Supercharged Python: Take Your Code to the Next Level [ PART I ]

15 16 4 31 32 5 63 64 6 The numbers in the leftmost column of Table 11.8 list ranges of numbers in the game; not all numbers are listed, but only those that “step up”—that is, require an additional guess. Each of these is an upper limit—so that for N = 15 or less, for example, up to four guesses are required. But for any range greater than 15, more guesses are required. The numbers in the leftmost column are each 1 less than a power of 2. When added to 1, they correspond to a power of 2. Therefore, to get the numbers in the rightmost column—which contains the number of guesses needed—you must take logarithm base 2 of N+1. The final step is to round upward to the nearest integer, because the number of steps taken must be an integer, and not floating point. The correct formula is Maximum guesses needed = ceiling(log-base-2(N + 1)) Writing the program, with the aid of the math package, is now easy. Click here to view code image from math import log2, ceil n = int(input('Enter size of range: ')) x = ceil(log2(n + 1)) print('Max. number of guesses needed is', x)

This program, in addition to using the math.log2 function, also uses math.ceil, one of the miscellaneous functions. The ceil function takes any number and rounds it upward to the lowest integer greater than or equal to its input. Now, if you run the program, you can answer the question we posed earlier. As usual, user input is shown in bold. Click here to view code image Enter size of range: 50 Max. number of guesses needed is 6. So that’s the answer. If you follow the ideal strategy—which is to make a guess in the middle of the available range—you should never need more than six guesses. As for the strategy, you pick a number as close as you can to the midpoint of the available range. This range should always be what’s left over after you use all the information you’ve gotten from previous guesses. For example, if you guess 25 and the computer says, “Too high,” you should adjust the range to 1 to 24 instead of 1 to 50. This strategy reflects a binary-search pattern, which should, on average, reduce the number of available choices by roughly 50 percent each time, until the result is found. CHAPTER 11 SUMMARY This chapter explored how two of the most commonly used packages—random and math—can be used in practical ways in your programs. Both of these packages come preinstalled with the Python download. The random package provides a variety of distributions. The most commonly used ones were explored in this chapter: randint, returning a random integer with uniform distribution across a given range; shuffle, which rearranges

the contents of a list as if it were a deck of cards; and normalvariate. The classic normal probability distribution tends to generate values close to the specified mean. Outlier values are always possible, but the farther a value is from the mean, the less frequently it’s generated. The chapter then showed how to use some of the most common functions from the math package, including tan, which calculates tangents, and the logarithmic functions. The Python implementation of logarithms includes log10, log2, and finally log, which calculates logarithms in any base. CHAPTER 11 REVIEW QUESTIONS 1 What exactly is a probability distribution? How can you predict the values at all, if they are supposed to be random? 2 What is the difference, if any, between true random numbers and pseudo-random numbers? Why are the latter considered “good enough”? 3 What are the two major factors that govern how a “normal” probability distribution behaves? 4 Give an example of a normal distribution in real life. 5 How would you expect a probability distribution to behave in the short run? How would you expect it to change as the number of trials increases? 6 What kind of object can be shuffled by using random.shuffle? 7 Name several general categories of functions in the math package. 8 How is exponentiation related to logarithms?

9 What are the three logarithmic functions supported by Python? CHAPTER 11 SUGGESTED PROBLEMS 1 Revise the number guessing game in Section 11.4, “A Random Integer Game,” so that it lets the user specify a range of values at the beginning, rather than always using 1 to 50. 2 Write an application that determines the length of a hypotenuse of a right triangle, given two pieces of information: the nearest angle, measured in degrees, and the length of the adjacent side. 3 By taking advantage of the Deck object presented in Section 11.5, write a game program that deals a Poker hand of five cards. Then prompt the user to enter a series of numbers (for example: “1, 3, 5”) that selects cards to be replaced during a draw phase. Then print the result of drawing the new cards.