Algorithms For Dummies

 

   

  PART 5 

 Challenging Difficult Problems

In a normal distribution, most of the values are around the mean value. Therefore, 

if you pick a random number from the input, you most likely get a number around 

the center of the distribution. However; though less likely, you may also draw a 

number far from the center. If your algorithm works better by using the mean 

than it does with any other number, picking a number at random makes sense and 

may be less trouble than devising a smarter way to draw values from your input.

Another  important  distribution  mentioned  in  this  chapter  is  the  uniform  dis-

tribution. You can represent it using some Python code (the output appears in 

 Figure 17-2), too:

uniform_distribution = uniform(size=10000) * 100

weights = np.ones_like(uniform_distribution

                      ) / len(uniform_distribution)

plt.hist(uniform_distribution, bins=20, weights=weights)

plt.xlabel("Value")

plt.ylabel("Probability")

plt.show()

The  uniform  distribution  is  noticeably  different  from  the  normal  distribution 

because each number has the same probability of being in the input as any other. 

Consequently, the histogram bars are all roughly of the same size, and picking a 

number in a uniform distribution means giving all the numbers the same chance 

to appear. It’s a way to avoid systematically picking the same groups of numbers 

when your algorithm works better with varied inputs. For instance, uniform dis-

tributions work well when your algorithm works fine with certain numbers, so-so 

with most, and badly with a few others, and you prefer to pick numbers randomly 

FIGURE 17-1: 

A histogram  

of a normal 

distribution.

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CHAPTER 17