pat甲级1107

1107 Social Clusters （30 分）

When register on a social network, you are always asked to specify your hobbies in order to find some potential friends with the same hobbies. A social cluster is a set of people who have some of their hobbies in common. You are supposed to find all the clusters.

Input Specification:

Each input file contains one test case. For each test case, the first line contains a positive integer N (≤1000), the total number of people in a social network. Hence the people are numbered from 1 to N. Then N lines follow, each gives the hobby list of a person in the format:

K​i​​: h​i​​[1] h​i​​[2] ... h​i​​[K​i​​]

where K​i​​ (>0) is the number of hobbies, and h​i​​[j] is the index of the j-th hobby, which is an integer in [1, 1000].

Output Specification:

For each case, print in one line the total number of clusters in the network. Then in the second line, print the numbers of people in the clusters in non-increasing order. The numbers must be separated by exactly one space, and there must be no extra space at the end of the line.

Sample Input:

8
3: 2 7 10
1: 4
2: 5 3
1: 4
1: 3
1: 4
4: 6 8 1 5
1: 4

Sample Output:

3
4 3 1

这道题考察并查集。

开始遇到了数组越界的问题，后来调试发现是最近考研复习计算机系统基础遇到的一个知识点：

1     for (i = 1; i < 1001; i++)
2     {
3         for (j = 0; j < hobby[i].size() - 1; j++)
4             _union(hobby[i][j], hobby[i][j + 1]);
5     }

我开始是这么写的，看似不会发生数组越界的问题，但是因为hobby[i].size()是无符号数unsigned型，当hobby[i].size()等于0时，减去1就成了无符号数2^32-1，所以发生了越界。

看来了解底层的一些原理确实很重要，usigned型要慎用。

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

vector<vector<int>> hobby(1001);
vector<int> father(1001, -1);
void _union(int i, int j);
int find(int i);

int main()
{
    int N;
    cin >> N;
    int i, j, k, t;
    char c;
    for (i = 1; i <= N; i++)
    {
        cin >> k >> c;
        for (j = 0; j < k; j++)
        {
            cin >> t;
            hobby[t].push_back(i);
        }
    }
    for (i = 1; i < 1001; i++)
    {
        for (j = 1; j < hobby[i].size(); j++)
            _union(hobby[i][j], hobby[i][j - 1]);
    }
    vector<int> cluster;
    for (i = 1; i <= N; i++)
    {
        if (father[i] < 0)
            cluster.push_back(-father[i]);
    }
    sort(cluster.begin(), cluster.end());
    cout << cluster.size() << endl << cluster[cluster.size() - 1];
    for (i = cluster.size() - 2; i >= 0; i--) cout << " " << cluster[i];
    return 0;
}

void _union(int i, int j)
{
    int a = find(i);
    int b = find(j);
    if (a == b) return;
    if (father[a] < father[b])
    {
        father[a] += father[b];
        father[b] = a;
    }
    else
    {
        father[b] += father[a];
        father[a] = b;
    }
}
int find(int i)
{
    while (father[i] > 0) i = father[i];
    return i;
}