PAT 甲级 1053. 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 2410 2 4 3 5 10 2 18 9 7 2 2 1 3 12 1 8 6 2 200 4 01 02 03 0402 1 0504 2 06 0703 3 11 12 1306 1 0907 2 08 1016 1 1513 3 14 16 1717 2 18 19

Sample Output:

10 5 2 710 4 1010 3 3 6 210 3 3 6 2

#include <iostream>#include <vector>#include <algorithm>#include <cstring>#include <stack>using namespace std;int target;struct NODE {int w;vector<int> child;};vector<NODE> v;vector<int> path;void dfs(int index, int nodeNum, int sum) {if (sum > target) return;if (sum == target) {if (v[index].child.size() != 0) return;for (int i = 0; i < nodeNum; i++)printf("%d%c", v[path[i]].w, i != nodeNum - 1 ? ' ' : '\n'); //骚操作return;}for (int i = 0; i < v[index].child.size(); i++) {int node = v[index].child[i];path[nodeNum] = node;dfs(node, nodeNum + 1, sum + v[node].w);}}int cmp1(int a, int b) {return v[a].w > v[b].w;}int main() {int n, m, node, k;scanf("%d %d %d", &n, &m, &target);v.resize(n), path.resize(n);for (int i = 0; i < n; i++) {scanf("%d", &v[i].w);}for (int i = 0; i < m; i++) {scanf("%d %d", &node, &k);v[node].child.resize(k);for (int j = 0; j < k; j++)scanf("%d", &v[node].child[j]);sort(v[node].child.begin(), v[node].child.end(), cmp1);}dfs(0, 1, v[0].w);return 0;}