Add more python solutions

Added solutions for problems 16, 17 and 18

Python/p016.py

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+#!/usr/bin/python3
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+    res = str(2 ** 1000)
+
+    sum_ = 0
+
+    for i in range(len(res)):
+        sum_ = sum_ + int(res[i])
+
+    end = default_timer()
+
+    print('Project Euler, Problem 16')
+    print('Answer: {}'.format(sum_))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p017.py

@@ -0,0 +1,40 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+
+def main():
+    start = default_timer()
+
+    n_letters = [[3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 8],\
+                [60, 60, 50, 50, 50, 70, 60, 60],\
+                [1300, 1300, 1500, 1400, 1400, 1300, 1500, 1500, 1400],\
+                [11]]
+
+    sum_ = 0
+
+    for i in range(19):
+        sum_ = sum_ + n_letters[0][i]
+
+    for i in range(8):
+        for j in range(9):
+            n_letters[1][i] = n_letters[1][i] + n_letters[0][j]
+        sum_ = sum_ + n_letters[1][i]
+
+    for i in range(9):
+        for j in range(19):
+            n_letters[2][i] = n_letters[2][i] + n_letters[0][j]
+        for j in range(8):
+            n_letters[2][i] = n_letters[2][i] + n_letters[1][j]
+        sum_ = sum_ + n_letters[2][i] - 3
+
+    sum_ = sum_ + n_letters[3][0]
+
+    end = default_timer()
+
+    print('Project Euler, Problem 17')
+    print('Answer: {}'.format(sum_))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/p018.py

@@ -0,0 +1,48 @@
+#!/usr/bin/python3
+
+from timeit import default_timer
+
+def sum_triangle(triang, n, i, j, sum_):
+    global max_
+
+    if i == n:
+        if sum_ > max_:
+            max_ = sum_
+        return max_
+
+    sum_triangle(triang, n, i+1, j, sum_+triang[i][j])
+    sum_triangle(triang, n, i+1, j+1, sum_+triang[i][j])
+
+def main():
+    global max_
+
+    start = default_timer()
+
+    try:
+        fp = open('triang.txt', 'r')
+    except:
+        print('Error while opening file {}'.format('triang.txt'))
+        exit(1)
+
+    triang = list()
+
+    for line in fp:
+        triang.append(line.strip('\n').split())
+    
+    fp.close()
+
+    for i in range(len(triang)):
+        triang[i] = list(map(int, triang[i]))
+   
+    max_ = 0
+    sum_triangle(triang, 15, 0, 0, 0)
+
+    end = default_timer()
+
+    print('Project Euler, Problem 18')
+    print('Answer: {}'.format(max_))
+
+    print('Elapsed time: {:.9f} seconds'.format(end - start))
+
+if __name__ == '__main__':
+    main()

Python/triang.txt

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+75
+95 64
+17 47 82
+18 35 87 10
+20 04 82 47 65
+19 01 23 75 03 34
+88 02 77 73 07 63 67
+99 65 04 28 06 16 70 92
+41 41 26 56 83 40 80 70 33
+41 48 72 33 47 32 37 16 94 29
+53 71 44 65 25 43 91 52 97 51 14
+70 11 33 28 77 73 17 78 39 68 17 57
+91 71 52 38 17 14 91 43 58 50 27 29 48
+63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23