PAT 1053. Path of Equal Weight (30)

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_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

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

struct Node
{
    int parent  = -1;
    int weight;
    vector<int> child;
};

Node tree[100];
int weight[100];


void CalculateWeight(int root)
{
    vector<int>& vec = tree[root].child;

    for (int i = 0; i < vec.size(); i++)
    {
        tree[vec[i]].weight = tree[root].weight + weight[vec[i]];
        CalculateWeight(vec[i]);
    }
}

bool cmp(vector<int> v1, vector<int> v2)
{
    int i = 0;
    while (i < v1.size() && i < v2.size())
    {
        if (v1[i] != v2[i])
            return v1[i] > v2[i];
        i++;
    }
    return false;
}

int main()
{
    int nodeNum, nonLeafNum, givenWeight;
    cin >> nodeNum >> nonLeafNum >> givenWeight;

    for (int i = 0; i < nodeNum; i++)
        cin >> weight[i];
    for (int i = 0; i < nonLeafNum; i++)
    {
        int parent, childNum;
        cin >> parent >> childNum;
        for (int i = 0; i < childNum; i++)
        {
            int child;
            cin >> child;
            tree[parent].child.push_back(child);
            tree[child].parent = parent;
        }
    }

    tree[0].weight = weight[0];
    CalculateWeight(0);

    vector< vector<int> > seq;
    for (int i = 0; i < nodeNum; i++)
    {
        if (tree[i].child.empty() && tree[i].weight == givenWeight)
        {
            vector<int> vec;
            int j = i;
            while (j != -1)
            {
                vec.push_back(weight[j]);
                j = tree[j].parent;
            }
            seq.push_back(vector<int>(vec.rbegin(), vec.rend()));
        }
    }
    sort(seq.begin(), seq.end(), cmp);
    for (int i = 0; i < seq.size(); i++)
    {
        vector<int>& vec = seq[i];
        for (int j = 0; j < vec.size() - 1; j++)
            cout << vec[j] << " ";
        cout << vec.back() << endl;
    }
}