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I am writing a binary addition program but am unsure as to why when the inputs start with a zero the output is incorect.The output is also incorrect when the program has to add zeros to the start of one of the inputs to make them the same length.
a = input('Enter first binary number\t')
b = input('Enter second binary number\t')
carry = 0
answer = ""
length = (max(len(a),len(b))) - min(len(a),len(b))
if b > a:
a = length * '0' + a
elif a > b:
b = length * '0' + b
print(a)
print(b)
for i in range(len(a)-1, -1, -1):
x = carry
if a[i] == '1': x += 1
else: x = 0
if b[i] == '1': x += 1
else: x = 0
if x % 2 == 1: answer = '1' + answer
else: answer = '0' + answer
if x < 2: carry = 0
else: carry = 1
if carry == 1: answer = '1' + answer
print(answer)
What an excellent opportunity to explore some Boolean Logic.
Adding binary like this can be done with two "half adders" and an "or"
First of all the "Half Adder" which is a XOR to give you a summed output and an AND to give you a carry.
[EDIT as per comments: python does have an XOR implemented as ^ but not as a "word" like and not or. I am leaving the answer as is, due to the fact it is explaining the Boolean logic behind a binary add]
As python doesn't come with a XOR, we will have to code one.
XOR itself is two AND's (with reversed inputs) and an OR, as demonstrated by this:
This would result is a simple function, like this:
def xor(bit_a, bit_b):
A1 = bit_a and (not bit_b)
A2 = (not bit_a) and bit_b
return int(A1 or A2)
Others may want to write this as follows:
def xor(bit_a, bit_b):
return int(bit_a != bit_b)
which is very valid, but I am using the Boolean example here.
Then we code the "Half Adder" which has 2 inputs (bit_a, bit_b) and gives two outputs the XOR for sum and the AND for carry:
def half_adder(bit_a, bit_b):
return (xor(bit_a, bit_b), bit_a and bit_b)
so two "Half Adders" and an "OR" will make a "Full Adder" like this:
As you can see, it will have 3 inputs (bit_a, bit_b, carry) and two outputs (sum and carry). This will look like this in python:
def full_adder(bit_a, bit_b, carry=0):
sum1, carry1 = half_adder(bit_a, bit_b)
sum2, carry2 = half_adder(sum1, carry)
return (sum2, carry1 or carry2)
If you like to look at the Full Adder as one logic diagram, it would look like this:
Then we need to call this full adder, starting at the Least Significant Bit (LSB), with 0 as carry, and work our way to the Most Significant Bit (MSB) where we carry the carry as input to the next step, as indicated here for 4 bits:
This will result is something like this:
def binary_string_adder(bits_a, bits_b):
carry = 0
result = ''
for i in range(len(bits_a)-1 , -1, -1):
summ, carry = full_adder(int(bits_a[i]), int(bits_b[i]), carry)
result += str(summ)
result += str(carry)
return result[::-1]
As you see we need to reverse the result string, as we built it up "the wrong way".
Putting it all together as full working code:
# boolean binary string adder
def rjust_lenght(s1, s2, fill='0'):
l1, l2 = len(s1), len(s2)
if l1 > l2:
s2 = s2.rjust(l1, fill)
elif l2 > l1:
s1 = s1.rjust(l2, fill)
return (s1, s2)
def get_input():
bits_a = input('input your first binary string ')
bits_b = input('input your second binary string ')
return rjust_lenght(bits_a, bits_b)
def xor(bit_a, bit_b):
A1 = bit_a and (not bit_b)
A2 = (not bit_a) and bit_b
return int(A1 or A2)
def half_adder(bit_a, bit_b):
return (xor(bit_a, bit_b), bit_a and bit_b)
def full_adder(bit_a, bit_b, carry=0):
sum1, carry1 = half_adder(bit_a, bit_b)
sum2, carry2 = half_adder(sum1, carry)
return (sum2, carry1 or carry2)
def binary_string_adder(bits_a, bits_b):
carry = 0
result = ''
for i in range(len(bits_a)-1 , -1, -1):
summ, carry = full_adder(int(bits_a[i]), int(bits_b[i]), carry)
result += str(summ)
result += str(carry)
return result[::-1]
def main():
bits_a, bits_b = get_input()
print('1st string of bits is : {}, ({})'.format(bits_a, int(bits_a, 2)))
print('2nd string of bits is : {}, ({})'.format(bits_b, int(bits_b, 2)))
result = binary_string_adder(bits_a, bits_b)
print('summarized is : {}, ({})'.format(result, int(result, 2)))
if __name__ == '__main__':
main()
two internet sources used for the pictures:
https://www.electronics-tutorials.ws/combination/comb_7.html
https://www.allaboutcircuits.com/textbook/digital/chpt-7/the-exclusive-or-function-xor/
For fun, you can do this in three lines, of which two is actually getting the input:
bits_a = input('input your first binary string ')
bits_b = input('input your second binary string ')
print('{0:b}'.format(int(bits_a, 2) + int(bits_b, 2)))
And in your own code, you are throwing away a carry if on second/subsequent iteration one of the bits are 0, then you set x = 0 which contains the carry of the previous itteration.
this is how i managed to complete this, hope you find this useful.
#Binary multiplication program.
def binaryAddition(bin0, bin1):
c = 0
answer = ''
if len(bin0) > len(bin1):
bin1 = (len(bin0) - len(bin1))*"0" + bin1
elif len(bin1) > len(bin0):
bin0 = (len(bin1) - len(bin0))*"0" + bin0
#Goes through the binary strings and tells the computer what the anser should be.
for i in range(len(bin0)-1,-1,-1):
j = bin0[i]
k = bin1[i]
j, k = int(j), int(k)
if k + j + c == 0:
c = 0
answer = '0' + answer
elif k + j + c == 1:
c = 0
answer = '1' + answer
elif k + j + c == 2:
c = 1
answer = '0' + answer
elif k + j + c == 3:
c = 1
answer = '1' + answer
else:
print("There is something wrong. Make sure all the numbers are a '1' or a '0'. Try again.") #One of the numbers is not a 1 or a 0.
main()
return answer
def binaryMultiplication(bin0,bin1):
answer = '0'*8
if len(bin0) > len(bin1):
bin1 = (len(bin0) - len(bin1))*"0" + bin1
elif len(bin1) > len(bin0):
bin0 = (len(bin1) - len(bin0))*"0" + bin0
for i in range(len(bin0)-1,-1,-1):
if bin1[i] == '0':
num = '0'*len(answer)
elif bin1[i] == '1':
num = bin0 + '0'*((len(bin0)-1)-i)
answer = binaryAddition(num, answer)
print(answer)
def main():
try:
bin0, bin1 = input("Input both binary inputs separated by a space.\n").split(" ")
except:
print("Something went wrong. Perhaps there was not a space between you numbers.")
main()
binaryMultiplication(bin0,bin1)
choice = input("Do you want to go again?y/n\n").upper()
if choice == 'Y':
main()
else: input()
main()
The following adds integers i1 and i2 using bitwise logical operators (i1 and i2 are overwritten). It computes the bitwise sum by i1 xor i2 and the carry bit by (i1 & i2)<<1. It iterates until the shift register is empty. In general this will be a lot faster than bit-by-bit
while i2: # check shift register != 0
i1, i2 = i1^i2, (i1&i2) << 1 # update registers
I am trying to integrate a polynomial function via the Trapezoidal Method (I can change to a more accurate method later). My code isn't perfect, and I'd like to understand exactly why it doesn't work. One problem I have is that the while loop does not end. My code thus far is as follows.
def Integrate_Trapezoidal(x_LoBound,x_HiBound,N):
"""
INPUT :
x_LoBound -- lower bound of integral
x_HiBound -- upper bound of integral
N -- number of slices (N --> inf ==> integral)
OUTPUT :
-- approximate value of integral
"""
## CREATE ALPHABET
alphabet = [chr(i) for i in range(ord('a'),ord('z')+1)]
## alphabet = ['a','b','c',...,'z'] ##
## WOULD LOVE TO TRY FLOATING INPUTS VIA ARRAY COMPREHENSION
a = float(input("What is the coefficient of the lowest order term: "))
CoeffList = []
CoeffNumList = []
LengthCoeffList = [] ## [1,2,3,...,max] where max = coefficient of highest-order term
for letter in alphabet:
AddOne = int(1)
AddOne += int(1)
for i in range(int(1),int(AddOne)):
letter = alphabet[int(i)]
while letter in alphabet:
CoeffList.append(letter)
LengthCoeffList.append(len(CoeffList))
# alphabet[i]
# i = i + 1
letter = float(input("What is the coefficient of the next-order term: ")) ## GO FROM a = ___ TO b = ___ TO c = ___ ...
CoeffNumList.append(letter)
if float(input("What is the coefficient of the next-order term: ")) == '0':
print("Type 'Y for YES and 'N' for NO")
YESorNO = str(input("Is that the last term of the polynomial: "))
endterm = YESorNO[-1] ## look at last character of string
if endterm == 'N' or endterm == 'n' or endterm == 'no' or endterm == 'NO' or endterm == 'No':
pass
elif endterm == 'Y' or endterm == 'y' or endterm == 'YES' or endterm == 'yes' or endterm == 'Yes':
break
def f(x):
"""
INPUT :
x -- variable of function
EX: x = x_LoBound OR x = x_HiBound
OUTPUT :
function -- f(x) = a x^0 + b x^1 + ...
EX: f(x_LoBound) OR f(x_HiBound)
"""
for expval in LengthCoeffList and CoeffNum in CoeffNumList:
# function = 0
function += CoeffNum * x**expval
return function
letter = alphabet[int(i+1)] ## GO FROM a TO b TO c ...
## TRAPEZOIDAL RULE
# def f(x):
# return x**4 - 2*x + 1
ht = (x_HiBound - x_LoBound) / N
ss = 0.5 * f(x_LoBound) + 0.5 * f(x_HiBound)
for num in range(1,N):
ss += f(x_LoBound + num*ht)
return ht*ss
checkanswer = Integrate_Trapezoidal(0,2,10)
print(checkanswer)
I've had a go at looking over your code and found something that I think works, checking against a couple of college handouts I downloaded. As you have said in the comments, there were a lot of extra lists which aren't necessary, so I've cut back the code a lot there.
In particular, if the presumption if that each coefficient is added in sequence from lowest to highest order, and 0 is added for any that aren't there, all you need is the number of the element in the list to know the power of x.
I also moved the definition of f() to create the helper function solve_point() which works the same I think. In particular, sum and enumerate are built in, with enumerate iterating through coeff_list and also returning a count to give the power (0 upwards).
get_coefficients() was from your old Integrate_Trapezoidal() but more focused on just one thing - which is why it then returns CoeffList to be finally processed at the end.
def solve_point(x, coeff_list):
return sum(coeff * x**e for e, coeff in enumerate(coeff_list))
def get_coefficients():
CoeffList = []
while True:
# GO FROM a = ___ TO b = ___ TO c = ___ ...
coeff = float(input("What is the coefficient of the next-order term: "))
CoeffList.append(coeff)
if coeff == 0:
YESorNO = raw_input("Is that the last term of the polynomial: [Y/N] ")
if YESorNO.upper() == 'Y':
return CoeffList[:-1]
lo, hi, n = 0, 2, 6
coeff_list = get_coefficients()
ht = (hi - lo) / float(n)
ss = 0.5 * solve_point(lo, coeff_list) + 0.5 * solve_point(hi, coeff_list)
for num in range(1,n):
ss += solve_point(lo + num*ht, coeff_list)
checkanswer = ht*ss
print(checkanswer)
I think its right - I have done a couple of checks. Hopefully it may be of help for your rewrite! If you have any examples that don't work, it would be good to know, or any errors you can see...
My algorithm to find the HCF of two numbers, with displayed justification in the form r = a*aqr + b*bqr, is only partially working, even though I'm pretty sure that I have entered all the correct formulae - basically, it can and will find the HCF, but I am also trying to provide a demonstration of Bezout's Lemma, so I need to display the aforementioned displayed justification. The program:
# twonumbers.py
inp = 0
a = 0
b = 0
mul = 0
s = 1
r = 1
q = 0
res = 0
aqc = 1
bqc = 0
aqd = 0
bqd = 1
aqr = 0
bqr = 0
res = 0
temp = 0
fin_hcf = 0
fin_lcd = 0
seq = []
inp = input('Please enter the first number, "a":\n')
a = inp
inp = input('Please enter the second number, "b":\n')
b = inp
mul = a * b # Will come in handy later!
if a < b:
print 'As you have entered the first number as smaller than the second, the program will swap a and b before proceeding.'
temp = a
a = b
b = temp
else:
print 'As the inputted value a is larger than or equal to b, the program has not swapped the values a and b.'
print 'Thank you. The program will now compute the HCF and simultaneously demonstrate Bezout\'s Lemma.'
print `a`+' = ('+`aqc`+' x '+`a`+') + ('+`bqc`+' x '+`b`+').'
print `b`+' = ('+`aqd`+' x '+`a`+') + ('+`bqd`+' x '+`b`+').'
seq.append(a)
seq.append(b)
c = a
d = b
while r != 0:
if s != 1:
c = seq[s-1]
d = seq[s]
res = divmod(c,d)
q = res[0]
r = res[1]
aqr = aqc - (q * aqd)#These two lines are the main part of the justification
bqr = bqc - (q * aqd)#-/
print `r`+' = ('+`aqr`+' x '+`a`+') + ('+`bqr`+' x '+`b`+').'
aqd = aqr
bqd = bqr
aqc = aqd
bqc = bqd
s = s + 1
seq.append(r)
fin_hcf = seq[-2] # Finally, the HCF.
fin_lcd = mul / fin_hcf
print 'Using Euclid\'s Algorithm, we have now found the HCF of '+`a`+' and '+`b`+': it is '+`fin_hcf`+'.'
print 'We can now also find the LCD (LCM) of '+`a`+' and '+`b`+' using the following method:'
print `a`+' x '+`b`+' = '+`mul`+';'
print `mul`+' / '+`fin_hcf`+' (the HCF) = '+`fin_lcd`+'.'
print 'So, to conclude, the HCF of '+`a`+' and '+`b`+' is '+`fin_hcf`+' and the LCD (LCM) of '+`a`+' and '+`b`+' is '+`fin_lcd`+'.'
I would greatly appreciate it if you could help me to find out what is going wrong with this.
Hmm, your program is rather verbose and hence hard to read. For example, you don't need to initialise lots of those variables in the first few lines. And there is no need to assign to the inp variable and then copy that into a and then b. And you don't use the seq list or the s variable at all.
Anyway that's not the problem. There are two bugs. I think that if you had compared the printed intermediate answers to a hand-worked example you should have found the problems.
The first problem is that you have a typo in the second line here:
aqr = aqc - (q * aqd)#These two lines are the main part of the justification
bqr = bqc - (q * aqd)#-/
in the second line, aqd should be bqd
The second problem is that in this bit of code
aqd = aqr
bqd = bqr
aqc = aqd
bqc = bqd
you make aqd be aqr and then aqc be aqd. So aqc and aqd end up the same. Whereas you actually want the assignments in the other order:
aqc = aqd
bqc = bqd
aqd = aqr
bqd = bqr
Then the code works. But I would prefer to see it written more like this which is I think a lot clearer. I have left out the prints but I'm sure you can add them back:
a = input('Please enter the first number, "a":\n')
b = input('Please enter the second number, "b":\n')
if a < b:
a,b = b,a
r1,r2 = a,b
s1,s2 = 1,0
t1,t2 = 0,1
while r2 > 0:
q,r = divmod(r1,r2)
r1,r2 = r2,r
s1,s2 = s2,s1 - q * s2
t1,t2 = t2,t1 - q * t2
print r1,s1,t1
Finally, it might be worth looking at a recursive version which expresses the structure of the solution even more clearly, I think.
Hope this helps.
Here is a simple version of Bezout's identity; given a and b, it returns x, y, and g = gcd(a, b):
function bezout(a, b)
if b == 0
return 1, 0, a
else
q, r := divide(a, b)
x, y, g := bezout(b, r)
return y, x - q * y, g
The divide function returns both the quotient and remainder.
The python program that does what you want (please note that extended Euclid algorithm gives only one pair of Bezout coefficients) might be:
import sys
def egcd(a, b):
if a == 0:
return (b, 0, 1)
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def main():
if len(sys.argv) != 3:
's program caluclates LCF, LCM and Bezout identity of two integers
usage %s a b''' % (sys.argv[0], sys.argv[0])
sys.exit(1)
a = int(sys.argv[1])
b = int(sys.argv[2])
g, x, y = egcd(a, b)
print 'HCF =', g
print 'LCM =', a*b/g
print 'Bezout identity: %i * (%i) + %i * (%i) = %i' % (a, x, b, y, g)
main()
Right now I am attempting to code the knapsack problem in Python 3.2. I am trying to do this dynamically with a matrix. The algorithm that I am trying to use is as follows
Implements the memoryfunction method for the knapsack problem
Input: A nonnegative integer i indicating the number of the first
items being considered and a nonnegative integer j indicating the knapsack's capacity
Output: The value of an optimal feasible subset of the first i items
Note: Uses as global variables input arrays Weights[1..n], Values[1...n]
and table V[0...n, 0...W] whose entries are initialized with -1's except for
row 0 and column 0 initialized with 0's
if V[i, j] < 0
if j < Weights[i]
value <-- MFKnapsack(i - 1, j)
else
value <-- max(MFKnapsack(i -1, j),
Values[i] + MFKnapsack(i -1, j - Weights[i]))
V[i, j} <-- value
return V[i, j]
If you run the code below that I have you can see that it tries to insert the weight into the the list. Since this is using the recursion I am having a hard time spotting the problem. Also I get the error: can not add an integer with a list using the '+'. I have the matrix initialized to start with all 0's for the first row and first column everything else is initialized to -1. Any help will be much appreciated.
#Knapsack Problem
def knapsack(weight,value,capacity):
weight.insert(0,0)
value.insert(0,0)
print("Weights: ",weight)
print("Values: ",value)
capacityJ = capacity+1
## ------ initialize matrix F ---- ##
dimension = len(weight)+1
F = [[-1]*capacityJ]*dimension
#first column zeroed
for i in range(dimension):
F[i][0] = 0
#first row zeroed
F[0] = [0]*capacityJ
#-------------------------------- ##
d_index = dimension-2
print(matrixFormat(F))
return recKnap(F,weight,value,d_index,capacity)
def recKnap(matrix, weight,value,index, capacity):
print("index:",index,"capacity:",capacity)
if matrix[index][capacity] < 0:
if capacity < weight[index]:
value = recKnap(matrix,weight,value,index-1,capacity)
else:
value = max(recKnap(matrix,weight,value,index-1,capacity),
value[index] +
recKnap(matrix,weight,value,index-1,capacity-(weight[index]))
matrix[index][capacity] = value
print("matrix:",matrix)
return matrix[index][capacity]
def matrixFormat(*doubleLst):
matrix = str(list(doubleLst)[0])
length = len(matrix)-1
temp = '|'
currChar = ''
nextChar = ''
i = 0
while i < length:
if matrix[i] == ']':
temp = temp + '|\n|'
#double digit
elif matrix[i].isdigit() and matrix[i+1].isdigit():
temp = temp + (matrix[i]+matrix[i+1]).center(4)
i = i+2
continue
#negative double digit
elif matrix[i] == '-' and matrix[i+1].isdigit() and matrix[i+2].isdigit():
temp = temp + (matrix[i]+matrix[i+1]+matrix[i+2]).center(4)
i = i + 2
continue
#negative single digit
elif matrix[i] == '-' and matrix[i+1].isdigit():
temp = temp + (matrix[i]+matrix[i+1]).center(4)
i = i + 2
continue
elif matrix[i].isdigit():
temp = temp + matrix[i].center(4)
#updates next round
currChar = matrix[i]
nextChar = matrix[i+1]
i = i + 1
return temp[:-1]
def main():
print("Knapsack Program")
#num = input("Enter the weights you have for objects you would like to have:")
#weightlst = []
#valuelst = []
## for i in range(int(num)):
## value , weight = eval(input("What is the " + str(i) + " object value, weight you wish to put in the knapsack? ex. 2,3: "))
## weightlst.append(weight)
## valuelst.append(value)
weightLst = [2,1,3,2]
valueLst = [12,10,20,15]
capacity = 5
value = knapsack(weightLst,valueLst,5)
print("\n Max Matrix")
print(matrixFormat(value))
main()
F = [[-1]*capacityJ]*dimension
does not properly initialize the matrix. [-1]*capacityJ is fine, but [...]*dimension creates dimension references to the exact same list. So modifying one list modifies them all.
Try instead
F = [[-1]*capacityJ for _ in range(dimension)]
This is a common Python pitfall. See this post for more explanation.
for the purpose of cache illustration, I generally use a default dict as follows:
from collections import defaultdict
CS = defaultdict(lambda: defaultdict(int)) #if i want to make default vals as 0
###or
CACHE_1 = defaultdict(lambda: defaultdict(lambda: int(-1))) #if i want to make default vals as -1 (or something else)
This keeps me from making the 2d arrays in python on the fly...
To see an answer to z1knapsack using this approach:
http://ideone.com/fUKZmq
def zeroes(n,m):
v=[['-' for i in range(0,n)]for j in range(0,m)]
return v
value=[0,12,10,20,15]
w=[0,2,1,3,2]
v=zeroes(6,5)
def knap(i,j):
global v
if i==0 or j==0:
v[i][j]= 0
elif j<w[i] :
v[i][j]=knap(i-1,j)
else:
v[i][j]=max(knap(i-1,j),value[i]+knap(i-1,j-w[i]))
return v[i][j]
x=knap(4,5)
print (x)
for i in range (0,len(v)):
for j in range(0,len(v[0])):
print(v[i][j],end="\t\t")
print()
print()
#now these calls are for filling all the boxes in the matrix as in the above call only few v[i][j]were called and returned
knap(4,1)
knap(4,2)
knap(4,3)
knap(4,4)
for i in range (0,len(v)):
for j in range(0,len(v[0])):
print(v[i][j],end="\t\t")
print()
print()
I'm trying to figure out what's wrong with my code. Could anyone fix it?
def main():
fname = input("Enter filename:")
infile = open(fname, "r")
SD()
def SD():
b= []
a = 5.0
r = len(b)
for n in range(r-1):
b.append((r[n] -a)**2)
m = (float(b)/r)**0.5
print("The standard deviation is", m)
main()
You have a handful of errors:
def SD():
# b is empty
b= []
a = 5.0
#this will always be 0
r = len(b)
# range(r-1) == [] because it is range(-1)
# whole loop is skipped
for n in range(r-1):
b.append((r[n] -a)**2)
# float(b) should throw an error, maybe sum(b) ?
m = (float(b)/r)**0.5
print("The standard deviation is", m)
main()
b is a list; you can't cast a list into a float.
perhaps you want to pass an array to SD()? You should read() the files contents and then perhaps split() that into an array and pass it to SD() as an argument (where you'll call int() on them.)
For a sample:
def SD(numList):
cntN=len(numList)
sumN=0
for i in numList:
sumN+=i
avgVal=float(sumN)/float(cntN)
sumVar=0.0
for i in range(cntN):
sumVar+=float((numList[i]-avgVal)**2)
return ((float(sumVar)/float((cntN-1)))**0.5)