Created
August 12, 2017 07:16
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zz from newsmth e进制是信息表示的最优解 | |
先考虑最优的定义 | |
假定总共有n位,每位m个状态,m*n=v | |
在v一定时,使得m^n最大 | |
也就是k(n)=(v/n)^n最大 | |
考虑一般情况下 | |
ln(k(n))=(ln(v)-ln(n))*n=ln(v)*n - ln(n)*n | |
对n求导 ln(v) - (n*1/n + ln(n)) = ln(v) - 1 - ln(n) | |
解得ln(n)=ln(v)-1是k(n)唯一的极值点 | |
易知是k(n)最大值点 | |
所以n=v/e m=e时,k(n)最大 |
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