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Python Challenges: Compute the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed

Python Challenges - 1: Exercise-59 with Solution

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21
22
23
24
25
20
7
8
9
10
19
6
1
2
11
18
5
4
3
12
17
16
15
14
13

Diagonals Numbers: 21 + 7 + 1 + 3 + 13 + 25 + 9 + 5 + 17 = 101
It can be verified that the sum of the numbers on the diagonals is 101.
Write a Python program to compute the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the above way.

Sample Solution:

Python Code:

MAX_SIZE = 1001  
result = 1 
result += sum(4 * i * i - 6 * (i - 1) for i in range(3, MAX_SIZE + 1, 2))
print(str(result))

Sample Output:

669171001

Flowchart:

Python Flowchart: Compute the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed.

#Ref: https://bit.ly/2GZmz51

Python Code Editor:

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

  • The os and os.path modules.
  • The __file__ constant
  • os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
  • os.path.dirname(path) (returns "the directory name of pathname path")
  • os.getcwd() (returns "a string representing the current working directory")
  • os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m