算法4-1.1.27二項分布

二項分布。估計用以下代碼計算binomial(100,50,0.25)将會産生的遞歸調用次數：

public static double binomial(int N,int k,double p)
 {
 if (N0 && k0) return 1.0;
 if (N<0 || k<0) return 0.0;
 return (1.0-p)binomial(N-1,k,p)+pbinomial(N-1,k-1,p);
 }      

public static void main(String[] args) {

        int N = 100;
        double p = 0.25;
        int k = 50;
        binomial(N,50,p);
        double[][] f = new double[N+1][k+1];
        f[0][0] = 1.0;
        for (int i = 1; i < N+1; i ++){
            f[i][0] = f[i-1][0]*(1-p);
        }
        for (int i = 1; i < N+1; i ++){
            for (int j = 1; j < i+1 && j < k+1; j ++){
                f[i][j] = f[i][j]*(1-p)+f[i-1][j-1]*p;
            }
        }
        System.out.println(f[N][k]);
    }
}