1053 Path of Equal Weight (30 分)
Given a non-empty tree with root R, and with weight Wi assigned to each tree node Ti. 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 the following figure: 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 the figure.
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 Wi (<1000) corresponds to the tree node Ti. 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,⋯,An} is said to be greater than sequence {B1,B2,⋯,Bm} if there exists 1≤k<min{n,m} such that Ai=Bi for i=1,⋯,k, and Ak+1>Bk+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:
10 5 2 7
10 4 10
10 3 3 6 2
10 3 3 6 2
#include<iostream>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
using namespace std;
struct Node{
int date;
vector<int> child;
}node[110];
int n,m,s,a,b,c;
int ans[110]={0};
int cmp(int A,int B){
return node[A].date>node[B].date;
}
void DFS(int root,int num,int sum){
if(sum>s)
return;
bool flag = true;
if(sum==s){
if(node[root].child.size()==0){
for(int i=0;i<num;i++){
printf("%s%d",flag==true?"":" ",node[ans[i]].date);
flag = false;
}
cout<<endl;
return;
}
}
for(int i=0;i<node[root].child.size();i++){
int child = node[root].child[i];
ans[num] = child;
DFS(child,num+1,sum+node[child].date);
}
}
int main(){
cin>>n>>m>>s;
for(int i=0;i<n;i++){
cin>>node[i].date;
}
for(int i=0;i<m;i++){
cin>>a>>b;
for(int j=0;j<b;j++){
cin>>c;
node[a].child.push_back(c);
}
sort(node[a].child.begin(),node[a].child.end(),cmp);
}
DFS(0,1,node[0].date);
return 0;
}