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

# In[109]:


get_ipython().run_line_magic('matplotlib', 'inline')

import numpy as np
import matplotlib.pyplot as plt
from random import shufflem=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[112]:


base = [[1,0], [0,1], [-1,0], [0,-1]]


# In[113]:


w = [[0,0]]


# In[114]:


def walk():
    L = base.copy()
    shuffle(L)
    work = True
    while work:
        d = L.pop()
        new_step = [w[-1][0] + d[0], w[-1][1] + d[1]]
        if new_step not in w:
            w.append(new_step)
            work = False
        


# In[115]:


for i in range(1000):
    walk()


# In[116]:


i


# In[118]:


walk_arr = np.array(w)


# In[119]:


plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[86]:


d


# In[87]:


new_step = [w[-1][0] + d[0], w[-1][1] + d[1]]


# In[89]:


[0,0] in w


# In[81]:


w


# In[122]:


def new_walk(n):
    base = [[1,0], [0,1], [-1,0], [0,-1]]
    w = [[0,0]]
    for i in range(n):
        walk()
    


# In[125]:


i


# In[128]:


walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[130]:


new_walk(n=1000)


# In[131]:


walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[127]:


plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[132]:


L = base.copy()
shuffle(L)


# In[133]:


L


# In[134]:


L = base.copy()
shuffle(L)


# In[135]:


L


# In[196]:


def saw(n=1000):
    base = [[1,0], [0,1], [-1,0], [0,-1]]
    w = [[0,0]]
    L = []
    for i in range(n):
        L_new = base.copy()
        shuffle(L_new)
        L.append(L_new)
    for i in range(n):
        thewalk = L[i]
        work = True
        do_break = False
        while work:
            d = thewalk.pop()
            new_step = [w[-1][0] + d[0], w[-1][1] + d[1]]
            if new_step not in w:
                w.append(new_step)
                work = False
            if thewalk == []:
                work = False
                do_break = True
        if do_break:
            break
                
                
    return w
    
    


# In[153]:


w = saw(100)


# In[154]:





# In[155]:


walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[169]:


w = saw(100)


# In[170]:


walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[171]:


w = saw(100)
walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[185]:


w = saw(100)
walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[203]:


w = saw(1000)
walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[213]:


w = saw(1000)
walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[214]:


w = saw(1000)
walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[215]:


w = saw(1000)
walk_arr = np.array(w)
plt.plot(walk_arr[:,0], walk_arr[:,1])


# In[220]:


for k in range(1000):
    m = 0
    theone = saw(1000)
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 


# In[231]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 


# In[235]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 


# In[237]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[244]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[246]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[250]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[254]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[255]:


m=0
for k in range(10000):
    theone = saw(1000)
    # print(len(theone), end=' ')
    if m < len(theone):
        w_max = theone
        m = len(theone)
walk_arr = np.array(w_max)
plt.plot(walk_arr[:,0], walk_arr[:,1]) 

print(m)


# In[ ]: