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Time complexity 时间复杂度:O(logn)与O(log2n)_Time Complexity_Language Agnostic_Big O_Logarithm - Fatal编程技术网

Time complexity 时间复杂度:O(logn)与O(log2n)

Time complexity 时间复杂度:O(logn)与O(log2n),time-complexity,language-agnostic,big-o,logarithm,Time Complexity,Language Agnostic,Big O,Logarithm,O(logn)和O(log2n)一样吗?By,log(2n)=log(2)+log(n)既然你是用大O来写的,你得到的是O(log(2))+O(log(n))=O(log(n)是的,O(logn)和O(log2n)的意思是一样的。这是因为 log2n=log2+logn 因为log2是一个常数,所以它被big-O符号忽略 更广泛地说,对数的属性意味着许多常用表达式的log最终都等价于O(logn) log nk=k log n=O(log n) log(2n)=log(2)+log(n)=log

O(logn)和O(log2n)一样吗?

By,
log(2n)=log(2)+log(n)
既然你是用大O来写的,你得到的是
O(log(2))+O(log(n))=O(log(n)

是的,O(logn)和O(log2n)的意思是一样的。这是因为

log2n=log2+logn

因为log2是一个常数,所以它被big-O符号忽略

更广泛地说,对数的属性意味着许多常用表达式的log最终都等价于O(logn)

log nk=k log n=O(log n)


log(2n)=log(2)+log(n)=log(n)+常量,只有n是重要的,乘法因子可以忽略。在log的情况下,它甚至是“更可忽略的”,事实上,log(2n)=log(n)+log(2),因此只要n是“大的”,log 2项就可以忽略