Euler50

project_euler/problem_50/sol1.py

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+
+
+
+#fills the primes dict with prime numbers <=u 
+#        primes: Global Dictionary To fill     
+#       l: (optional) Starting value    
+def prma(u:int,primes:dict, l:int=2)->None:
+    """
+    >>> primes = {}
+    >>> prma(10,primes)
+    >>> primes
+    {2: 1, 3: 3, 5: 3, 7: 4}
+    """
+
+    if len(primes) <= 1:
+        primes[2] = 1
+        primes[3] = 2
+
+    psrt = 2
+    while l <= u:                               # while the number (l) is less than(or equal to ) the given
+
+        if l > psrt**2:                         # if l exceeds the previous val of psrt
+
+            psrt = (l**0.5)                     # psrt = sqrt(l)
+
+        for i in primes:                          #for the primes currently in primes
+
+            if i > psrt:                        # You need to only check till the sqrt(l) to see if it is a prime..
+                primes[l] = len(primes)+1                 #if it exceeds the value then it must be prime..
+                break
+
+            if l % i == 0:                      # if it is divisible.. it jumps to the next number for l i.e: l++
+                break
+        l += 1
+
+
+
+
+def solution(MX:int = 1000000)->int:
+    """
+    >>> solution()
+    997651
+    >>> solution(1000)  #lessthan 1000
+    953
+    """
+    primes= {}      # using a dict To maintain order and o(1) searching..
+    prma(MX,primes)    #fill dict with primes < MX
+    primes_tuple = tuple(primes) 
+    running_sum = 0
+    count=0
+    while running_sum<MX:
+        running_sum+=primes_tuple[count]
+        count+=1
+    count-=1                    #deleting off the last prime..
+    running_sum-=primes_tuple[count] 
+
+
+
+    #counting from left 
+    si = 0
+    ei = count-1
+    running_sum1 = running_sum
+    while not running_sum1 in primes and ei>=0:
+        running_sum1-=primes_tuple[ei]
+        ei-=1
+    countL = ei-si+1
+    # print(countL,running_sum1,primes_tuple[0:ei])    #debug
+
+
+
+    # counting from right
+    ei = count-1
+    running_sum2 = running_sum
+    while not running_sum2 in primes and si<=ei:
+        running_sum2-=primes_tuple[si]
+        si+=1
+    countR = ei-si+1
+    # print(countR,running_sum2,primes_tuple[0:count]) #debug
+
+    return running_sum1 if countL>countR else running_sum2
+
+if __name__ == "__main__":
+    print(solution())
+