while loopsA while loop is similar to a for loop in that it is a tool used to automate a repetive task. The core difference between while and for loops is as follows:
for loop executes a predetermined number of times. A for loop that begins with "for i in range(a,b)" will execute exactly once for each value of the counter i that falls within the given range. while loop executes as long as some supplied condition is true. Depending on the nature of this condition, we do not necessarily know ahead of time how many times the loop will execute. At a basic level, for loops and while loops behave similarly, as shown by the following examples.
n = 0
while n < 10:
print(n**2)
n += 1
The task above could have been accomplished more succintly using a for loop:
for n in range(0,10):
print(n**2)
The usefulnes of while loops arises from sitautions in which we aren't sure how many times the loop should execute.
As a simple example, lets say that we want to print out all perfect squares less than 1000.
x = 0
while x**2 < 1000:
print(x**2)
x += 1
� Exercise
Find the largest power of 2 less than 10,000. Print this number.
n = 0
while 2**n < 10000:
n +=1
print(2**(n-1))
� Exercise
Find the smallest integer n whose factorial is greater than 1,000,000. Once you have found n, print the following two messages:
The smallest integer whose factorial is less than 1,000,000 is [n].
[n] factorial is equal to [n!]. n = 1
nFact = 1
while nFact < 1000000:
n +=1
nFact = nFact * n
print("The smallest integer whose factorial is less than 1,000,000 is " + str(n) + ".")
print(str(n) + " factorial is equal to " + str(nFact) + ".")
� Exercise
Determine the number of times that 2 evenly divides 3,620,864. In other words, determine how many factors of 2 are in 3,620,864. Print the message:
3,620,864 can be divided by 2 a total of [count] times. x = 3620864
count = 0
while(x % 2 == 0):
x = x/2
count += 1
print("3,620,854 can be divided by 2 a total of " + str(count) + " times.")
� Exercise
Find all of the factors of the number 14,267,352. Store the factors in a list called factors. Print this list.
x = 14267352
fctr = 2
factors = []
while(x > 1):
while(x % fctr == 0):
x = x / fctr
factors.append(fctr)
fctr += 1
print(factors)
Programs often require input from the user. Python's input() function provides a method of prompting the user for input. For example, consider the following code:
name = input("What is your name? ")
This code will print the string, "What is your name? " and will then wait for user input. The value entered by the user will then be stored in the variable myVar.
name = input("What is your name? ")
print("Hello, " + name + "!")
User input can be combined with while loops to create interactive programs.
import random
n = random.choice(range(0, 1000))
print("I have selected a random number between 0 and 999, inclusive. Can you guess it?")
done = False
count = 1
while done == False:
guess = int(input("Please enter guess number " + str(count) + ": "))
if(guess < n):
print("Your guess was too small.")
elif(guess > n):
print("Your guess was too large.")
else:
print("That's it! It took you " + str(count) + " guesses to find the right answer.")
done = True
count += 1
� Exercise
Newton's Method is a calculus-based technique for finding approximate solutions to mathematical equations. We will not discuss the details of Netwon's Method here, but one application of this technique is finding square roots of numbers. The process works as follows:
Apply this technique 10 times to approximate the square root of 734,123,454,324.
# K is the number whe want to take the square root of.
K = 734123454324
# x will be equal to our first guess
x = 5
# We will create a loop that runs 10 times, improving our guess each time.
for i in range(0,10):
x = x - (x**2 - K) / (2*x)
print(x)
It tuns out that the true square root of 734,123,454,324 is approximately 856,810.0457. Our approximation is way off. We didn't let the algorithm run enough times.
Let's try again with a while loop. We will continue to make improvements on our estimate until two consecutive estimates are within 1/1000 of each other.
# K is the number whe want to take the square root of.
K = 734123454324
# x will be equal to our first guess
x = 5
# We create a flag that tells us when to stop
keep_going = True
# We will create a loop that runs 10 times, improving our guess each time.
while (keep_going):
for i in range(0,10):
x_old = x
x = x - (x**2 - K) / (2*x)
diff = x_old - x
# We need to take the absolute value of diff
if diff < 0:
diff = -diff
if(diff < 0.001):
keep_going = False
print(x)