1053. Path of Equal Weight

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_i for i=1, ... k, and A_k+1 > B_k+1.

#include <stdio.h>#include <stdlib.h>#include <vector>#include <algorithm>using namespace std;#define N 100typedef struct {        int data;        vector<int> child;        }Node;Node node[N];int n,m,s;int ans[N];void DFS (int a,int num,int sum);bool cmp (int a,int b);int main (){    int i,temp;    scanf("%d %d %d",&n,&m,&s);    for( i=0;i<n;i++)    {         scanf("%d",&temp);         node[i].data=temp;         }    int id,num,childs,j;    for( i=0;i<m;i++)    {         scanf("%d %d",&id,&num);         for( j=0;j<num;j++)         {              scanf("%d",&childs);              node[id].child.push_back(childs);              }         sort(node[id].child.begin(),node[id].child.end(),cmp);         }    ans[0]=node[0].data;    DFS(0,1,node[0].data);    system("pause");    return 0;    }bool cmp (int a,int b){     return node[a].data>node[b].data;     }void DFS (int a,int num,int sum){     int i;     if( sum>s) return;     if( sum==s)      {         if( node[a].child.size()==0)         {             for( i=0;i<num-1;i++) printf("%d ",ans[i]);             printf("%d\n",ans[i]);             }         return;         }     for( i=0;i<node[a].child.size();i++)     {          int child=node[a].child[i];          ans[num]=node[child].data;          DFS(child,num+1,sum+node[child].data);          }     }