组合问题和数值问题有什么区别
您能否分别举出至少两个例子。谢谢。
Could you please give at least two examples of each. Thanks.
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您能否分别举出至少两个例子。谢谢。
Could you please give at least two examples of each. Thanks.
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数值问题是指计算某些数值量的问题。输入、输出和状态往往分布在连续集合上，例如实数。一个例子是：在给定角度和初始速度的情况下，计算炮弹的飞行高度。数值问题通常可以通过近似来解决。由于变量是连续的，因此存在“平滑性”假设，即如果 f(xa) 太低，而 f(x+a) 太高，则 f(x) 很可能接近正确。 （我可能在这里缺少正确的术语。）
组合问题是指输入、输出和状态往往分布在离散集合上的问题。一个例子是：计算该图中有多少条从 a 到 b 的不同路径。
请注意，将每个问题的各个方面组合到一个问题中很容易。例如，从 a 到 b 的路径平均长度是多少？或者怎么样：“黎曼 zeta 函数的任何非平凡零的实部是 0.5” http:// /en.wikipedia.org/wiki/Riemann_hypothesis。
Numerical problems are those in which there is a calculation of some numerical quantity. The inputs, outputs, and states tend to range over the continuous sets, such as the real numbers. An examples would be: calculate how high this cannon ball will fly, given its angle and initial velocity. Numerical problems can often be solved by approximation. Because the variables are continuous, there is an assumption of "smoothness" in that if f(x-a) is too low, and f(x+a) is too high, then f(x) is likely to be closr to correct. (I may be missing the proper terminology here.)
Combinatorial problems are those in which the inputs, outputs and states tend to range over discrete sets. An example would be: calculate how many distinct paths from a to b there are in this graph.
Note that it's easy to combine aspects of each in a single problem. For example, what is the average length of the paths from a to b? Or how about: "The real part of any non-trivial zero of the Riemann zeta function is 0.5" http://en.wikipedia.org/wiki/Riemann_hypothesis.
组合问题是有效的计数问题；这些出现在离散数学的研究中。有限集有多少种排列？给定
n个麦片盒，每个盒中包含k个不同的奖品之一，有多少种方法可以收集所有k个奖品？数值问题实际上是计算问题；这些通常出现在工程和科学中，试图近似方程的解（例如求根或微分方程）或尝试近似数值（例如定积分或特征值）。
Combinatorial problems are effectively counting problems; these arise in the study of discrete mathematics. How many permutations are there of a finite set? Given
ncereal boxes each containing one ofkdifferent prizes, how many ways are there to collect allkprizes?Numerical problems are effectively calculation problems; these typically arise in engineering and the sciences in attempts to approximate solutions to equations (root finding or differential equations, for example) or in attempts to approximate numerical values (definite integrals or eigenvalues, for example).