Rebased projecteuler folder, now includes all contest programming stuff

projecteuler/058/main.py

@@ -0,0 +1,67 @@
+'''
+Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
+
+37 36 35 34 33 32 31
+38 17 16 15 14 13 30
+39 18  5  4  3 12 29
+40 19  6  1  2 11 28
+41 20  7  8  9 10 27
+42 21 22 23 24 25 26
+43 44 45 46 47 48 49
+
+It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.
+
+If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?
+'''
+
+import time
+import math
+import numpy as np
+from sympy import isprime
+
+def sieve(n):
+    assert n > 1
+
+    ns = [True] * n
+
+    for i in range(2, math.ceil(np.sqrt(n))):
+        if ns[i]:
+            j = pow(i, 2)
+
+            while j < n:
+                ns[j] = False
+                j = j + i
+
+    return [i for i,val in enumerate(ns) if val][2:]
+
+def corners(n):
+    if n == 1:
+        return [1]
+    
+    layer = list(range((n*2-3)**2+1, (n*2-1)**2+1))
+    cList = []
+    for i in range(4):
+        cList.append(layer[-1 - (2*n-2)*i])
+    
+    return cList
+
+def main():
+    print("Hello, this is Patrick")
+    t0 = time.time()
+
+    # primes = set(sieve(1000000000))
+    numberPrimes = 0
+    n = 2
+
+    while True:
+        cs = corners(n)
+        for c in cs:
+            if isprime(c):
+                numberPrimes += 1
+        if numberPrimes / ((n-1)*4 + 1) < 0.1:
+            print(n*2-1, time.time() - t0)
+            break
+        n += 1
+
+if __name__ == "__main__":
+    main()