#!/usr/bin/env python
# coding: utf-8

# ## Supplementary exercises for Week 1 Day 3 notebook B

# ### Run the following cell first.

# In[201]:


def check(actual, expected):
    if expected != actual:
        print(
            f"Function should return the value {expected}, it is returning the value {actual}")
    else:
        print(f"Congratulations, the test case passed!")


# ## Exercise 1 (Basic)

# Write a `while` loop that prints the integers between `0` and `10` (inclusive on both ends).

# In[ ]:





# Change the loop above to be a `for` loop.

# In[ ]:





# ## Exercise 2 (Basic)
# Let `lst = [12, 34, 15, 11, 9, 34, 433, 23, 24, 121, 343, 32, 111, 4454, 323]` be a list of integers. Use a `while` loop to print all the elements in `lst`
# 

# In[202]:


lst = [12, 34, 15, 11, 9, 34, 433, 23, 24, 121, 343, 32, 111, 4454, 323]


# In[ ]:





# ### 2.1 
# Change the loop above to be a `for` loop.

# In[ ]:





# ### 2.2
# Print only the odd elements in `lst` using a `for` loop.

# In[ ]:





# ### 2.3 
# Print every other element in `lst` using a `for` loop.

# In[ ]:





# ## Exercise 3(Easy)
# Given an empty dictionary `dic`, and two equal-length lists `keys` and `vals`. Put every corresponding  key and value from `keys` and `vals` (with the same index) into the dictionary `dic`. For example, if the list are `keys = ["Jelani", "Daniel"]` and `vals = ["Week 4", "Week 1"]`, then your dictionary `dic` should contain two keys, and `dic["Jelani"] = "Week 4"`, `dic["Daniel"] = "Week 1"`.

# In[203]:


keys = ["Jelani", "Daniel"]

vals = ["Week 4", "Week 1"]


# In[ ]:





# ## Exercise 4 (Medium)
# Use a `for` loop to print the following:
# $\newline *
# \newline * \ \ \ *
# \newline * \ \ \ * \ \ \ *
# \newline *\ \ \  *\ \ \  *\ \ \  *$
# 

# In[204]:


for i in range(1, 5):
    print("*  " * i)


# ### 4.2 (Hard)
# Use a nested `for` loop to print the following:
# $\newline 1
# \newline 2 \ \ \ 3
# \newline 4 \ \ \ 5 \ \ \ 6
# \newline 7\ \ \  8\ \ \  9\ \ \  10$

# In[205]:


start = 1
for i in range(1, 5):
    st =  ""
    for j in range(i):
        st += str(start) + " "
        start += 1
    print(st)


# ### 4.3 (Hard)
# Use a nested `for` loop to print the following:
# $\newline 7\ \ \  8\ \ \  9\ \ \  10
# \newline 4 \ \ \ 5 \ \ \ 6
# \newline 2 \ \ \ 3
# \newline 1$

# In[206]:


start = 10
for i in range(4, 0, -1):
    st =  ""
    for j in range(i):
        st = str(start) + " " + st
        start -= 1
    print(st)


# ## Exercise 5 (Hard)
# Print out the following.
# $
# \newline 11\ \ \  12\ \ \   13 \ \ \  14\ \ \  15
# \newline 20\ \ \  19\ \ \  18\ \ \  17 \ \ \  16
# \newline 21\ \ \  22\ \ \  23\ \ \  24\ \ \  25
# \newline 30\ \ \  29\ \ \  28\ \ \  27\ \ \  26
# \newline 31\ \ \  32\ \ \  33\ \ \  34\ \ \  35$

# ### 5.1
# Use a nested `for` loop to solve it

# In[ ]:





# ### 5.2
# Use just one `for` loop to solve it

# In[ ]:





# ## Exercise 6 (Easy)
# For a given number `n`, use a `for` loop to print a list contains all the factors of `n`. For example, for `n = 20`, your output should be `[1, 2, 4, 5, 10, 20]`.

# In[ ]:





# ## Exercise 7 (Basic)

# Write a function `isEven` with input `x`, so that `isEven` checks if `x` is even. The function returns `True` if `x` is even, and returns `False` otherwise.

# Write your solution in the following cell.

# In[ ]:





# Run the following code cell to check your solution.

# In[207]:


check(isEven(2), True)
check(isEven(-2), True)
check(isEven(3), False)


# ## Exercise 8 (Medium)

# Write a function `isPrime` with input `x`. The function returns `True` if `x` is a prime, returns `False` otherwise. Please use a `for` loop instead of a `while` loop.
# 
# Hint: You can use `isEven` function you definied above.

# In[ ]:





# Use the following code cell to check your solution.

# In[208]:


check(isPrime(1), False)
check(isPrime(2), True)
check(isPrime(3), True)
check(isPrime(97), True)
check(isPrime(85), False)
check(isPrime(87), False)


# ## Exercise 9 (Medium)
# Write a function `factors` that, given an input `n`, returns a list contains all the prime factors of `n`. For example, for `n = 20`, your function should return `[2, 5]`. You can use the function `isPrime` from the previous question.

# In[ ]:





# Use the following code cell to check your solution.

# In[209]:


check(sorted(factors(20)),[2, 5])
check(sorted(factors(8)),[2])
check(sorted(factors(1)),[])
check(sorted(factors(100)),[2, 5])
check(sorted(factors(105)),[3, 5, 7])


# ### Exercise 10 (Hard)
# Define a function `twinPrimes` with no input to print all the pairs of twin primes between 2 and 200 in the form of a nested list.
# 
# For example, a pair of twin primes is both of the numbers are prime numbers and they have the difference of 2. Ex. [5, 7], [11, 13], [29, 31]
# 
# The result should be in the form of the following `[[..., ...], [..., ...], ....]`
# 
# Use a `for` loop and the function `isPrime`.

# In[ ]:





# Run the following code cell to check your solution.

# In[210]:


lst = twinPrimes()
correct_samples = [[5, 7], [137, 139], [107, 109], [11, 13], [197, 199]]
c_cnt = 0
wrong_samples = [[2, 3], [9, 11], [23, 25], [17, 18], [31, 33], [87, 89], [227, 229]] 
for c_sample in correct_samples:
    if c_sample not in lst:
        print("Unfortunately, your twinPrimes function does not work properly, please edit your solution.")
        break
    else: c_cnt += 1
for w_sample in wrong_samples:
    if w_sample in lst:
        print("Unfortunately, your twinPrimes function does not work properly, please edit your solution.")
        break
    else: c_cnt += 1
if c_cnt == len(correct_samples) + len(wrong_samples): print("Congratulations, the test case passed!")


# ## Exercise 11 (Medium)
# Write a function `pi` that approximates $\pi$. Use the following approximation of $\pi$:
# $$\pi = 4(\frac{1}{1} - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + ... )$$ 
# Your function should get an input `n` and compute the sum of the first `n` terms in the above approximation.
# 
# Play around the input number see when it converges to $\pi$. 

# In[ ]: