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解题报告【pat-1076】
最近一直在忙项目都没时间好好总结写博客,说起来真实惭愧啊。
下面就把自己最近做的几题好好总结一下,主要记录一些注意点,以防以后遇到再犯。
1076. Forwards on Weibo (30)
Weibo is known as the Chinese version of Twitter. One user on Weibo may have many followers, and may follow many other users as well. Hence a social network is formed with followers relations. When a user makes a post on Weibo, all his/her followers can view and forward his/her post, which can then be forwarded again by their followers. Now given a social network, you are supposed to calculate the maximum potential amount of forwards for any specific user, assuming that only L levels of indirect followers are counted.
Input Specification:
Each input file contains one test case. For each case, the first line contains 2 positive integers: N (<=1000), the number of users; and L (<=6), the number of levels of indirect followers that are counted. Hence it is assumed that all the users are numbered from 1 to N. Then N lines follow, each in the format:
M[i] user_list[i]
where M[i] (<=100) is the total number of people that user[i] follows; anduser_list[i] is a list of the M[i] users that are followed by user[i]. It is guaranteed that no one can follow oneself. All the numbers are separated by a space.
Then finally a positive K is given, followed by K UserID‘s for query.
Output Specification:
For each UserID, you are supposed to print in one line the maximum potential amount of forwards this user can triger, assuming that everyone who can view the initial post will forward it once, and that only L levels of indirect followers are counted.
Sample Input:7 3 3 2 3 4 0 2 5 6 2 3 1 2 3 4 1 4 1 5 2 2 6Sample Output:
4 5
这个题目的坑在题意不好理解,尤其是像我这种英语比较拙计的人。最后查了几个单词总算理解了题意,本质上就是做搜索。但是涉及到一个是选择dfs还是bfs的问题。刚开始没多想,感觉差不多,后来就用了dfs。
dfs需要注意的几点:
【1】邻居存储数据结构的选择,这里用了邻接表,比较清楚。
【2】注意不能存在回路的情况,比如说1是4的粉丝,4也是1的粉丝。如果先1后4,那么到4的时候就不应该回去再访问1!也就是不能存在回路。
【3】在不能存在回路的基础上,要考虑一种特殊情况,5-1-4 这时候L==0了,也就是说到了限定的最外层。这时候不能再往下搜索,应该退回到5。但是4的邻居此时没有被搜索过。若5的下一个邻居是4,这时候4也要被访问,因为4的邻居可能存在没被访问过的点。
为了解决环路问题,同时兼顾【3】我们设一个点有3种状态
#define discover 0 #define cnted 1 #define undsicover 2
每次访问一个点若该点为 undsicover,那么置为dsicover并cnt++,如果该点本身是dsicover,那么说明存在回路,不再继续。一个点回退后要置为cnted。避免下次访问被跳过,即【3】的情况。
代码:
// pat-1076.cpp : 定义控制台应用程序的入口点。 // #include "stdafx.h" #include"iostream" #include "vector" #include "algorithm" #include "fstream" using namespace std; #define discover 0 #define cnted 1 #define undsicover 2 int cnt=0; class node{ public: int id; vector<node*> neiber; int statues; node():neiber(NULL),statues(undsicover),id(-1){} }; void resetall(node* an,int n) { for (int i=0;i<n+1;i++) { an[i].statues=undsicover; } cnt=0; } void forward(node* p,int l) { if (p->statues==discover||l==0)//避免形成回环 { return; } if ((p->statues==undsicover))//false { cnt++;//计数加一 p->statues=discover;//cnted } if (p->neiber.empty())//没有邻居不用遍历 { return; } int len=p->neiber.size(); for (int i=0;i<len;i++) { forward(p->neiber[i],l-1);//dfs } p->statues=cnted; } int main() { fstream fcin; fcin.open("C:\\Users\\Administrator\\Desktop\\456.txt"); int n=0,l=0; fcin>>n>>l; node *an=new node[n+1];//编号从1-n for (int i=1;i<=n;i++) { an[i].id=i; } for (int i=1;i<=n;i++) { int temp=0,j=0; fcin>>temp; while(temp--) { fcin>>j; an[j].neiber.push_back(&an[i]);//作为目标的邻居而不是把目标作为自己的邻居 } } int k=0,index=0; fcin>>k; for(int i=0;i<k;i++) { fcin>>index; forward(&an[index],l+1); cout<<cnt-1<<endl; resetall(an,n); } return 0; }
上述算法的逻辑没错,但是最后一个点会超时!!!呵呵,随后又写了一个bfs版本的。
// pat-1076.cpp : 定义控制台应用程序的入口点。 // #include "stdafx.h" #include"iostream" #include "vector" #include "algorithm" #include "fstream" #include "queue" using namespace std; #define discover 0 #define cnted 1 #define undsicover 2 int cnt=0; class node{ public: int id; vector<node*> neiber; int statues; node():neiber(NULL),statues(undsicover),id(-1){} }; void resetall(node* an,int n) { for (int i=0;i<n+1;i++) { an[i].statues=undsicover; } cnt=0; } void bfs(node* p,int l) { queue<vector<node*>> q; queue<vector<node*>> qq; p->statues=discover; q.push(p->neiber); while(!q.empty()) { if (qq.empty()) { l--; qq=q; } if (l==0) { return ; } vector<node*> v=q.front(); q.pop(); qq.pop(); int len=v.size(); for (int i=0;i<len;i++) { if (v[i]->statues==undsicover) { cnt++; v[i]->statues=discover; if (!v[i]->neiber.empty()&&l>0) { q.push(v[i]->neiber); } } } } } int main() { fstream fcin; fcin.open("C:\\Users\\Administrator\\Desktop\\456.txt"); int n=0,l=0; fcin>>n>>l; node *an=new node[n+1];//编号从1-n for (int i=1;i<=n;i++) { an[i].id=i; } for (int i=1;i<=n;i++) { int temp=0,j=0; fcin>>temp; while(temp--) { fcin>>j; an[j].neiber.push_back(&an[i]);//作为目标的邻居而不是把目标作为自己的邻居 } } int k=0,index=0; fcin>>k; for(int i=0;i<k;i++) { fcin>>index; bfs(&an[index],l+1); cout<<cnt<<endl; resetall(an,n); } return 0; }
这个是可以ac的,果然递归是个坑啊!但是这里涉及到一个计算bfs深度的问题。在dfs里面这很自然,递归的深度就是目前所处树的深度。但是在用stack实现的bfs算法里面没有可用的量。所以这里用了比较笨的办法,开了两个stack,一个是用来计数的。还好stl重载了运算符=,否则代码会有点啰嗦。
如果大家有什么跟好的想法,欢迎交流!