HDU4405：Aeroplane chess（概率dp & 期望）

Aeroplane chess Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 4200    Accepted Submission(s): 2659 Problem Description Hzz loves aeroplane chess very much. The chess map contains N+1 grids labeled from 0 to N. Hzz starts at grid 0. For each step he throws a dice(a dice have six faces with equal probability to face up and the numbers on the faces are 1,2,3,4,5,6). When Hzz is at grid i and the dice number is x, he will moves to grid i+x. Hzz finishes the game when i+x is equal to or greater than N. There are also M flight lines on the chess map. The i-th flight line can help Hzz fly from grid Xi to Yi (0 Please help Hzz calculate the expected dice throwing times to finish the game.   Input There are multiple test cases.  Each test case contains several lines. The first line contains two integers N(1≤N≤100000) and M(0≤M≤1000). Then M lines follow, each line contains two integers Xi,Yi(1≤Xi The input end with N=0, M=0.    Output For each test case in the input, you should output a line indicating the expected dice throwing times. Output should be rounded to 4 digits after decimal point.   Sample Input 2 0 8 3 2 4 4 5 7 8 0 0   Sample Output 1.1667 2.3441   Source 2012 ACM/ICPC Asia Regional Jinhua Online

题意：X轴上玩家在1点，每次抛色子向前走，或者有些点相连的要直接飞过去，问到N点抛色子的期望数。

思路：求期望，dp[i]表示在i点到N点的期望值，显然dp[N]=0，需要求dp[0]，无直飞路线下dp[i]=dp[i+1]/6+dp[i+2]/6+...+dp[i+6]/6+1，倒推求解即可。

# include 
# include 
# include 
# include 
using namespace std;
int son[100010];
double dp[100010];
int main()
{
    int n, m, a, b;
    while(~scanf("%d%d",&n,&m),n+m)
    {
        memset(son, 0, sizeof(son));
        memset(dp, 0, sizeof(dp));
        while(m--)
        {
            scanf("%d%d",&a,&b);
            son[a] = b;
        }
        dp[n] = 0;
        for(int i=n-1; i>=0; --i)
        {
            if(!son[i])
            {
                dp[i] = 1;
                for(int j=1; j<=6; ++j)
                    dp[i] += dp[i+j]/6;
            }
            else
                dp[i] = dp[son[i]];
        }
        printf("%.4f\n",dp[0]);
    }
    return 0;
}

Aeroplane chess Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 4200    Accepted Submission(s): 2659 Problem Description Hzz loves aeroplane chess very much. The chess map contains N+1 grids labeled from 0 to N. Hzz starts at grid 0. For each step he throws a dice(a dice have six faces with equal probability to face up and the numbers on the faces are 1,2,3,4,5,6). When Hzz is at grid i and the dice number is x, he will moves to grid i+x. Hzz finishes the game when i+x is equal to or greater than N. There are also M flight lines on the chess map. The i-th flight line can help Hzz fly from grid Xi to Yi (0 Please help Hzz calculate the expected dice throwing times to finish the game.   Input There are multiple test cases.  Each test case contains several lines. The first line contains two integers N(1≤N≤100000) and M(0≤M≤1000). Then M lines follow, each line contains two integers Xi,Yi(1≤Xi The input end with N=0, M=0.    Output For each test case in the input, you should output a line indicating the expected dice throwing times. Output should be rounded to 4 digits after decimal point.   Sample Input 2 0 8 3 2 4 4 5 7 8 0 0   Sample Output 1.1667 2.3441   Source 2012 ACM/ICPC Asia Regional Jinhua Online