Untitled - HackMD

def f(n, p):
    if n == 1:
        return 1
    else:
        return 1.0/n + 1.0 - (1.0- p)**n

def argmin_f(keys, f):
    return min(keys, key=f)

def main():
    interval = 1000
    max_people = 100
    print("| positive rate | optimal group size|")
    print("| -- | -- |")
    for i in range(interval):
        p = i/interval
        best = argmin_f(range(1, max_people), lambda x: f(x, p))
        print(f"| {p} | {best}|")

main()

positive rate	optimal group size
0.0	99
0.001	32
0.002	23
0.003	19
0.004	16
0.005	15
0.006	13
0.007	12
0.008	12
0.009	11
0.01	11
0.011	10
0.012	10
0.013	9
0.014	9
0.015	9
0.016	8
0.017	8
0.018	8
0.019	8
0.02	8
0.021	7
0.022	7
0.023	7
0.024	7
0.025	7
0.026	7
0.027	7
0.028	7
0.029	6
0.03	6
0.031	6
0.032	6
0.033	6
0.034	6
0.035	6
0.036	6
0.037	6
0.038	6
0.039	6
0.04	6
0.041	6
0.042	5
0.043	5
0.044	5
0.045	5
0.046	5
0.047	5
0.048	5
0.049	5
0.05	5
0.051	5
0.052	5
0.053	5
0.054	5
0.055	5
0.056	5
0.057	5
0.058	5
0.059	5
0.06	5
0.061	5
0.062	5
0.063	5
0.064	5
0.065	5
0.066	4
0.067	4
0.068	4
0.069	4
0.07	4
0.071	4
0.072	4
0.073	4
0.074	4
0.075	4
0.076	4
0.077	4
0.078	4
0.079	4
0.08	4
0.081	4
0.082	4
0.083	4
0.084	4
0.085	4
0.086	4
0.087	4
0.088	4
0.089	4
0.09	4
0.091	4
0.092	4
0.093	4
0.094	4
0.095	4
0.096	4
0.097	4
0.098	4
0.099	4
0.1	4
0.101	4
0.102	4
0.103	4
0.104	4
0.105	4
0.106	4
0.107	4
0.108	4
0.109	4
0.11	4
0.111	4
0.112	4
0.113	4
0.114	4
0.115	4
0.116	4
0.117	4
0.118	4
0.119	4
0.12	4
0.121	4
0.122	4
0.123	4
0.124	3
0.125	3
0.126	3
0.127	3
0.128	3
0.129	3
0.13	3
0.131	3
0.132	3
0.133	3
0.134	3
0.135	3
0.136	3
0.137	3
0.138	3
0.139	3
0.14	3
0.141	3
0.142	3
0.143	3
0.144	3
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0.15	3
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0.18	3
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0.19	3
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0.192	3
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0.194	3
0.195	3
0.196	3
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0.198	3
0.199	3
0.2	3
0.201	3
0.202	3
0.203	3
0.204	3
0.205	3
0.206	3
0.207	3
0.208	3
0.209	3
0.21	3
0.211	3
0.212	3
0.213	3
0.214	3
0.215	3
0.216	3
0.217	3
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0.219	3
0.22	3
0.221	3
0.222	3
0.223	3
0.224	3
0.225	3
0.226	3
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0.23	3
0.231	3
0.232	3
0.233	3
0.234	3
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0.24	3
0.241	3
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0.244	3
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0.28	3
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0.29	3
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0.297	3
0.298	3
0.299	3
0.3	3
0.301	3
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0.303	3
0.304	3
0.305	3
0.306	3
0.307	1
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0.309	1
0.31	1
0.311	1
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0.315	1
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0.32	1
0.321	1
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0.371	1
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0.4	1
0.401	1
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0.41	1
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0.571	1
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0.581	1
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0.601	1
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