Write a function square_floor(n) that takes a positive integer n and returns the largest perfect square that is less than or equal to n.
For example:
square_floor(9) should return 9, because 3**2 = 9 <= 9 but 4**2 = 16 > 9.square_floor(20) should return 16 because 4**2 = 16 <= 20 but 5**2 = 25 > 20Put this function in a file quiz2prob2.py (with the usual required header and file-level docstring) and submit it. The file quiz2prob2.py doesn't need to do anything other than defining that single function.
# MCS 275 Quiz 2 Problem 2
# Jennifer Vaccaro
# I have created this code in accordance with the course syllabus.
def square_floor(n):
"""Finds the largest square smaller than the given integer"""
ans_sqrt = int(n**0.5) # Take the square root, then convert to an integer
return ans_sqrt**2 # Square and return
In this solution, it may be helpful to recall that when int() converts a float to an integer, it discards any fractional part, e.g. int(1.02) and int(1.999) both return 1.
Write a function longest_run_length(text) that takes a string text and returns an integer which is the length of the longest consecutive block of any single character in the string.
The function should consider any character, and use case-sensitive comparisons.
Therefore:
longest_run_length("heliotrope!!") should return 2 because "!" appears twice in a row, and no character appers 3 or more times in a rowlongest_run_length("Distinguished raccoons") should return 3 because there are three spaces in a row in the string, and no character appears 4 times in a rowlongest_run_length("") should return 0longest_run_length("Eels have a complicated life cycle with many stages") should return 1 because the string is not empty, but no character appears twice (or more) in a rowPut this function in a file quiz2prob3.py (with the usual required header and file-level docstring) and submit it. The file quiz2prob3.py doesn't need to do anything other than defining that single function.
Note: It is expected that you can make this function pretty easily by modifying the solution to one of the problems on Worksheet 2.
# MCS 275 Quiz 2 Problem 3
# Jennifer Vaccaro
# I have created this code in accordance with the course syllabus.
def longest_run_length(text):
"""Given a text string, returns the length of the longest sequence of repeated characters"""
last_char = ""
current_run = 1
longest_run = 0
# Compare each character to the previous character
# Count the number of consecutive repeats
for c in text:
if c == last_char:
current_run += 1
else:
current_run = 1
if current_run > longest_run:
longest_run = current_run #update longest_run
last_char = c
# Return the value of the longest run
return longest_run
Recall the RATS process described in Worksheet 2. This associated to any integer n a sequence of numbers, such as n=12 leading to the sequence 12, 33, 66, 123, 444, 888, 1677, 3489, 12333, 44556, ....
In Worksheet 2 you wrote a program to compute this sequence for one starting value, and to stop if a cycle was found. When we determine whether a certain starting value leads to a cycle, we'll say that we have classified the that starting value. So the Worksheet 2 program classifies a single starting value provided by the user.
Modify the program developed in Worksheet 2 so that instead of classifying one starting value, it tries each value of n between 1 and 100 (inclusive) and prints what it finds for each one. Each line of output should show the starting value and the observed behavior. The modified program shouldn't require any command line arguments or keyboard input.
When it is run, the first six lines of output should be:
1: No periodic sequence found in 150 iterations
2: No periodic sequence found in 150 iterations
3: Ends at periodic sequence [444, 888, 1677, 3489, 12333, 44556, 111, 222]
4: No periodic sequence found in 150 iterations
5: No periodic sequence found in 150 iterations
6: Ends at periodic sequence [444, 888, 1677, 3489, 12333, 44556, 111, 222]and the last two lines of output should be:
99: Ends at periodic sequence [117, 288]
100: No periodic sequence found in 150 iterationsNote the slightly different way of printing the output compared to Worksheet 2.
Call this program quiz2prob4.py (with the usual required header and file-level docstring) and submit it.
# MCS 275 Quiz 2 Problem 4
# Jennifer Vaccaro
# I have adjusted this code from course worksheet solutions in accordance with the course syllabus.
def reverse_int(n):
"""Reverse the digits of integer n and return
the resulting integer"""
n_str = str(n)
# Note: int() drops leading zeros automatically, so
# e.g. int("0012") returns 12
return int(n_str[::-1])
def next_rats(n):
"""Reverses, adds, then sorts an integer n"""
sum_int = n + reverse_int(n)
sum_digits = list(str(sum_int))
sum_digits.sort()
sorted_sum_str = "".join(sum_digits)
return int(sorted_sum_str)
# Iterate start_n from 1-100 inclusive
for start_n in range(1,101):
# Instead of using a user input, use start_n to run RATS.
max_generations = 150
rats_list = [start_n]
n = start_n
periodic = False
for _ in range(max_generations):
n = next_rats(n)
if n in rats_list:
print("{}: RATS ends in a periodic sequence {}".format(start_n, rats_list[rats_list.index(n):]))
periodic = True
break
else:
rats_list.append(n)
if not periodic:
print("{}: RATS has no periodic sequence after {} iterations".format(start_n, max_generations))