Sage Interactions - Games and Diversions

Contents

Sage Interactions - Games and Diversions

Zeros

Have you ever wished you could count the number of zero digits in a long number like Rainman?

by William Stein and Sequoia Lefthand

xxxxxxxxxx
 
import random
​
def init():
    global B,Br,n,round,tm,t,v
    B = 40
    Br = 15
    n = 1
    round = 0
    tm = 0
    t = walltime()
    
    
init()    
​
print "<html><h1 align=center>Zeros</h1></html>"
print "<html><h2 align=center><font color='blue'>How many zeros?</font></h2></html>"
    
@interact
def zeros(a=("",selector(buttons=True, nrows=1, values=['Reset'] + [1..B], default=1))):
    if a == 'Reset': 
        init()
    print "<html><center>"    
    global B,Br,n,round,tm,t,v
    if a == n:
        if round > 0:
           print "<font size=+3 color='red'>RIGHT</font>"
        r = walltime() - t
        tm += r
        round += 1
        t = walltime()
        while True:
           n2 = random.randrange(1,Br)
           if n2 != n:
               n = n2
               break
        if Br < B:
            Br += 2
    elif round > 0:
        print "<font size=+2 color='blue'>Wrong. Try again...</font>"
    print "</center>"
    print "<font size=+%s color='#333'>"%random.randrange(-2,5)
    print  ' '*random.randrange(20) + '0'*n
    print "</font>"
    if round > 0:
        print "<br><br><center>Score: %s rounds, Average time: %.1f seconds</center>"%(
                 round, float(tm)/round)
    print "</html>"

Queens on board

An interaction to play with the problem of placing eight queens on a board so that they do not threaten each other. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. by Pablo Angulo

xxxxxxxxxx
 
queens=[]
opciones=['Clean board', 'Add queen', 'Remove queen' ]
​
@interact
def _(queen=input_box(default=(0,0)), opcion=selector(opciones, buttons=True), auto_update=False ):
    global queens
    if opcion=='Clean board':
        queens=[]
    elif opcion=='Add queen':
        if queen not in queens:
            queens.append(queen)
    else:
        queens.remove(queen)
        
    board=matrix(ZZ,8,8)
    for x in range(8):
        for y in range(8):
            board[x,y]=(x+y)%2*7
    for x,y in queens:
        for i in range(8):
            if i!=y:  board[x,i]=1+(x+i)%2*5
            if i!=x:  board[i,y]=1+(i+y)%2*5
        for i in range(-min(x,y),min(8-x,8-y)):
            if i!=0: board[x+i,y+i]=1+(x+y)%2*5
        for i in range(max(-x,y-7),min(8-x,y+1)):
            if i!=0: board[x+i,y-i]=1+(x+y)%2*5
    for x,y in queens:
        if ( board[x,y]==1 or board[x,y]==6 ):
            print 'Queen at (%d,%d) is threatened by another queen'%(x,y)
            board[x,y]=4  
        else:
            board[x,y]=3
    show(matrix_plot(board, cmap='Oranges' ))

Nim

Play nim against a perfect opponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. by Pablo Angulo

xxxxxxxxxx
 
#El juego del nim
def game_repr(heap_sizes):
    return '\n'.join('%d:'%i+'*'*n for i,n in enumerate(heap_sizes))
def bitlist2number(bitlist):
    return int('0'+''.join([str(bit) for bit in reversed(bitlist)]),2)
def move_nim(heap_sizes):
    '''Given a nim game, returns the next move (heap and amount)
    '''
    all_digits=[n.bits() for n in heap_sizes]
    N=max(len(l) for l in all_digits)
    digi=[0]*N
    for l in all_digits:
        for i in range(len(l)):
            digi[i]+=l[i]
    digi2=[digi[i]%2 for i in range(len(digi))]
    if max(digi2)==0:raise Exception("I cannot win!")
    maxInd=max(i for i in range(N) if digi2[i])
    
    heap=min(i for i in range(len(heap_sizes)) if len(all_digits[i])>maxInd and all_digits[i][maxInd]>0)
    localbits=heap_sizes[heap].bits()[0:maxInd]
    globalbits=digi2[0:maxInd]
    correction=bitlist2number( [b2 if b2 and not b1 else 0 for b1,b2 in zip(localbits,globalbits)] ) - bitlist2number( [b2 if b2 and b1 else 0 for b1,b2 in zip(localbits,globalbits)] )
    amount=2^maxInd -correction
    return (heap,amount)

xxxxxxxxxx
 
nim=[1,3,5,6]
@interact
def _(heap=selector(range(len(nim)), buttons=True),
      amount=selector(range(max(nim)+1), buttons=True),
      auto_update=False):
    global nim
    if max(nim)==0:
        print 'You have lost'
        return
    else:
        print 'Try to take the last item'
    if heap>=0 and 0<amount<=nim[heap]:
        print 'Previous situation:'
        print game_repr(nim)
        
        nim[heap]-=amount
        print 'Your move:'
        print game_repr(nim)
        if max(nim)==0:
            print 'You win'
            return
        
        print 'My move:'
        try:
            myheap,myamount=move_nim(nim)
        except:
            #cannot win, choose arbitrarily
            myheap=min(heap_number for heap_number, heap_size in enumerate(nim) if heap_size>0)
            myamount=1
        nim[myheap]-=myamount
        print game_repr(nim)
        if max(nim)==0:
            print 'I win'
        else:
            print 'Please move again'
    else:
        print 'Choose a heap and the amount to substract from that heap'
        print game_repr(nim)

interact/games

Sage Interactions - Games and Diversions

Zeros

Queens on board

Nim