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

# ![alt text](https://github.com/callysto/callysto-sample-notebooks/blob/master/notebooks/images/Callysto_Notebook-Banner_Top_06.06.18.jpg?raw=true)

# # The Bridge Problem

# In[1]:


#Import Youtube Video
from IPython.display import YouTubeVideo
YouTubeVideo('7yDmGnA8Hw0')


# ## Any solution to this problem must involve five steps, as in the animation below:
# ### Step 1: Two people cross the bridge.
# ### Step 2: One person goes back.
# ### Step 3: Two people cross the bridge.
# ### Step 4: One person goes back.
# ### Step 5: Two people cross the bridge.

# In[2]:


get_ipython().run_cell_magic('html', '', '<iframe src="files/BridgeAnimation.mp4"></iframe>\n')


# ## We just discovered two possible "algorithms" to solve this problem: 
# ### Option 1: Always sending the fastest person
# ### Option 2: Combining the two slowest people

# In[2]:


def CalculateTime(A, B, C, D):
    t=[A,B,C,D]
    t.sort()
    A=t[0] 
    B=t[1] 
    C=t[2] 
    D=t[3]
    print('Sending Fastest Person solves the problem in', B+A+C+A+D, 'minutes')
    print('Combining Two Slowest solves the problem in', B+A+D+B+B, 'minutes')
    return


# ## Let's compare our algorithms, and see which one is faster.
# ### Let's experiment by trying different input values for A, B, C, and D.

# In[3]:


from ipywidgets import interact
import ipywidgets as widgets
interact(CalculateTime,
A=widgets.IntSlider(min=1, max=20),
B=widgets.IntSlider(min=1, max=20),
C=widgets.IntSlider(min=1, max=20),
D=widgets.IntSlider(min=1, max=20))


# ## Two Challenge Questions
# ### For which values of (A,B,C,D) do the above solutions result in the same total time?
# ### How many different ways can the four people cross the bridge?  (Hint: the answer is more than 100!)

# ![alt text](https://github.com/callysto/callysto-sample-notebooks/blob/master/notebooks/images/Callysto_Notebook-Banners_Bottom_06.06.18.jpg?raw=true)