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How to write the Fibonacci Sequence?
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Closed 9 years ago.
A tutorial I am going through had the following program
# This program calculates the Fibonacci sequence
a = 0
b = 1
count = 0
max_count = 20
while count < max_count:
count = count + 1
old_a = a # we need to keep track of a since we change it
print(old_a,end=" ") # Notice the magic end=" " in the print function arguments that
# keeps it from creating a new line
a = b
b = old_a + b
print() # gets a new (empty) line
The code is perfect. However, I am not able to figure out how the sequence is calculated.
How are the values changed to create the sequence?
It'll make more sense if you remove all of that extraneous code:
while count < max_count:
old_a = a
a = b
b = old_a + b
The old_a is probably confusing you. It's the long way of writing this:
a, b = b, a + b
Which swaps a with b and (at the same time), b with a + b. Note that it isn't the same as writing:
a = b
b = a + b
Because by the time you re-define b, a already holds its new value, which is equal to b.
I'd also run through the code manually by writing it out on paper.
This code works fine:
a, b = 0, 1
for _ in range(20):
print a
a, b = b, a+b
Related
i = 1
i = i + 1
print(i)
I am pretty confused about the code's logic. Why would i eventually become 2?
Lets begin with the first assignment:
i = 1
This creates the variable i and initialize it to the integer value 1.
Then we get to what you seem to have problem understanding:
i = i + 1
This statement can be split into two parts:
The addition
The assignment
The addition i + 1 will take the current values of the variable i, which is 1, and add the value 1 to that. In essence the expression i + 1 is the same as 1 + 1.
The result of the addition will be 2. And this result is then assigned to the variable i, making the value of i be equal to 2.
You then print the (new) current value of i:
print(i)
This will of course print the value 2.
The difference is that one modifies the data-structure itself (in-place operation) b += 1 while the other just reassigns the variable a = a + 1.
Just for completeness:
x += y is not always doing an in-place operation, there are (at least) three exceptions:
If x doesn't implement an __iadd__ method then the x += y statement is just a shorthand for x = x + y. This would be the case if x was something like an int
If __iadd__ returns NotImplemented, Python falls back to x = x + y.
The __iadd__ method could theoretically be implemented to not work in place. It'd be really weird to do that, though.
As it happens your bs are numpy.ndarrays which implements __iadd__ and return itself so your second loop modifies the original array in-place.
You can read more on this in the Python documentation of "Emulating Numeric Types".
'i' is a variable which stored 1 if We add 1 again in 'i' that means
i=1;
i+1 means 1+1=2
i=1
i=i+1// i has already 1 and here we are adding 1 again so result will be 2.
hope you understood.
Let's start from i = 1. So you are assigning i to 1. Now your situation is:
i = i + 1
So if i is 1, then the abovementioned code would be "translated" to:
i = 1 + 1
That's why i = i + 1 is equal to 2.
records = [["chi", 20.0],["beta", 50.0],["alpha", 50.0]]
a = len(records)
i = 0
b = []
while i < a:
print(records[i][1])
b.append(records[i][1])
i = i + 1
print(b)
c = len(b)
#from previous question
unique_list = []
for el in b:
if el not in unique_list:
unique_list.append(el)
else:
print ("Element already in the list")
print(unique_list)
second_lowest_score = unique_list[1]
print(second_lowest_score)
names_list = []
g = 0
while g < a:
if records[g][1] == second_lowest_score:
names_list.append(records[g][0])
g = g + 1
print(names_list)
What I want to do is to append the names of records which have the second lowest score (50) to the names_list. However, the while loop gives me no result. There is no syntax error so I am not sure why my code is wrong. However, when I use the previous while loop for appending the numbers, it seems to work fine. Is it not possible to use an if statement in a while loop?
This is a pretty simple problem. The g variable is not getting incremented if the if statement does not run, so the loop will endlessly continue on the same value of g.
The fix for this is to move the increment of g outside of the if statement (but still in the while loop). That way it will continue past values even if they do not match the if condition.
if records[g][1] == second_lowest_score:
names_list.append(records[g][0])
g = g + 1
[Sorry in advance, I'm very new to programming.]
This is for project euler problem #2. The goal is to calculate the sum of all even fibonacci numbers that do not exceed 4 million. For anyone not familiar with fibonacci numbers, a fibonacci number is simply a number that is the sum of the two previous numbers in the sequence. For example, the first few fibonacci numbers are 1,2,3,5,8,13,21,34 ...
My code is below beginning with some variables, then my while loop, and finally my for loop.
n = 0
n2 = 1
fibsum = 0
fibrange = range(1,4000001)
while (n2 <= 4000000):
n2 = n2 + n
n = n2 - n
if n2 % 2 == 0:
fibsum += n2
print (fibsum)
# for n2 in fibrange:
# n2 = n2 + n
# n = n2 - n
# if n2 % 2 == 0:
# fibsum += n2
# print(fibsum)
As I said, my while loop works like a charm, but when I run the for loop the output of fibsum is 0. So the value is not changing at all.
I've tried range (1, 4000001) in place of fibrange. I really have no idea what else to try. This is like my 4th or 5th program ever.
Using for loop in range function, The Value of the variable n2 changes according only to range function.You cannot manually change the variable in for loop while using range function.
for and while and are different types of loops.
while: Repeats a statement or group of statements while a given condition is TRUE. It tests the condition before executing the loop body.
for: Executes a sequence of statements multiple times and abbreviates the code that manages the loop variable.
With while you can do something like this:
a = 0
b = 1
target = 4000000
result = 0
while a <= target:
if a % 2 == 0:
result +=a
a, b = b, a + b
print(result)
With for:
a, b = 0, 1
result = 0
target = 4000000
fib_sequence = 35 # -> the length of fibonacci sequence
for _ in range(fib_sequence):
if a % 2 == 0:
result +=a
a, b = b, a + b
if a >= target: break
print(result)
The Code below gives an answer for almost any number I have tested with, even a 64 digits *64 digits. But when tried with
a = 123456
b = 123456
The final answer is negative.
Up until
a = 12345
b = 12345
The answer is correct.
Not sure where this is going wrong. I am relatively new to python so is there something I am missing out?
import numpy as np
a = int(input("Enter Number 1: "))
b = int(input("Enter Number 2: "))
c = 1
pos_nums = []
while b != 0:
z = b % 10
pos_nums.append(z *c)
b = b // 10
c = c*10
pos_num = np.array([pos_nums])
multiply = pos_num *a
add = np.sum(multiply)
print(add)
I don't know why numpy is playing up, but something like this appears to work, and does the same thing.
All I've done is removed the conversion to a numpy array. Now when you multiply pos_num it essentially makes a copies of it into one list. sum counts the total value of the list, which has a amounts of b stored in it.
Hope this works for you :)
a = int(input("Enter Number 1: "))
b = int(input("Enter Number 2: "))
c = 1
pos_nums = []
while b != 0:
z = b % 10
pos_nums.append(z *c)
b = b // 10
c = c*10
#pos_num = np.array(pos_nums)
pos_num = pos_nums
multiply = pos_num *a
add = sum(multiply)
print(add)
Output:
Enter Number 1: 123456
Enter Number 2: 123456
15241383936
numpy can't guess your next move!
you see when you define a numpy array it will assume a type for the array (like np.int16) and its not will not change unless you multiply it into something with other formats
what happend here?
you have multiplied a dtype=np.int32 array into an int in line:
multiply = pos_num *a
the result will be another np.int32 array (you can see that with print(multiply.dtype))
numpy can not guess that you intend to extend the array into for example np.float64
(not like regular python code, because there is a great performace hit to that)
what to do?
just simply define the type for it! (it a good practice to do this in other codes)
pos_num = np.array(pos_nums, dtype=np.float64)
so this program predicts the first winning move of the famous Game of Nim. I just need a little help figuring out this problem in the code. The input file reads something like this.
3
13 4 5
29 5 1
34 4 50
The first number would represent the number of lines following the first line that the program has to read. So if the case was
2
**13 4 5
29 5 1**
34 4 50
it would only read the next two lines following it.
So far this has been the progress of my code
def main ():
nim_file = open('nim.txt', 'r')
first_line = nim_file.readline()
counter = 1
n = int (first_line)
for line in nim_file:
for j in range(1, n):
a, b, c = [int(i) for i in line.split()]
nim_sum = a ^ b ^ c
if nim_sum == 0:
print ("Heaps:", a, b, c, ": " "You Lose!")
else:
p = a ^ nim_sum
q = b ^ nim_sum
r = c ^ nim_sum
if p < a:
stack1 = a - p
print ("Heaps:", a, b, c, ": " "remove", stack1, "from Heap 1")
elif q < b:
stack2 = b - q
print ("Heaps:", a, b, c, ": " "remove", stack2, "from Heap 2")
elif r < c:
stack3 = c - r
print ("Heaps:", a, b, c, ": " "remove", stack3, "from Heap 3")
else:
print ("Error")
nim_file.close()
main()
I converted the first line number to an int and tried to set a while loop at first with a counter to see that the counter wouldn't go above the value of n but that didn't work. So any thoughts?
If the file is small, just load the whole thing:
lines = open('nim.txt').readlines()
interesting_lines = lines[1:int(lines[0])+1]
and continue from there.
Yo have two nested for statement, the second of which doesn't make much sence. You need to leave just one, like this:
for _ in range(n):
a, b, c = [int(i) for i in nim_file.readline()]
and remove for line in nim_file. Also check out this question and consider using the with statement to handle the file opening/closing.