3.9 Homework

In addition to passing all the tests, I also made a option to have to be precise to a decimal points

def sqrt(N,p): # sqrt with precision
    # to find the closest int
    low = 0
    end = N
    ans = 1
    while low <= end:
        mid = int((low + end) / 2)
        if mid **2 == N:
            ans = mid
            break
        if mid ** 2 < N:
            low = mid + 1
            ans = mid
        else:
            end = mid - 1
    
    # calculating for precision
    incre = 0.1
    for i in range(p):
        while ans ** 2 <= N:
            ans += incre
        ans -= incre
        incre /=  10

    return round(ans,p)

from math import sqrt as sq
test_cases = [0,1,4,85248289,22297284,18939904,91107025,69122596,9721924,37810201,1893294144,8722812816,644398225]
answers = [int(sq(x)) for x in test_cases]

def checkValid():
    for i in range(len(test_cases)):
        if sqrt(test_cases[i],0) == answers[i]:
            print("Check number {} passed".format(i+1))
        else:
            print("Check number {} failed".format(i+1))
 
checkValid()

for i in range(10):
    print(sqrt(2,i))

Check number 1 passed
Check number 2 passed
Check number 3 passed
Check number 4 passed
Check number 5 passed
Check number 6 passed
Check number 7 passed
Check number 8 passed
Check number 9 passed
Check number 10 passed
Check number 11 passed
Check number 12 passed
Check number 13 passed
1
1.4
1.41
1.414
1.4142
1.41421
1.414213
1.4142135
1.41421356
1.414213562

Determine the outcome of algorithms

  1. What does the algorithm do? Please explain in words.

If num divided by num2 has no remainder, return True, else, return False

  1. What if I put in 30 as num and 4 as num2. What would be the output?

False

Determine the outcome of similar algorithms

What is the output of this algorithm?

If Temp is higher than 90, it prints it's too hot outside, if it is between 65 and 90, it prints I will go outside, else, it prints it's too cold outside

temp = 95
if (temp >= 90):
    print("it is too hot outside")
else:
    if (temp >= 65):
        print("I will go outside")
    else:
        print("it is too cold outside")

What is the output of this algorithm? it looks similar but the output is different!

If Temp is higher than 90, it prints it's too hot outside, if Temp is higher than 65, it prints I will go outside, if Temp is lower than 65, it prints it's too cold outside

temp = 95
if (temp >= 90):
    print("it is too hot outside")
if (65 <=temp < 90):
    print("i will go outside")
if (temp < 65):
    print("it is too cold outside")

it is too hot outside

Editing Algorithms

Task: Please edit the algorithm above to have it yield the same results as the previous algorithm! (no matter what temp you put in)

Developing Algorithms

Task: Write an algorithm in python that sums up the first 5 odd integers. You can use the following code as a starter.

sum = 0
counter = 1
for i in range (0, 5):
    sum = sum + counter
    counter = counter + 2

Homework

Create an algorithm that will start with any positive integer n and display the full sequence of numbers that result from the Collatz Conjecture. The COllatz Conjecture is as follows:

  1. start with any positive integer
  2. if the number is even, divide by 2
  3. if the number is odd, multiply by 3 and add 1
  4. repeat steps 2 and 3 until you reach 1

Example: if the starting number was 6, the output would be 6, 3, 10, 5, 16, 8, 4, 2, 1

def procedure(num):
    counter=0
    while num !=1:
        print(num)
        if num%2==0:
            num//=2
        else:
            num*=3
            num+=1
        counter+=1
    print(num)
    print("After "+str(counter)+ " iterations")
procedure(int(input()))