first commit

util/python/sieve.py

@@ -0,0 +1,78 @@
+from math import sqrt, floor
+
+class sieve:
+    
+    def __init__(self):
+        self.sieve = [False]
+        self._length = 1
+        self._target = 1
+
+    def run(self, n):
+        self._target = n
+        self._elongate()
+    
+    def get(self, n):
+        if n > self._length:
+            self.run(n)
+        return self.sieve[n-1]
+    
+    def _elongate(self):
+        length = self._length
+        target = self._target
+        diff = target - length
+        if diff > 0:
+            self.sieve += [True for _ in range(diff)]
+            for i in range(floor(sqrt(target))):
+                if self.sieve[i]:
+                    _floor = length//(i+1)
+                    _ceil = target//(i+1)
+                    for j in range(_floor, _ceil):
+                        actual = (i+1)*(j+1)-1
+                        if actual > i+1:
+                            self.sieve[actual] = False
+            self._length = target
+
+class extended_sieve:
+
+    def __init__(self):
+        self.sieve = [[False, 1, []]]
+        self._length = 1
+        self._target = 1
+        self.prerun_step = 1000
+
+    def run(self, n):
+        self._target = n
+        self._elongate()
+    
+    def get(self, n):
+        if n > self._length:
+            self.run(n+self.prerun_step)
+        prime_decomp = {}
+        for e in self.sieve[n-1][2]:
+            if e in list(prime_decomp.keys()):
+                prime_decomp[e] += 1
+            else:
+                prime_decomp[e] = 1
+        return [self.sieve[n-1][0], prime_decomp]
+    
+    def _elongate(self):
+        length = self._length
+        target = self._target
+        diff = target - length
+        if diff > 0:
+            self.sieve += [[True, length+i+1, []] for i in range(diff)]
+            for i in range(target):
+                if self.sieve[i][0]:
+                    if i+1 > length:
+                        self.sieve[i][2] += [i+1]
+                    _floor = length//(i+1)
+                    _ceil = target//(i+1)
+                    for j in range(_floor, _ceil):
+                        actual = (i+1)*(j+1)-1
+                        if actual > i+1:
+                            old_entry = self.sieve[actual]
+                            self.sieve[actual] = [False, old_entry[1]//(i+1), old_entry[2]+[i+1]]
+                elif self.sieve[i][1] != 1:
+                        old_entry = self.sieve[i]
+                        self.sieve[i] = [False, 1, old_entry[2]+self.sieve[old_entry[1]-1][2]]
+            self._length = target