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110 lines
3.5 KiB
Python
110 lines
3.5 KiB
Python
#ProjectEuler/Python/Problem28.py
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#Matthew Ellison
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# Created: 09-22-19
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#Modified: 09-22-19
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#What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed by starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral
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#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
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"""
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Copyright (C) 2019 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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"""
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from Stopwatch import Stopwatch
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def setupGrid() -> list:
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#Setup the grid to be the right size and fill it with 0's
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grid = [[0 for x in range(1001)] for y in range(1001)]
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finalLocation = False #A flag to indicate if the final location to be filled has been reached
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currentNum = 1 #Set the number that is going to be put at each location
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#Start with the middle location and set it correctly and advance the tracker to the next number
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xLocation = 500
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yLocation = 500
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grid[yLocation][xLocation] = currentNum
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currentNum += 1
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#Move right the first time
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xLocation += 1
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#Move in a circular pattern until you reach the final location
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while(not finalLocation):
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#Move down until you reach a blank location on the left
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while(grid[yLocation][xLocation - 1] != 0):
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grid[yLocation][xLocation] = currentNum
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currentNum += 1
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yLocation += 1
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#Move left until you reach a blank location above
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while(grid[yLocation - 1][xLocation] != 0):
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grid[yLocation][xLocation] = currentNum
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currentNum += 1
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xLocation -= 1
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#Move up until you reach a blank location to the right
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while(grid[yLocation][xLocation + 1] != 0):
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grid[yLocation][xLocation] = currentNum
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currentNum += 1
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yLocation -= 1
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#Move right until you reach a blank location below
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while(grid[yLocation + 1][xLocation] != 0):
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grid[yLocation][xLocation] = currentNum
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currentNum += 1
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xLocation += 1
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#Check if you are at the final location and break the loop if you are
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if(xLocation == len(grid)):
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finalLocation = True
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break
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return grid
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def findSum(grid: list) -> int:
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sumOfDiagonals = 0
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leftSide = 0
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rightSide = len(grid) - 1
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row = 0
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while(row < len(grid)):
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#This ensure the middle location is only counted once
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if(leftSide == rightSide):
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sumOfDiagonals += grid[row][leftSide]
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else:
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sumOfDiagonals += grid[row][leftSide]
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sumOfDiagonals += grid[row][rightSide]
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row += 1
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leftSide += 1
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rightSide -= 1
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return sumOfDiagonals
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def Problem28():
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#Setup the grid
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grid = setupGrid()
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#Find the sum of the diagonals in the grid
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diagSum = findSum(grid)
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#Print the results
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print("The sum of the diagonals in the given grid is " + str(diagSum))
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#This calls the appropriate functions if the script is called stand alone
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if __name__ == "__main__":
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timer = Stopwatch()
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timer.start()
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Problem28()
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timer.stop()
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print("It took " + timer.getString() + " to run this algorithm")
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""" Results:
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The sum of the diagonals in the given grid is 669171001
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It took 197.764 milliseconds to run this algorithm
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"""
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