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98 lines
3.1 KiB
Python
98 lines
3.1 KiB
Python
#ProjectEuler/Python/Problem15.py
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#Matthew Ellison
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# Created: 01-31-19
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#Modified: 07-24-21
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#How many routes from the top left corner to the bottom right corner are there through a 20×20 grid if you can only move right and down?
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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) 2021 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 Problems.Problem import Problem
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class Problem15(Problem):
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#Variables
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__gridWidth = 20 #The height of the grid
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__gridHeight = 20 #The width of the grid
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#Functions
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#Constructor
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def __init__(self) -> None:
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super().__init__("How many routes from the top left corner to the bottom right corner are there through a 20x20 grid if you can only move right and down?")
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self.numOfRoutes = 0
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#Operational functions
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#Solve the problem
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def solve(self) -> None:
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#If the problem has already been solved do nothing and end the function
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if(self.solved):
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return
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#Start the timer
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self.timer.start()
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#Start the recursion at the right location and catch what is returned
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self.numOfRoutes = self.movement(0, 0)
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#Stop the timer
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self.timer.stop()
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#Throw a flag to show the problem is solved
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self.solved = True
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#This function acts as a handler for moving the position on the grid and counting the distance
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#It moves right first, then down
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def movement(self, currentX: int, currentY: int) -> int:
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#Return 1 if you are at the finish location
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if((currentX == self.__gridWidth) and (currentY == self.__gridHeight)):
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return 1
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numberMoves = 0
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#Otherwise move one right if you can and recurse
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if(currentX < self.__gridWidth):
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numberMoves = self.movement(currentX + 1, currentY)
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#Then move one down and recurse
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if(currentY < self.__gridHeight):
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numberMoves += self.movement(currentX, currentY + 1)
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return numberMoves
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#Reset the problem so it can be run again
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def reset(self) -> None:
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super().reset()
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self.numOfRoutes = 0
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#Gets
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#Returns the result of solving the problem
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def getResult(self) -> str:
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self.solvedCheck("result")
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return f"The number of paths from 1 corner of a {self.__gridWidth} x {self.__gridHeight} grid to the opposite corner is {self.numOfRoutes}"
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#Returns the number of routes found
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def getNumberOfRoutes(self) -> int:
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self.solvedCheck("number of routes")
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return self.numOfRoutes
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"""Results:
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The number of paths from 1 corner of a 20 x 20 grid to the opposite corner is 137846528820
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It took 32.903 hours to solve this algorithm
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"""
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