A1053. Path of Equal Weight (30)

Given a non-empty tree with root R, and with weight W_i assigned to each tree node T_i. The weight of a path from R to L is defined to be the sum of the weights of all the nodes along the path from R to any leaf node L.

Now given any weighted tree, you are supposed to find all the paths with their weights equal to a given number. For example, let's consider the tree showed in Figure 1: for each node, the upper number is the node ID which is a two-digit number, and the lower number is the weight of that node. Suppose that the given number is 24, then there exists 4 different paths which have the same given weight: {10 5 2 7}, {10 4 10}, {10 3 3 6 2} and {10 3 3 6 2}, which correspond to the red edges in Figure 1.

Figure 1

Input Specification:

Each input file contains one test case. Each case starts with a line containing 0 < N <= 100, the number of nodes in a tree, M (< N), the number of non-leaf nodes, and 0 < S < 2³⁰, the given weight number. The next line contains N positive numbers where W_i (<1000) corresponds to the tree node T_i. Then M lines follow, each in the format:

ID K ID[1] ID[2] ... ID[K]

where ID is a two-digit number representing a given non-leaf node, K is the number of its children, followed by a sequence of two-digit ID's of its children. For the sake of simplicity, let us fix the root ID to be 00.

Output Specification:

For each test case, print all the paths with weight S in non-increasing order. Each path occupies a line with printed weights from the root to the leaf in order. All the numbers must be separated by a space with no extra space at the end of the line.

Note: sequence {A₁, A₂, ..., A_n} is said to be greater than sequence {B₁, B₂, ..., B_m} if there exists 1 <= k < min{n, m} such that A_i = B_ifor i=1, ... k, and A_k+1 > B_k+1.

Sample Input:

20 9 24
10 2 4 3 5 10 2 18 9 7 2 2 1 3 12 1 8 6 2 2
00 4 01 02 03 04
02 1 05
04 2 06 07
03 3 11 12 13
06 1 09
07 2 08 10
16 1 15
13 3 14 16 17
17 2 18 19

Sample Output:

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 #include <iostream>
 4 #include <string.h>
 5 #include <math.h>
 6 #include <algorithm>
 7 #include <string>
 8 #include <stack> 
 9 #include <queue>
10 using namespace std;
11 const int maxn=110; 
12 int n,m,s;
13 struct node{
14 int weight;
15 vector<int> child; 
16 }Node[maxn]; 
17 
18 int path[maxn];
19 bool cmp(int a,int b)
20 {
21   return Node[a].weight>Node[b].weight;    
22 }
23 void DFS(int root,int num,int sum)
24 {
25     if(sum>s)return;
26     if(sum==s)
27     {
28         if(Node[root].child.size()==0)
29         {
30             //打印
31             for(int i=0;i<num;i++)
32             {
33             printf("%d",Node[path[i]].weight);
34             if(i<num-1)printf(" ");
35             else printf("
");    
36             } 
37         }else
38         {
39             return;
40         }
41     }
42     for(int i=0;i<Node[root].child.size();i++)
43     {
44         int child=Node[root].child[i];
45         path[num]=child;
46         DFS(child,num+1,sum+Node[child].weight);
47     }
48 }
49 int main(){
50     scanf("%d %d %d",&n,&m,&s);
51     for(int i=0;i<n;i++)
52     {
53         int tmp;
54         scanf("%d",&tmp);
55         Node[i].weight=tmp;
56     }
57     for(int i=0;i<m;i++)
58     {
59         int id,k,child;
60         scanf("%d %d",&id,&k);
61         for(int j=0;j<k;j++)
62         {
63             scanf("%d",&child);
64             Node[id].child.push_back(child);
65         }
66         sort(Node[id].child.begin(),Node[id].child.end(),cmp);
67     }
68     path[0]=0;
69     DFS(0,1,Node[0].weight);
70     return 0;
71 }