PAT1053 Path of Equal Weight（30 分）

Posted 2021-01-01 pgzhang

1053 Path of Equal Weight（30 分）

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 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<2?30??, 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 {A?1??,A?2??,?,A?n??} is said to be greater than sequence {B?1??,B?2??,?,B?m??} if there exists 1≤k<min{n,m} such that A?i??=B?i?? for 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

C++代码如下：

 1 #include<iostream>
 2 #include<vector>
 3 #include<algorithm>
 4 using namespace std;
 5 #define maxn 105
 6 
 7 struct Node {
 8     int weight;
 9     vector<int>child;
10 };
11 
12 int n, m, s;
13 Node num[maxn];
14 
15 bool cmp(int a, int b) {
16     return num[a].weight > num[b].weight;
17 }
18 
19 vector<int>v;   //存放路径对应的权值
20 void path(int r,int sum) {
21     if (sum > s) {
22         v.pop_back(); return;
23     }
24     if (sum == s) {
25         if ( num[r].child.size() == 0) {
26             cout << v[0];
27             for (vector<int>::iterator it = v.begin() + 1; it != v.end(); it++)
28                 cout << ‘ ‘ << *it;
29             cout << endl;
30             v.pop_back();
31             return;
32         }
33         else {
34             v.pop_back(); return;
35         }
36     }
37     for (int i = 0; i < num[r].child.size(); i++) {
38         int t = num[r].child[i];
39         v.push_back(num[t].weight);
40         path(t, sum + num[t].weight);        
41     }
42     if (!v.empty()) v.pop_back();
43 }
44 int main() {
45     cin >> n >> m >> s;
46     int w;
47 
48     for (int i = 0; i < n; i++) {
49         cin >> w;
50         num[i].weight = w;
51     }
52     int id,k,t;
53     for (int i = 0; i < m; i++) {
54         cin >> id>>k;
55         for (int j = 0; j < k; j++) {
56             cin >> t;
57             num[id].child.push_back(t);
58         }
59         sort(num[id].child.begin(), num[id].child.end(), cmp);
60     }
61     v.push_back(num[0].weight);
62     path(0,num[0].weight);
63     return 0;
64 }