ID : 467

viewed : 221

Tags : PythonPython Array

100

Pascal’s triangle is defined as a type of number pattern in which numbers are arranged so that they look like a triangle. A triangular array is formed in this Mathematics concept, formed by numbers that are the sum of the adjacent row. Additionally, the external edges are always 1.

To form a pascal triangle in Python, there is a stepwise in the software.

- Firstly, an input number is taken from the user to define the number of rows.
- Secondly, an empty list is defined, which is used to store values.
- Then, a
`for`

loop is used to iterate from`0`

to`n-1`

that append the sub-lists to the initial list. - After that,
`1`

is appended to the list. - Then, a
`for`

loop is used again to put the values of the number inside the adjacent row of the triangle. - Finally, the Pascal Triangle is printed according to the given format.

`input_num = int(input("Enter the number of rows: ")) list = [] #an empty list for n in range(input_num): list.append([]) list[n].append(1) for m in range(1, n): list[n].append(list[n - 1][m - 1] + list[n - 1][m]) if(input_num != 0): list[n].append(1) for n in range(input_num): print(" " * (input_num - n), end = " ", sep = " ") for m in range(0, n + 1): print('{0:5}'.format(list[n][m]), end = " ", sep = " ") print() `

Output:

`Enter the number: 5 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 `

In this method, every line in the triangle consists of just `1`

, and the `nth`

number in a row is equal to the Binomial Coefficient. Look at the example program below.

`num = int(input("Enter the number of rows:")) for n in range(1, num+1): for m in range(0, num-n+1): print(' ', end='') # first element is always 1 B = 1 for m in range(1, n+1): # first value in a line is always 1 print(' ', B, sep='', end='') # using Binomial Coefficient BC = B * (n - m) // m print() `

Output:

`Enter the number of rows:5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 `

In this method, the formula used for the Binomial Coefficient is:

`BC = B(line(m), n-1) * (line(m) - n + 1) / n `

`11`

in PythonThis method is completely based on the power of the number `11`

as the increasing values of the power on the number `11`

form the Pascal Triangle pattern.

Mathematically, here’s how it goes.

`11*0 = 1 11*1 = 11 11*2 = 121 11*3 = 1331 11*4 = 14641 `

Now applying this technique in Python, refer to the code block below.

`num = int(input("Enter the number of rows:")) for n in range(num): print(' '*(num-n), end='') print(' '.join(map(str, str(11**n)))) `

Output:

`Enter the number of rows:5 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 `