《Cracking the Coding Interview》——第10章：可扩展性和存储空间限制——题目2

2014-04-24 20:44

题目：对于Facebook、Linkedin这样的社交网站，你要如何设计一个数据结构来表示用户之间的关系呢？比如两个用户互为2nd-degree connection。你要如何设计算法来找出他们之间的联系路径呢？

解法：显然，社交网络的数据是平方级别的，因为任何人的联系往往是C(n, 2) = n * (n - 1) / 2。所以这种数据结构应该是个无向图和有向图的结合。人脉之间是互相建立的，所以是无向图，而“Follow”行为是单向的，所以应该为有向图。如果要发掘两个用户间的人脉路径，广度优先搜索肯定是最简单直白的。单向或是双向广搜可能效率上有一定差别，但对于这样的大型网站肯定都不行，因为响应时间要求很高。如果用空间换取时间，用动态规划的思想，把一度人脉、二度人脉逐层计算并保存下来，这样就能避免重复计算了。算法分为在线和离线两种设计，这样开销巨大的搜索过程，就应该以合理的间隔进行离线计算，保证在线查询的高效响应。如果你问：“我的人脉情况会变化，这样显示出来的结果岂不是错的？”那么我说，下次重新计算的时候，就会对了，你对错误的容忍程度决定了下次服务器重新计算人脉的时间间隔。

代码：

// 10.2 Describe how you would design the data structure for people in social network. How would you determine the degree of connections between two people.
// Answer:
// Appartently social network involves a lot of graph thoery. It describes the connections between people.
class Person {
// A lot of data
vector<Person *> friends;
};
// Basically every people is a node in the grap.
// For two people, if you want to find out through how many people they're connected, BFS may be a practical way.
// But it's not effiecient enough, double-end BFS will be a little better.
// You may record the list of 2nd degree connections, so you can retrieve 3rd degree connections faster.
// And you surely wouldn't be interested in 10th degree connections, as anyone on this earth may be your 10th degree connection.
// So it's important to limit the connection search to a small scale of no more than 3rd degree.
int main()
{
return 0;
}