#ProjectEuler/Python/Problem11.py #Matthew Ellison # Created: 01-31-19 #Modified: 10-30-20 #What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid? """ 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48 """ #Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses """ Copyright (C) 2020 Matthew Ellison This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this program. If not, see . """ from Problems.Problem import Problem from Unsolved import Unsolved from Algorithms import prod class Problem11(Problem): #Variables __grid = [[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8], [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 00], [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65], [52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91], [22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80], [24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50], [32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70], [67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21], [24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72], [21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95], [78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92], [16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57], [86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58], [19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40], [ 4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66], [88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69], [ 4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36], [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16], [20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54], [ 1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]] #Functions #Constructor def __init__(self): super().__init__("What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?") self.greatestProduct = [] #Operational functions #Solve the problem def solve(self): #If the problem has already been solved do nothing and end the function if(self.solved): return #Setup the variables self.greatestProduct = [0, 0, 0, 0] #Holds the numbers that give the greatest product currentNumbers = [0, 0, 0, 0] #Holds the numbers that you are currently working with #Start the timer self.timer.start() #Loop through every location in the grid for row in range(0, len(self.__grid)): for col in range (0, len(self.__grid[row])): #Setup variables for knowing what direction you can move moveLeft = False moveRight = False moveDown = False #Check which directions you will be able to move if((col - 3) >= 0): moveLeft = True if((col + 3) < len(self.__grid[row])): moveRight = True if((row + 3) < 20): moveDown = True #With these movements check for the greatest product of 4 adjacent numebrs #Move Right if moveRight: currentNumbers[0] = self.__grid[row][col] currentNumbers[1] = self.__grid[row][col + 1] currentNumbers[2] = self.__grid[row][col + 2] currentNumbers[3] = self.__grid[row][col + 3] if(prod(currentNumbers) > prod(self.greatestProduct)): self.greatestProduct = currentNumbers.copy() #Move Down if moveDown: currentNumbers[0] = self.__grid[row][col] currentNumbers[1] = self.__grid[row + 1][col] currentNumbers[2] = self.__grid[row + 2][col] currentNumbers[3] = self.__grid[row + 3][col] if(prod(currentNumbers) > prod(self.greatestProduct)): self.greatestProduct = currentNumbers.copy() #Move Down & Left if(moveDown and moveLeft): currentNumbers[0] = self.__grid[row][col] currentNumbers[1] = self.__grid[row + 1][col - 1] currentNumbers[2] = self.__grid[row + 2][col - 2] currentNumbers[3] = self.__grid[row + 3][col - 3] if(prod(currentNumbers) > prod(self.greatestProduct)): self.greatestProduct = currentNumbers.copy() #Move Down & Right if(moveDown and moveRight): currentNumbers[0] = self.__grid[row][col] currentNumbers[1] = self.__grid[row + 1][col + 1] currentNumbers[2] = self.__grid[row + 2][col + 2] currentNumbers[3] = self.__grid[row + 3][col + 3] if(prod(currentNumbers) > prod(self.greatestProduct)): self.greatestProduct = currentNumbers.copy() #Stop the timer self.timer.stop() #Throw a flag to show the problem is solved self.solved = True #Reset the problem so it can be run again def reset(self): super().reset() self.greatestProduct.clear() #Gets #Returns the result of solving the problem def getResult(self): #If the problem hasn't been solved throw an exception if(not self.solved): raise Unsolved("You must solve the problem before you can see the result") return f"The greatest product of 3 numbers in a line is {prod(self.greatestProduct)}" #Returns the numbers that were being searched def getNumbers(self) -> list: #If the problem hasn't been solved throw an exception if(not self.solved): raise Unsolved("You must solve the problem before you can get the numbers being searched") return self.greatestProduct #Returns the product that was requested def getProduct(self) -> int: #If the problem hasn't been solved throw an exception if(not self.solved): raise Unsolved("You must solve the problem before you can get the product") return prod(self.greatestProduct) """Results: The greatest product of 3 numbers in a line is 70600674 It took an average of 1.071 milliseconds to run this problem through 100 iterations """