Path of Equal Weight

1053. Path of Equal Weight (30)

時間限制

100 ms

內存限制

65536 kB

代碼長度限制

16000 B

判題程序

Standard

作者

CHEN, Yue

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:

10 5 2 7
10 4 10
10 3 3 6 2
10 3 3 6 2

---

提交代碼

#include<stdio.h>
#include<string.h>
#include<vector>
#include<algorithm>
using namespace std;
const int maxn=110;
struct node{
	int weight;
	vector<int> child;
}Node[maxn];
bool cmp(int a,int b)
{
	return Node[a].weight>Node[b].weight;
}
int n,m,s;
int path[maxn];
void DFS(int index,int numNode,int sum)
{
	if(sum>s) return ;
	if(sum==s)
	{
		if(Node[index].child.size()!=0) return;
		for(int i=0;i<numNode;i++)
		{
			printf("%d",Node[path[i]].weight);
			if(i<numNode-1) printf(" ");
			else printf("\n");	
		} 
		return ;
	}
	for(int i=0;i<Node[index].child.size();i++)
	{
		int child=Node[index].child[i];
		path[numNode]=child;
		DFS(child,numNode+1,sum+Node[child].weight);
	} 
}
int main()
{
	scanf("%d%d%d",&n,&m,&s);
	for(int i=0;i<n;i++)
	{
		scanf("%d",&Node[i].weight);
	}
	int id,k,child;
	for(int i=0;i<m;i++)
	{
		scanf("%d%d",&id,&k);
		for(int j=0;j<k;j++)
		{
			scanf("%d",&child);
			Node[id].child.push_back(child);
		}
		sort(Node[id].child.begin(),Node[id].child.end(),cmp);
	}
	path[0]=0;
	DFS(0,1,Node[0].weight);
	return 0;
}