		}
    		reslut = 0 ;
    		dfs(1, -1) ;
    		out.println(reslut) ;
    	}
        out.flush() ;  
    }  
    
}  
  
class InputReader {      
    public BufferedReader reader;      
    public StringTokenizer tokenizer;      
      
    public InputReader(InputStream stream) {      
        reader = new BufferedReader(new InputStreamReader(stream), 32768);      
        tokenizer = new StringTokenizer("");      
    }      
      
    private void eat(String s) {      
        tokenizer = new StringTokenizer(s);      
    }      
      
    public String nextLine() {       
        try {      
            return reader.readLine();      
        } catch (Exception e) {      
            return null;      
        }      
    }      
      
    public boolean hasNext() {      
        while (!tokenizer.hasMoreTokens()) {      
            String s = nextLine();      
            if (s == null)      
                return false;      
            eat(s);      
        }      
        return true;      
    }      
      
    public String next() {      
        hasNext();      
        return tokenizer.nextToken();      
    }      
      
    public int nextInt() {      
        return Integer.parseInt(next());      
    }      
      
    public int[] nextInts(int n) {      
        int[] nums = new int[n];      
        for (int i = 0; i < n; i++) {      
            nums[i] = nextInt();      
        }      
        return nums;      
    }      
      
    public long nextLong() {      
        return Long.parseLong(next());      
    }      
      
    public double nextDouble() {      
        return Double.parseDouble(next());      
    }      
      
    public BigInteger nextBigInteger() {      
        return new BigInteger(next());      
    }      
      
}