Comparing two numbers written in index form like 211 and 37 is not difficult,
as any calculator would confirm that 211 = 2048 < 37 = 2187.
However, confirming that 632382518061 > 519432525806 would be much more difficult,
as both numbers contain over three million digits.
Using base_exp.txt (right click and 'Save Link/Target As...'), a 22K text file containing one thousand lines
with a base/exponent pair on each line, determine which line number has the greatest numerical value.
NOTE: The first two lines in the file represent the numbers in the example given above. '''
import Functions
import time
import math
start = time.clock()
best_line = 1
current_line = 1
best_num = 0
ls = Functions.import_csv('base_exp.txt')
for pair in ls:
print('Current line under test...',current_line)
test = int(pair[1]) * math.log(int(pair[0])) #instead of compare actual base**exp, compare exponent * log(base)
if test > best_num:
best_num = test
best_line = current_line
current_line += 1
print('The line with the largest number is ', best_line)
Functions.runtime(start)
The prime 41, can be written as the sum of six consecutive primes:
41 = 2 + 3 + 5 + 7 + 11 + 13
This is the longest sum of consecutive primes that adds to a prime below one-hundred.
The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.
Which prime, below one-million, can be written as the sum of the most consecutive primes? '''
# This program uses brute force solution, and loads a csv of all primes < 1e6.
# Answer in approx 16s. Not best solution.
import Functions
import time
global primes_ls
primes_ls = Functions.import_csv('primes_1e6.csv')
primes_ls = list(map(int, primes_ls)) # Need to add list on outside, Python 3
def sum_of_primes(num_terms, start):
global primes_ls
ans = primes_ls[start]
for i in range(1, num_terms):
ans += primes_ls[i]
return ans
start_time = time.clock()
prime_sum = 0
start_index = primes_ls.index(953)
return False
start = time.clock()
x1 = 0
x2 = 0
x3 = 0
y1 = 0
y2 = 0
y3 = 0
''' Need to determine if origin is in triangle. If this is the case, then the y intercept of 2 of the
lines which enclose the triangle will be within the upper and lower y bounds formed by the points at
the vertices. '''
ls = Functions.import_csv('triangles.txt')
enc_origin = []
num = 0
for coords in ls:
x1 = int(coords[0])
y1 = int(coords[1])
x2 = int(coords[2])
y2 = int(coords[3])
x3 = int(coords[4])
y3 = int(coords[5])
#print('current coords under test...',coords)
test = triangle(x1,y1,x2,y2,x3,y3)
if test == True:
num += 1
