约瑟环问题

  1 /*
  2 约瑟环问题其实就是一个循环链表的问题 
  3 */ 
  4 #include <iostream>
  5 #include<ctime>
  6 using namespace std;
  7 
  8 //动态规划的思想，有点类似解决主元素问题的思路 
  9 //巧妙的用0，1数组代替链表节点的删除 
 10 int sun1(const int N,const int C)
 11 {
 12     int i=0,j=0,n=N,s=0;
 13     int t=0;
 14     int *a=new int [N];
 15     for (i=0;i<N;i++)
 16     {
 17         a[i]=1;
 18     }
 19     
 20     while(0!=n)
 21     {
 22         s+=a[j]; //前面的数相加每加够C出列一个数 
 23         if(C==s)
 24         {
 25             a[j]=0;
 26             s=0; //要清0 
 27             --n;
 28             if(0!=n)
 29                 cout<<j+1<<"->"; //s[j]实际对应的是第j+1个人 
 30             else
 31             {
 32                 cout<<j+1<<endl;
 33                 t=j+1;
 34             }
 35                 
 36         }
 37         //j=(j+1)%N; // 循环队列，这里处理很巧妙
 38         j= (j==N-1)?0:j+1;
 39     }
 40     delete []a;
 41     return t;
 42     
 43 }
 44 /*
 45 递推的方法 
 46 N=1,winner=0;
 47 N=i,winner=(winner(0)+C)%i;
 48 winner +=1;
 49 */
 50 int sun2(const int N, const int C)
 51 {
 52     int f=0;
 53     for(int i=2;i<=N;i++)
 54     {
 55         f=(f+C)%i;
 56     }
 57     return f+1;
 58 }
 59 /*循环链表 */ 
 60 int sun3(const int N,const int C)
 61 {
 62     struct node
 63     {
 64         int num;
 65         node *next;
 66         node(const int i)
 67         {
 68             num=i;
 69             next=NULL;
 70         }
 71     };
 72     //初始化链表 
 73     node *first=NULL;
 74     node *opp=first;
 75     for(int i=1;i<=N;i++)
 76     {
 77         node *t=new node(i);
 78         if(first==NULL)
 79             first=t;
 80         else
 81             opp->next=t;
 82         opp=t;
 83     }
 84     
 85     opp->next=first;
 86     int winner=0;
 87     opp=first;
 88     while(true)
 89     {    
 90         for(int i=2;i<=C-1;i++)// 这里注意找到的是出列的节点的父节点 
 91             opp=opp->next;
 92         node *temp=opp->next;
 93         cout<<temp->num;
 94         if(opp!=temp)
 95         {
 96             cout<<"->";
 97             //删除节点 
 98             opp->next=temp->next;
 99             opp=opp->next;
100             delete temp;
101         }
102         else
103         {
104             winner=temp->num;
105             cout<<"
";    
106             delete opp;
107             break;
108         }
109     }
110     return winner;
111         
112 }
113     
114     
115 
116 int main()
117 {
118     ios::sync_with_stdio(false);
119     int N=0,C=0;
120     cout<<"Please enter the number of people:N=";
121     cin>>N;
122     cout<<"Please enter:C=";
123     cin>>C;
124     cout<<"winner is "<<sun1(N,C)<<endl;
125     clock_t end1=clock();
126     cout<<"winner is "<<sun2(N,C)<<endl;
127     clock_t end2=clock();
128     cout<<(end2-end1)/float(CLOCKS_PER_SEC)<<"seconds"<<endl;
129     cout<<"winner is "<<sun3(N,C)<<endl;
130     return 0;
131 }