python.p0028 Namespace Reference

Functions
def	spiral_corners
def	square_corner_sum
def	spiral_diagonal_sum
def	main ()

Detailed Description

Project Euler Problem 28

1       ends at 1^2
2-9     ends at 3^2
10-25   ends at 5^2
26-49   ends at 7^2

perimeter[0] = (1, )
perimeter[i] = ((2 * i - 1)^2, (2 * i + 1)^2]

i = 1
2 3 4 5 6 7 8 9
  ^   ^   ^   ^
2i - 1, 2 * 2i - 1, 3 * 2i - 1, 4 * 2i - 1

i = 2
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
      ^           ^           ^           ^
2i - 1, 2 * 2i - 1, 3 * 2i - 1, 4 * 2i - 1

i = 3
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
            ^                 ^                 ^                 ^

the corners are:
perimeter[i][x * 2i - 1 for x in (1, 2, 3, 4)]

Revision 1:

Extracted the code that finds the corners

Problem:

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

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

Function Documentation

def python.p0028.main

(

int

)

Here is the call graph for this function:

def python.p0028.spiral_corners

(

i

)

Here is the caller graph for this function:

def python.p0028.spiral_diagonal_sum

(

size

)

Here is the call graph for this function:

Here is the caller graph for this function:

def python.p0028.square_corner_sum

(

i

)

Here is the call graph for this function:

Here is the caller graph for this function: