1053 Path of Equal Weight（附测试点6思路）

题目：

Given a non-empty tree with root

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

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

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:

思路：

1、为保证非增序输出，开始采用的方法是：对每个非叶子结点的子结点根据权值从大到小排序，从而保证在DFS遍历时，总是先遍历权值大的子节点，从而使得结果非增。

但是存在一个例外的情况，如下：

对应的树为：

1
/ \
2 2
/ \
2 3
/ \
3 2

按照现在的解法来处理这样就会导致输出为：

1 2 2 3
1 2 3 2

而实际上期望的正确输出为：

1 2 3 2
1 2 2 3

因此，对代码进行了改进。即将所有可能的情况都存在一个vector<vector<int>> paths 的二维容器内，再对容器内的结果按照字典序进行排序，最后按顺序输出即可。

代码：（29分：最后一个测试点答案错误）

#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int n, m, s;
int w[105];
struct Node{
    int w, id;
};
bool cmp(Node s1, Node s2){
    return s1.w > s2.w;
}
vector<Node> children[105];
vector<int> len;
void dfs(int x, vector<int>&v, int l){
    if(l == s && children[x].size() == 0){
        bool flag = false;
        for(int i = 0; i < v.size(); i++){
            if(!flag){
                flag = true;
            }else{
                printf(" ");
            }
            printf("%d", v[i]);
        }
        printf("\n");
    }
    for(int i = 0; i < children[x].size(); i++){
        int child = children[x][i].id;
        if(l + w[child] <= s){
            v.push_back(w[child]);
            dfs(child, v, l + w[child]);
            v.pop_back();
        }
    }
}
int main(){
    scanf("%d%d%d", &n, &m, &s);
    for(int i = 0; i < n; i++){
        scanf("%d", &w[i]);
    }
    for(int i = 0; i < m; i++){
        int id, num;
        scanf("%d%d", &id, &num);
        for(int j = 0; j < num; j++){
            int child;
            scanf("%d", &child);
            Node node;
            node.w = w[child];
            node.id = child;
            children[id].push_back(node);
        }
        sort(children[id].begin(), children[id].end(), cmp);
    }
    len.push_back(w[0]);
    dfs(0, len, w[0]);
}

(满分)

#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int n, m, s;
int w[105];
vector<int> children[105];
vector<int> path;
vector<vector<int>> paths;
void dfs(int x, vector<int>&v, int l){
    if(l == s && children[x].size() == 0){
        paths.push_back(v);
        return;
    }
    for(int i = 0; i < children[x].size(); i++){
        int child = children[x][i];
        if(l + w[child] <= s){
            v.push_back(w[child]);
            dfs(child, v, l + w[child]);
            v.pop_back();
        }
    }
}
int main(){
    scanf("%d%d%d", &n, &m, &s);
    for(int i = 0; i < n; i++){
        scanf("%d", &w[i]);
    }
    for(int i = 0; i < m; i++){
        int id, num;
        scanf("%d%d", &id, &num);
        for(int j = 0; j < num; j++){
            int child;
            scanf("%d", &child);
            children[id].push_back(child);
        }
    }
    path.push_back(w[0]);
    dfs(0, path, w[0]);
    sort(paths.begin(), paths.end(), greater<vector<int>>());
    for (int i = 0; i < paths.size(); i++) {
        printf("%d", paths[i][0]);
        for (int j = 1; j < paths[i].size(); j++) {
            printf(" %d", paths[i][j]);
        }
        printf("\n");
    }
}