CODEWITHSUNDEEP
python
Don Marko
Don Marko

Reputation: 53

Pascal's triangle in Python

I'm making a Pascal's triangle and I can't figure out why this code isn't working. It prints out something like this:

[]
[1]
[1, 2]
[1, 3, 3]
[1, 4, 6, 4]
[1, 5, 10, 10, 5]
[1, 6, 15, 20, 15, 6]
[1, 7, 21, 35, 35, 21, 7]
[1, 8, 28, 56, 70, 56, 28, 8]
[1, 9, 36, 84, 126, 126, 84, 36, 9]

Which is almost correct, however it seems that the values seem to be the row number too high, so 1,2 , If you count 2 as the first row and 1 as the 0th row, 2 is 1 value too high since it is in the first row, it should be 1,1. The next row should be 1,2,1, the first value is correct but the next one is 1 value too high and the one after that is 2 values too high.

I tried doing something like append(a-i), but it doesn't seem to work. How would I get this to print correctly?

def triangle(rows):

    for rownum in range (rows):
        newValue=1
        PrintingList = list()
        for iteration in range (rownum):
            newValue = newValue * ( rownum-iteration ) * 1 / ( iteration + 1 )
            PrintingList.append(int(newValue))
        print(PrintingList)
    print()

Upvotes: 4

Views: 27704

Answers (4)

user3267130
user3267130

Reputation: 11

I get an error but you should try something like this:

row1 = whatever

pascal = [[row/(colum*(row-colum) for row in range(0, colum)] for row in range(1, row1)]]

Upvotes: 1

user5511824
user5511824

Reputation: 

import math

coef = 1

rows = int(input("Enter the number of rows :"))

stringVal = ""

for i in range(rows):

    for space in range(1,rows - i + 1):

        stringVal = stringVal + "  "
    for j in range(0,i + 1):
        if(i == 0 or j == 0):
            coef = 1
        else:
            coef = coef * (i - j + 1) / j

        temp = coef
        TotalSpace=0
        while(temp != 0):
            TotalSpace = TotalSpace + 1
            temp = int(math.floor(temp / 10))
        p=0
        while((p+TotalSpace)!=4):
            stringVal = stringVal + " "
            p=p+1
        stringVal = stringVal + str(int(math.floor(coef)))
    stringVal = stringVal + "\n"
print(stringVal)

Upvotes: 0

MountainX
MountainX

Reputation: 6337

My code below has some print statements that help show how it works. I'm running it in an IPython notebook. My output looks like this:

                   [1]                        
                  [1, 1]                      
                [1, 2, 1]                     
               [1, 3, 3, 1]                   
             [1, 4, 6, 4, 1]

Beyond the fact that the output looks like it should, the computation method actually follows the original definition of Pascal's Triangle where each row is built from the one above. (Some methods use combinatorics/factorials, which might give the right answer, but don't follow the original spirit of Pascal's Triangle, afaik.)

Here's the code: 

def MakeTriangle(numberOfRows):
    """the print statements are not required. They are just to help see how it works."""
    triangle=[[1]] #base case (i.e., 0th row)
    print 'triangle[-1] is ', triangle[-1]
    for _x in range(numberOfRows - 1): #_x isn't used
        zipperd = zip([0] + triangle[-1], triangle[-1] + [0]) 
        print "zipperd: ", zipperd
        newRow = map(sum, zipperd) 
        triangle.append(list(newRow))
        print 'triangle[-1] is ', triangle[-1] #to help see how tri is built
    print "\n\n"
    return triangle

for row in MakeTriangle(5):
    print('{0:^50}'.format(row))

To begin to understand how it works, note the following simple cases of the above functions zip and map:

x = [1, 2, 3]
y = [4, 5, 6]
zipped = zip(x, y)
print zipped #output is [(1, 4), (2, 5), (3, 6)]
print map(sum, zipped) #output is [5, 7, 9]

With the print statements in place in the MakeTriangle function, you will get this output to help you further see how the code works:

triangle[-1] is  [1]
zipperd:  [(0, 1), (1, 0)]
triangle[-1] is  [1, 1]
zipperd:  [(0, 1), (1, 1), (1, 0)]
triangle[-1] is  [1, 2, 1]
zipperd:  [(0, 1), (1, 2), (2, 1), (1, 0)]
triangle[-1] is  [1, 3, 3, 1]
zipperd:  [(0, 1), (1, 3), (3, 3), (3, 1), (1, 0)]
triangle[-1] is  [1, 4, 6, 4, 1]

Read the docs below while looking at this output and it will begin to make sense:

If it still doesn't make sense, stick these print statements in the for loop of MakeTriangle:

    print "[0] + triangle[-1] is ", [0] + triangle[-1]
    print "triangle[-1] + [0] is ", triangle[-1] + [0]

Note that the aligned (centered) printing is accomplished using the examples from http://docs.python.org/2/library/string.html#format-examples.

See also https://stackoverflow.com/a/19895685/463994

Upvotes: 2

JAB
JAB

Reputation: 21089

I would change PrintingList = list() to PrintingList = [newValue].

triangle(10) then gives you the following:

[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 6, 4, 1]
[1, 5, 10, 10, 5, 1]
[1, 6, 15, 20, 15, 6, 1]
[1, 7, 21, 35, 35, 21, 7, 1]
[1, 8, 28, 56, 70, 56, 28, 8, 1]
[1, 9, 36, 84, 126, 126, 84, 36, 9, 1]

Which is a valid Pascal's triangle.

Upvotes: 10

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