Add more solutions

Added solutions for problems from 41 to 5, both in C and python

Python/p041.py

@@ -0,0 +1,29 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+from projecteuler import is_pandigital, is_prime
+
+def count_digits(n):
+    i = 0
+
+    while n > 0:
+        i = i + 1
+        n = n // 10
+
+    return i
+
+def main():
+    start = default_timer()
+
+    for i in range(7654321, 0, -2):
+        if is_pandigital(i, count_digits(i)) and is_prime(i):
+            print('Project Euler, Problem 41')
+            print('Answer: {}'.format(i))
+            break
+
+    end = default_timer()
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p042.py

@@ -0,0 +1,50 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+
+def is_triang(n):
+    i = 1
+    j = 1
+
+    while j <= n:
+        if n == j:
+            return True
+        i = i + 1
+        j = j + i
+
+    return False
+
+def main():
+    start = default_timer()
+
+    try:
+        fp = open('words.txt', 'r')
+    except:
+        print('Error while opening file {}'.format('words.txt'))
+        exit(1)
+
+    words = list(fp.readline().replace('"', '').split(','))
+
+    fp.close()
+
+    count = 0
+
+    for word in words:
+        value = 0
+        l = len(word)
+
+        for j in range(l):
+            value = value + ord(word[j]) - ord('A') + 1
+
+        if is_triang(value):
+            count = count + 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 42')
+    print('Answer: {}'.format(count))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p043.py

@@ -0,0 +1,64 @@
+#!/usr/bin/python3
+
+from itertools import permutations
+
+from timeit import default_timer
+
+def has_property(n):
+    value = int(n[1]) * 100 + int(n[2]) * 10 + int(n[3])
+
+    if value % 2 != 0:
+        return False
+
+    value = int(n[2]) * 100 + int(n[3]) * 10 + int(n[4])
+
+    if value % 3 != 0:
+        return False
+
+    value = int(n[3]) * 100 + int(n[4]) * 10 + int(n[5])
+
+    if value % 5 != 0:
+        return False
+
+    value = int(n[4]) * 100 + int(n[5]) * 10 + int(n[6])
+
+    if value % 7 != 0:
+        return False
+
+    value = int(n[5]) * 100 + int(n[6]) * 10 + int(n[7])
+
+    if value % 11 != 0:
+        return False
+
+    value = int(n[6]) * 100 + int(n[7]) * 10 + int(n[8])
+
+    if value % 13 != 0:
+        return False
+    
+    value = int(n[7]) * 100 + int(n[8]) * 10 + int(n[9])
+
+    if value % 17 != 0:
+        return False
+
+    return True
+
+def main():
+    start = default_timer()
+
+    perm = list(permutations('0123456789'))
+
+    sum_ = 0
+
+    for i in perm:
+        if has_property(i):
+            sum_ = sum_ + int(''.join(map(str, i)))
+
+    end = default_timer()
+
+    print('Project Euler, Problem 43')
+    print('Answer: {}'.format(sum_))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p044.py

@@ -0,0 +1,34 @@
+#!/usr/bin/python3
+
+from math import sqrt
+
+from timeit import default_timer
+from projecteuler import is_pentagonal
+
+def main():
+    start = default_timer()
+
+    found = 0
+    n = 2
+
+    while not found:
+        pn = n * (3 * n - 1) // 2
+
+        for m in range(1, n):
+            pm = m * (3 * m - 1) // 2
+
+            if is_pentagonal(pn+pm) and is_pentagonal(pn-pm):
+                found = 1
+                break
+
+        n = n + 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 44')
+    print('Answer: {}'.format(pn-pm))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p045.py

@@ -0,0 +1,29 @@
+#!/usr/bin/python3
+
+from math import sqrt
+
+from timeit import default_timer
+from projecteuler import is_pentagonal
+
+def main():
+    start = default_timer()
+
+    found = 0
+    i = 143
+
+    while not found:
+        i = i + 1
+        n = i * (2 * i - 1)
+
+        if is_pentagonal(n):
+            found = 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 45')
+    print('Answer: {}'.format(n))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p046.py

@@ -0,0 +1,52 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+from projecteuler import sieve
+
+def goldbach(n):
+    global primes
+
+    for i in range(2, n):
+        if primes[i] == 1:
+            j = 1
+
+            while True:
+                tmp = i + 2 * j * j
+
+                if tmp == n:
+                    return True
+
+                j = j + 1
+
+                if tmp >= n:
+                    break
+
+    return False
+
+def main():
+    start = default_timer()
+
+    global primes
+
+    N = 10000
+
+    primes = sieve(N)
+
+    found = 0
+    i = 3
+
+    while not found and i < N:
+        if primes[i] == 0:
+            if not goldbach(i):
+                found = 1
+        i = i + 2
+
+    end = default_timer()
+
+    print('Project Euler, Problem 46')
+    print('Answer: {}'.format(i-2))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p047.py

@@ -0,0 +1,59 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+from projecteuler import sieve
+
+def count_distinct_factors(n):
+    global primes
+    count = 0
+
+    if n % 2 == 0:
+        count = count + 1
+
+        while True:
+            n = n // 2
+
+            if n % 2 != 0:
+                break
+
+    i = 3
+
+    while n > 1:
+        if primes[i] == 1 and n % i == 0:
+            count = count + 1
+
+            while True:
+                n = n // i
+
+                if n % i != 0:
+                    break
+        i = i + 2
+
+    return count
+
+def main():
+    start = default_timer()
+
+    global primes
+
+    N = 150000
+
+    primes = sieve(N)
+    found = 0
+    i = 645
+
+    while not found and i < N - 3:
+        if primes[i] == 0 and primes[i+1] == 0 and primes[i+2] == 0 and primes[i+3] == 0:
+            if count_distinct_factors(i) == 4 and count_distinct_factors(i+1) == 4 and count_distinct_factors(i+2) == 4 and count_distinct_factors(i+3) == 4:
+                found = 1
+        i  = i + 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 47')
+    print('Answer: {}'.format(i-1))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p048.py

@@ -0,0 +1,22 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+    sum_ = 0
+
+    for i in range(1, 1001):
+        power = i ** i
+        sum_ = sum_ + power
+
+    end = default_timer()
+
+    print('Project Euler, Problem 48')
+    print('Answer: {}'.format(str(sum_)[-10:]))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p049.py

@@ -0,0 +1,53 @@
+#!/usr/bin/python3
+
+from numpy import zeros
+
+from timeit import default_timer
+from projecteuler import sieve
+
+def check_digits(a, b):
+    digits1 = zeros(10, int)
+    digits2 = zeros(10, int)
+
+    while a > 0:
+        digits1[a%10] = digits1[a%10] + 1
+        a = a // 10
+
+    while b > 0:
+        digits2[b%10] = digits2[b%10] + 1
+        b = b // 10
+
+    for i in range(10):
+        if digits1[i] != digits2[i]:
+            return False
+
+    return True
+
+def main():
+    start = default_timer()
+
+    N = 10000
+
+    primes = sieve(N)
+
+    found = 0
+    i = 1489
+
+    while i < N and found == 0:
+        if primes[i] == 1:
+            for j in range(1, 4255):
+                if i + 2 * j < N and primes[i+j] == 1 and primes[i+2*j] == 1 and\
+                        check_digits(i, i+j) and check_digits(i, i+2*j):
+                            found = 1
+                            break
+        i = i + 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 49')
+    print('Answer: {}'.format(str(i-1)+str(i-1+j)+str(i-1+2*j)))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p050.py

@@ -0,0 +1,41 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+from projecteuler import sieve
+
+def main():
+    start = default_timer()
+
+    N = 1000000
+
+    primes = sieve(N)
+
+    max_ = 0
+    max_p = 0
+
+    for i in range(2, N):
+        if primes[i] == 1:
+            count = 1
+            sum_ = i
+            j = i + 1
+
+            while j < N and sum_ < N:
+                if primes[j] == 1:
+                    sum_ = sum_ + j
+                    count = count + 1
+
+                    if sum_ < N and primes[sum_] == 1 and count > max_:
+                        max_ = count
+                        max_p = sum_
+
+                j = j + 1
+
+    end = default_timer()
+
+    print('Project Euler, Problem 50')
+    print('Answer: {}'.format(max_p))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()