更改

Assuming the execution time follows power rule, , the coefficient a can be found  by taking empirical measurements of run time <math>\{t_1, t_2\}</math> at some problem-size points <math>\{n_1, n_2\}</math>, and calculating <math>t_2/t_1 = (n_2/n_1)^a</math> so that <math>a = \log(t_2/t_1) / \log(n_2/n_1)</math>. In other words, this measures the slope of the empirical line on the log–log plot of execution time vs. problem size, at some size point. If the order of growth indeed follows the power rule (and so the line on log–log plot is indeed a straight line), the empirical value of a will  stay constant at different ranges, and if not, it will change (and the line is a curved line) - but still could serve for comparison of any two given algorithms as to their empirical local orders of growth behaviour. Applied to the above table:

Assuming the execution time follows power rule, , the coefficient a can be found  by taking empirical measurements of run time <math>\{t_1, t_2\}</math> at some problem-size points <math>\{n_1, n_2\}</math>, and calculating <math>t_2/t_1 = (n_2/n_1)^a</math> so that <math>a = \log(t_2/t_1) / \log(n_2/n_1)</math>. In other words, this measures the slope of the empirical line on the log–log plot of execution time vs. problem size, at some size point. If the order of growth indeed follows the power rule (and so the line on log–log plot is indeed a straight line), the empirical value of a will  stay constant at different ranges, and if not, it will change (and the line is a curved line) - but still could serve for comparison of any two given algorithms as to their empirical local orders of growth behaviour. Applied to the above table:

假设执行时间遵循幂律，通过对一些问题规模点<math>\{n_1, n_2\}</math>的运行时间<math>\{t_1, t_2\}</math>进行经验测量，并计算出𝑡<math>t_2/t_1 = (n_2/n_1)^a</math>，从而得到系数<math>a = \log(t_2/t_1) / \log(n_2/n_1)</math>。

假设算法运行时间遵循幂律规则，通过对一些问题规模点<math>\{n_1, n_2\}</math>的运行时间<math>\{t_1, t_2\}</math>进行经验测量，并计算出𝑡<math>t_2/t_1 = (n_2/n_1)^a</math>，从而得到系数<math>a = \log(t_2/t_1) / \log(n_2/n_1)</math>。

换言之，这衡量了在某个规模点上，执行时间与问题大小的双对数曲线 log-log plot上经验线的斜率。如果增长顺序确实遵循幂律（因此双对数曲线图上的直线确实是一条直线），那么a的经验值将在不同的范围内将保持不变，如果不是，它将发生改变（而且这条线是一条曲线），但仍然可以用来比较任何两种给定算法的经验局部增长顺序。应用于上表：

换言之，这衡量了在某个规模点上，执行时间与问题大小的双对数曲线 log-log plot上经验线的斜率。如果增长顺序确实遵循幂律（因此双对数曲线图上的直线确实是一条直线），那么a的经验值将在不同的范围内将保持不变，如果不是，它将发生改变（而且这条线是一条曲线），但仍然可以用来比较任何两种给定算法的经验局部增长顺序。应用于上表：

It is clearly seen that the first algorithm exhibits a linear order of growth indeed following the power rule. The empirical values for the second one are diminishing rapidly, suggesting it follows another rule of growth and in any case has much lower local orders of growth (and improving further still), empirically, than the first one.

It is clearly seen that the first algorithm exhibits a linear order of growth indeed following the power rule. The empirical values for the second one are diminishing rapidly, suggesting it follows another rule of growth and in any case has much lower local orders of growth (and improving further still), empirically, than the first one.

=== 运行时复杂性度量 Evaluating run-time complexity ===

=== 运行时复杂性度量 Evaluating run-time complexity ===