数据结构中的二项式分布
二项分布是从N条伯努利路径中获得n次成功的离散概率分布Pp(n|N)(具有x=0和x=1标记的两个可能结果)。x=1是成功,x=0是成功发生的概率为p,失败发生的概率为q=1–p。)因此,二项分布可以写为
$$P_{p}\lgroupn\:\arrowvert\N\rgroup=\left(\begin{array}{c}N\\n\end{array}\right)p^{n}\lgroup1-p\rgroup^{Nn}$$
示例
#include <iostream> #include <random> using namespace std; int main(){ const int nrolls = 10000; // number of rolls const int nstars = 100; // maximum number of stars to distribute default_random_engine generator; binomial_distribution<int> distribution(9,0.5); int p[10]={}; for (int i=0; i<nrolls; ++i) { int number = distribution(generator); p[number]++; } cout << "binomial_distribution (9,0.5):" << endl; for (int i=0; i<10; ++i) cout << i << ": " << string(p[i]*nstars/nrolls,'*') << endl; }
输出结果
0: 1: * 2: ****** 3: *************** 4: ************************* 5: ************************ 6: **************** 7: ******* 8: * 9: