POJ 3744 Scout YYF I：概率dp

  1 // state expression:
  2 // dp[i] = probability moving to i
  3 //
  4 // find the answer:
  5 // dp[last mine + 1]
  6 //
  7 // transferring:
  8 // dp[i] = dp[i-1] * p + dp[i-2] * (1-p)
  9 //
 10 // boundary:
 11 // dp[1] = 1
 12 // others = 0
 13 //
 14 // optimization:
 15 // quick pow for matrix
 16 // from x to y
 17 // res = start * special ^ (y-x)
 18 // dp[i] = res.val[0][0]
 19 #include <iostream>
 20 #include <stdio.h>
 21 #include <string.h>
 22 #include <algorithm>
 23 #define MAX_N 15
 24 #define MAX_L 5
 25 
 26 using namespace std;
 27 
 28 struct Mat
 29 {
 30     int n;
 31     int m;
 32     double val[MAX_L][MAX_L];
 33     Mat()
 34     {
 35         n=0;
 36         m=0;
 37         memset(val,0,sizeof(val));
 38     }
 39     void print_mat()
 40     {
 41         for(int i=0;i<n;i++)
 42         {
 43             for(int j=0;j<m;j++)
 44             {
 45                 cout<<val[i][j]<<" ";
 46             }
 47             cout<<endl;
 48         }
 49         cout<<endl;
 50     }
 51 };
 52 
 53 int n;
 54 int pos[MAX_N];
 55 double p;
 56 double ans;
 57 
 58 Mat make_unit(int k)
 59 {
 60     Mat mat;
 61     mat.n=k;
 62     mat.m=k;
 63     for(int i=0;i<k;i++)
 64     {
 65         mat.val[i][i]=1;
 66     }
 67     return mat;
 68 }
 69 
 70 Mat make_start()
 71 {
 72     Mat mat;
 73     mat.n=1;
 74     mat.m=2;
 75     mat.val[0][0]=0;
 76     mat.val[0][1]=1;
 77     return mat;
 78 }
 79 
 80 Mat make_special()
 81 {
 82     Mat mat;
 83     mat.n=2;
 84     mat.m=2;
 85     mat.val[0][0]=0;
 86     mat.val[0][1]=1-p;
 87     mat.val[1][0]=1;
 88     mat.val[1][1]=p;
 89     return mat;
 90 }
 91 
 92 Mat mul_mat(const Mat &a,const Mat &b)
 93 {
 94     Mat c;
 95     if(a.m!=b.n)
 96     {
 97         cout<<"Error: mul_mat"<<endl;
 98         return c;
 99     }
100     c.n=a.n;
101     c.m=b.m;
102     for(int i=0;i<a.n;i++)
103     {
104         for(int j=0;j<b.m;j++)
105         {
106             for(int k=0;k<a.m;k++)
107             {
108                 c.val[i][j]+=a.val[i][k]*b.val[k][j];
109             }
110         }
111     }
112     return c;
113 }
114 
115 Mat quick_pow_mat(Mat mat,long long k)
116 {
117     Mat ans;
118     if(mat.n!=mat.m)
119     {
120         cout<<"Error: quick_pow_mat"<<endl;
121         return ans;
122     }
123     ans=make_unit(mat.n);
124     while(k)
125     {
126         if(k&1)
127         {
128             ans=mul_mat(ans,mat);
129         }
130         mat=mul_mat(mat,mat);
131         k>>=1;
132     }
133     return ans;
134 }
135 
136 void read()
137 {
138     pos[0]=0;
139     for(int i=1;i<=n;i++)
140     {
141         cin>>pos[i];
142     }
143 }
144 
145 void solve()
146 {
147     sort(pos+1,pos+1+n);
148     Mat special=make_special();
149     ans=1;
150     for(int i=1;i<=n;i++)
151     {
152         Mat start=make_start();
153         Mat res=mul_mat(start,quick_pow_mat(special,pos[i]-pos[i-1]));
154         ans*=(1-res.val[0][0]);
155     }
156 }
157 
158 void print()
159 {
160     printf("%.7f\n",ans);
161 }
162 
163 int main()
164 {
165     while(cin>>n>>p)
166     {
167         read();
168         solve();
169         print();
170     }
171 }