Problem42.py

# Code by @AmirMotefaker

# projecteuler.net
# https://projecteuler.net/problem=42

# Coded triangle numbers
# Problem 42

# The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:

#              1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

# By converting each letter in a word to a number corresponding to its alphabetical position
# and adding these values we form a word value. For example,
# the word value for SKY is 19 + 11 + 25 = 55 = t10. 
# If the word value is a triangle number then we shall call the word a triangle word.

# Using words.txt (right click and 'Save Link/Target As...'),
# a 16K text file containing nearly two-thousand common English words,
# how many are triangle words?


# Solution 1

# The quadratic formula:
# a x**2 + b x + c = 0 
# x = -b -+ sqrt(b**2 - 4 a c) / 2 a 
# The quadratic formula has two solutions as indicated by the plus–minus symbol "±" in the numerator.
# We only care about the plus solution as it produces a positive result.
# We can rearrange the equation to make it more readable.
# n = (sqrt (1 + 8 tn) - 1) / 2
# The result, n, is the index for tn in the sequence of triangle numbers, 
# which is useful for the Hackerrank version. For example, solving for tn = 55:
# n = (sqrt (1 + 8 *55) - 1) / 2  then n = (sqrt (441)-1) / 2 = 21 - 1 /2  then n =10

from math import sqrt
import time

start_time = time.time()   #Time at the start of program execution

score = lambda word: sum(ord(c)-ord('A')+1 for c in word)
is_tn = lambda t: (sqrt(1 + 8*t) - 1) / 2 % 1 == 0
print ("Number of triangle words =", 
    sum(is_tn(score(x[1:-1])) for x in open('Problem42_words.txt').read().split(',')))

end_time = time.time()   #Time at the end of execution
print ("Time of program execution:", (end_time - start_time))   # Time of program execution



# Solution 2

# import string
# import csv
# import math

# import time
# start_time = time.time()   #Time at the start of program execution


# def main():
#     letter_to_number_dict = dict(zip(string.ascii_uppercase, [ord(c) % 32 for c in string.ascii_uppercase]))
#     with open('Problem42_words.txt', 'r') as f:
#         reader = csv.reader(f)
#         words = list(reader)[0]
#     total = 0
#     for word in words:
#         score = 0
#         for letter in word:
#             score += letter_to_number_dict[letter]
#         if is_square(8*score+1):
#             total += 1
#     print(total)


# def is_square(integer):
#     root = math.sqrt(integer)
#     if int(root + 0.5) ** 2 == integer:
#         return True
#     else:
#         return False


# main()

# end_time = time.time()   #Time at the end of execution
# print ("Time of program execution:", (end_time - start_time))   # Time of program execution



### Answer:  162