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question11.py
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#!/usr/bin/env python3
import numpy as np
import operator as op
from functools import reduce
#question 11 product in grid
#In the 20×20 grid below, four numbers along a diagonal line have been
#marked in red.
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
'''
#The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
#What is the greatest product of four adjacent numbers in the same
#direction (up, down, left, right, or diagonally) in the 20×20 grid?
# idea - function to find max product of four numbers in a list
# - then slice up the string into lists of vertical, horiz, diag
# create matrix to hold data
grid_n = np.zeros(shape=(20,20))
#print(grid_n)
#print(grid_n[0,:]) #for one line
# convert string to matrix
lines = grid.splitlines()
#print(type(lines[1]))
for i in range(20):
num_str = lines[i]
nums = num_str.split(' ')
grid_n[i,] = np.asarray(nums)
def max_product(number,mylist):
count = 0
for l in range(len(mylist)-number+1):
temp1 = mylist[l:l+number]
temp = reduce(op.mul,temp1,1)
#print(temp1, temp)
if temp > count: count = temp
return (count)
def max_rows(number, grid):
count = 0
for row in grid:
temp = max_product(number, row)
if temp > count: count = temp
return count
def max_cols(number, grid):
return (max_rows(number,np.transpose(grid)))
def convert_diag(grid):
grid_1 = np.zeros(shape=(grid.shape[1]*2-1,grid.shape[1]))
#reshape grid into rows
for i in range(grid.shape[1]+1):
toprows = grid.diagonal(grid.shape[1]-i-1)
#print("top",i,grid.shape[1]-i-1, toprows)
grid_1[i,0:len(toprows)] = toprows
bottomrows = grid[i+1:,].diagonal()
#print("bot",i, bottomrows,grid.shape[1]+i)
if len(bottomrows) != 0:
grid_1[grid.shape[1]+i,0:len(bottomrows)] = bottomrows
return(grid_1)
def max_diag(number,grid):
grid1 = convert_diag(grid)
grid2 = convert_diag(np.fliplr(grid))
count1 = max_rows(number,grid1)
count2 = max_rows(number, grid2)
if count1>count2: return count1
return count2
#temp_matrix = grid[i:i+number,:]
#diag = temp_matrix.diagonal()
#temp = max_product
#test = np.array([[1,2,3],[4,5,6],[7,8,9]])
#test = np.array([[1,2,3,400],[5,6,7,8],[9,10,11,12],[13,14,15,16]])
#print(test)
#print(max_diag(2, test))
#print(max_rows(2,test))
#print(max_cols(2,test))
print(max_diag(4, grid_n))
print(max_rows(4, grid_n))
print(max_cols(4, grid_n))
# 70600674.0 YAY
# 48477312.0
# 51267216.0