{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 11:\n",
"\n",
"[Euler Project #11](https://projecteuler.net/problem=11)\n",
"\n",
"\n",
"> In the 20×20 grid below, four numbers along a diagonal line have been marked in red.\n",
"> \n",
"> 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
\n",
"> 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
\n",
"> 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
\n",
"> 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
\n",
"> 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
\n",
"> 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
\n",
"> 32 98 81 28 64 23 67 10 **26** 38 40 67 59 54 70 66 18 38 64 70
\n",
"> 67 26 20 68 02 62 12 20 95 **63** 94 39 63 08 40 91 66 49 94 21
\n",
"> 24 55 58 05 66 73 99 26 97 17 **78** 78 96 83 14 88 34 89 63 72
\n",
"> 21 36 23 09 75 00 76 44 20 45 35 **14** 00 61 33 97 34 31 33 95
\n",
"> 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
\n",
"> 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
\n",
"> 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
\n",
"> 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
\n",
"> 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
\n",
"> 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
\n",
"> 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
\n",
"> 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
\n",
"> 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
\n",
"> 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
\n",
"> \n",
"> The product of these numbers is 26 × 63 × 78 × 14 = 1788696.\n",
"> \n",
"> What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?\n",
"\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reserved Space For Imports\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import os\n",
"import pprint\n",
"import time # Typically imported for sleep function, to slow down execution in terminal.\n",
"import typing\n",
"import decorators # Typically imported to compute execution duration of functions.\n",
"import math\n",
"import numpy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Reserved Space For Method Definition\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def check_horizontal(table,solution):\n",
" '''\n",
" Args:\n",
" table: list of lists representing the input table\n",
" solution: a dictionary storing the product, and three tuples of cell coordinates \n",
" '''\n",
" # Let's scan the horizontals first.\n",
" # Acceptable cells would have a root position (on the LHS) which may reside anywhere in the table,\n",
" # except for the last three columns.\n",
"\n",
" # create a list of tuples to store cell coordinates while generating the products\n",
" cells=[(0,0),(0,0),(0,0),(0,0)]\n",
"\n",
" # loop over row dimension\n",
" for row in range(len(table)):\n",
" # loop over column dimension\n",
" for column in range(len(table[row])-4):\n",
" # calculate product\n",
" product = 1\n",
" for i in range(4):\n",
" product *= table[row][column+i]\n",
" cells[i]=(row,column+i)\n",
" #print(\"product=\",product)\n",
" if product>solution['product']:\n",
" solution['product']=product\n",
" solution['cella']=cells[0]\n",
" solution['cellb']=cells[1]\n",
" solution['cellc']=cells[2]\n",
" solution['celld']=cells[3]\n",
" \n",
" return solution"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def check_vertical(table,solution):\n",
" '''\n",
" Args:\n",
" table: list of lists representing the input table\n",
" solution: a dictionary storing the product, and three tuples of cell coordinates \n",
" '''\n",
" # Let's scan the verticals next.\n",
" # Acceptable cells would have a root position (at the top of column) which may reside anywhere in the table,\n",
" # except for the last three rows.\n",
"\n",
" # create a list of tuples to store cell coordinates while generating the products\n",
" cells=[(0,0),(0,0),(0,0),(0,0)]\n",
"\n",
" # loop over row dimension\n",
" count = 0\n",
" for row in range(len(table)-4):\n",
" # loop over column dimension\n",
" for column in range(len(table[row])):\n",
" # convert data type from string to int\n",
" product = 1\n",
" for i in range(4):\n",
" product *= table[row+i][column]\n",
" cells[i]=(row,column+i)\n",
" #print(\"product=\",product)\n",
" count+=1\n",
" #print(\"count=\",count)\n",
" if product>solution['product']:\n",
" solution['product']=product\n",
" solution['cella']=cells[0]\n",
" solution['cellb']=cells[1]\n",
" solution['cellc']=cells[2]\n",
" solution['celld']=cells[3]\n",
" \n",
" return solution"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def check_upwards_diagonals(table,solution):\n",
" '''\n",
" Args:\n",
" table: list of lists representing the input table\n",
" solution: a dictionary storing the product, and three tuples of cell coordinates \n",
" '''\n",
" # Let's scan the upward (left to right) diagonals next.\n",
" # Acceptable cells would have a root position (at the bottom-left of the diagonal) which may reside anywhere in the table,\n",
" # except for the first three rows, and the last three columns.\n",
"\n",
" # create a list of tuples to store cell coordinates while generating the products\n",
" cells=[(0,0),(0,0),(0,0),(0,0)]\n",
"\n",
" # loop over row dimension\n",
" count = 0\n",
" for row in range(len(table)-3):\n",
" # loop over column dimension\n",
" #print(\"row=\",row)\n",
" for column in range(len(table[row])-3):\n",
" # convert data type from string to int\n",
" product = 1\n",
" for i in range(4):\n",
" product *= table[row+3-i][column+i]\n",
" cells[i]=(row+3-i,column+i)\n",
" #print(\"cell=[\",row+3-i,\"][\",column+i,\"]\")\n",
" #print(\"product=\",product)\n",
" count += 1\n",
" if product>solution['product']:\n",
" solution['product']=product\n",
" solution['cella']=cells[0]\n",
" solution['cellb']=cells[1]\n",
" solution['cellc']=cells[2]\n",
" solution['celld']=cells[3]\n",
" \n",
" return solution"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def check_downwards_diagonals(table,solution):\n",
" '''\n",
" Args:\n",
" table: list of lists representing the input table\n",
" solution: a dictionary storing the product, and three tuples of cell coordinates \n",
" '''\n",
" # Let's scan the downward (left to right) diagonals next.\n",
" # Acceptable cells would have a root position (at the top-left of the diagonal) which may reside anywhere in the table,\n",
" # except for the last three rows, and the last three columns.\n",
"\n",
" # create a list of tuples to store cell coordinates while generating the products\n",
" cells=[(0,0),(0,0),(0,0),(0,0)]\n",
"\n",
" # loop over row dimension\n",
" count = 0\n",
" for row in range(len(table)-3):\n",
" # loop over column dimension\n",
" #print(\"row=\",row)\n",
" for column in range(len(table[row])-3):\n",
" # convert data type from string to int\n",
" product = 1\n",
" for i in range(4):\n",
" product *= table[row+i][column+i]\n",
" cells[i]=(row+i,column+i)\n",
" #print(\"cell=[\",row+i,\"][\",column+i,\"]\")\n",
" #print(\"product=\",product)\n",
" count += 1\n",
" #print(\"count=\",count)\n",
" if product>solution['product']:\n",
" solution['product']=product\n",
" solution['cella']=cells[0]\n",
" solution['cellb']=cells[1]\n",
" solution['cellc']=cells[2]\n",
" solution['celld']=cells[3]\n",
" \n",
" return solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Import the data table above. Let's be lazy and use the nice multi-cursor feature of the code editor."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"\n",
"table = \\\n",
" [\\\n",
" ['08', '02', '22', '97', '38', '15', '00', '40', '00', '75', '04', '05', '07', '78', '52', '12', '50', '77', '91', '08'],\n",
" ['49', '49', '99', '40', '17', '81', '18', '57', '60', '87', '17', '40', '98', '43', '69', '48', '04', '56', '62', '00'],\n",
" ['81', '49', '31', '73', '55', '79', '14', '29', '93', '71', '40', '67', '53', '88', '30', '03', '49', '13', '36', '65'],\n",
" ['52', '70', '95', '23', '04', '60', '11', '42', '69', '24', '68', '56', '01', '32', '56', '71', '37', '02', '36', '91'],\n",
" ['22', '31', '16', '71', '51', '67', '63', '89', '41', '92', '36', '54', '22', '40', '40', '28', '66', '33', '13', '80'],\n",
" ['24', '47', '32', '60', '99', '03', '45', '02', '44', '75', '33', '53', '78', '36', '84', '20', '35', '17', '12', '50'],\n",
" ['32', '98', '81', '28', '64', '23', '67', '10', '26', '38', '40', '67', '59', '54', '70', '66', '18', '38', '64', '70'],\n",
" ['67', '26', '20', '68', '02', '62', '12', '20', '95', '63', '94', '39', '63', '08', '40', '91', '66', '49', '94', '21'],\n",
" ['24', '55', '58', '05', '66', '73', '99', '26', '97', '17', '78', '78', '96', '83', '14', '88', '34', '89', '63', '72'],\n",
" ['21', '36', '23', '09', '75', '00', '76', '44', '20', '45', '35', '14', '00', '61', '33', '97', '34', '31', '33', '95'],\n",
" ['78', '17', '53', '28', '22', '75', '31', '67', '15', '94', '03', '80', '04', '62', '16', '14', '09', '53', '56', '92'],\n",
" ['16', '39', '05', '42', '96', '35', '31', '47', '55', '58', '88', '24', '00', '17', '54', '24', '36', '29', '85', '57'],\n",
" ['86', '56', '00', '48', '35', '71', '89', '07', '05', '44', '44', '37', '44', '60', '21', '58', '51', '54', '17', '58'],\n",
" ['19', '80', '81', '68', '05', '94', '47', '69', '28', '73', '92', '13', '86', '52', '17', '77', '04', '89', '55', '40'],\n",
" ['04', '52', '08', '83', '97', '35', '99', '16', '07', '97', '57', '32', '16', '26', '26', '79', '33', '27', '98', '66'],\n",
" ['88', '36', '68', '87', '57', '62', '20', '72', '03', '46', '33', '67', '46', '55', '12', '32', '63', '93', '53', '69'],\n",
" ['04', '42', '16', '73', '38', '25', '39', '11', '24', '94', '72', '18', '08', '46', '29', '32', '40', '62', '76', '36'],\n",
" ['20', '69', '36', '41', '72', '30', '23', '88', '34', '62', '99', '69', '82', '67', '59', '85', '74', '04', '36', '16'],\n",
" ['20', '73', '35', '29', '78', '31', '90', '01', '74', '31', '49', '71', '48', '86', '81', '16', '23', '57', '05', '54'],\n",
" ['01', '70', '54', '71', '83', '51', '54', '69', '16', '92', '33', '48', '61', '43', '52', '01', '89', '19', '67', '48']\n",
" ]\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Firstly, this data input creates a list-of-lists which have cells of the ```string``` data type."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"# loop over row dimension\n",
"for row in range(len(table)):\n",
" # loop over column dimension\n",
" for column in range(len(table[row])):\n",
" # convert data type from string to int\n",
" table[row][column] = int(table[row][column])\n",
"\n",
"# create a dictionary that stores information about the solution\n",
"solution = {\n",
" 'product':1,\n",
" 'cella':(0,0),\n",
" 'cellb':(0,0),\n",
" 'cellc':(0,0),\n",
" 'celld':(0,0)\n",
"}\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### We know brute force will work...\n",
"### Can we can scan through this list-of-lists, following the accepted pattern, and store the largest product?"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "{'product': 48477312, 'cella': (8, 10), 'cellb': (8, 11), 'cellc': (8, 12), 'celld': (8, 13)}\n{'product': 51267216, 'cella': (6, 15), 'cellb': (6, 16), 'cellc': (6, 17), 'celld': (6, 18)}\n{'product': 70600674, 'cella': (15, 3), 'cellb': (14, 4), 'cellc': (13, 5), 'celld': (12, 6)}\n{'product': 70600674, 'cella': (15, 3), 'cellb': (14, 4), 'cellc': (13, 5), 'celld': (12, 6)}\n"
}
],
"source": [
"solution = check_horizontal(table,solution)\n",
"print(solution)\n",
"\n",
"solution = check_vertical(table,solution)\n",
"print(solution)\n",
"\n",
"solution = check_upwards_diagonals(table,solution)\n",
"print(solution)\n",
"\n",
"solution = check_downwards_diagonals(table,solution)\n",
"print(solution)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
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