hdu 4487 Maximum Random Walk (概率dp)
阿新 • • 發佈:2019-02-19
Maximum Random Walk
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 219 Accepted Submission(s): 120Problem Description Consider the classic random walk: at each step, you have a 1/2 chance of taking a step to the left and a 1/2 chance of taking a step to the right. Your expected position after a period of time is zero; that is, the average over many such random walks is that you end up where you started. A more interesting question is what is the expected rightmost position you will attain during the walk.
Input The first line of input contains a single integer P, (1 <= P <= 15), which is the number of data sets that follow. Each data set should be processed identically and independently.
Each data set consists of a single line of input consisting of four space-separated values. The first value is an integer K, which is the data set number. Next is an integer n, which is the number of steps to take (1 <= n <= 100). The final two are double precision floating-point values L and R
which are the probabilities of taking a step left or right respectively at each step (0 <= L <= 1, 0 <= R <= 1, 0 <= L+R <= 1). Note: the probably of not taking a step would be 1-L-R.
Output For each data set there is a single line of output. It contains the data set number, followed by a single space which is then followed by the expected (average) rightmost position you will obtain during the walk, as a double precision floating point value to four decimal places.
Sample Input 3 1 1 0.5 0.5 2 4 0.5 0.5 3 10 0.5 0.4
Sample Output 1 0.5000 2 1.1875 3 1.4965
Source 思路:
#include <iostream> #include <cstdio> #include <cstring> #define maxn 201 using namespace std; int n,m; float pl,pr,pm,ans; float dp[101][maxn][maxn]; int main() { int i,j,k,t,test,l,r; scanf("%d",&t); while(t--) { scanf("%d%d%f%f",&test,&n,&pl,&pr); pm=1-pl-pr; memset(dp,0,sizeof(dp)); dp[0][100][100]=1; // 將一百設為起點 l=100-n; r=100+n; for(i=1;i<=n;i++) // 走了i步 { for(j=l;j<=r;j++) // 到達第j個位置 { for(k=100;k<=r;k++) // 最大到達的右邊界 { dp[i][j][k]+=dp[i-1][j][k]*pm; dp[i][j-1][k]+=dp[i-1][j][k]*pl; if(j+1>k) dp[i][j+1][j+1]+=dp[i-1][j][k]*pr; else dp[i][j+1][k]+=dp[i-1][j][k]*pr; } } } ans=0; for(k=100;k<=r;k++) { for(j=l;j<=r;j++) { ans+=dp[n][j][k]*(k-100); } } printf("%d %.4f\n",test,ans); } return 0; }