Merge pull request #395 from FarhanKasmani/ExtraAlgortihms

Extra Algorithms added

Maths/BasicMaths.py

@@ -0,0 +1,70 @@
+import math
+
+def primeFactors(n):
+    pf = []
+    while n % 2 == 0:
+        pf.append(2)
+        n = int(n / 2)
+        
+    for i in range(3, int(math.sqrt(n))+1, 2):
+        while n % i == 0:
+            pf.append(i)
+            n = int(n / i)
+    
+    if n > 2:
+        pf.append(n)
+    
+    return pf
+
+def numberOfDivisors(n):
+    div = 1
+    
+    temp = 1
+    while n % 2 == 0:
+        temp += 1
+        n = int(n / 2)
+    div = div * (temp) 
+    
+    for i in range(3, int(math.sqrt(n))+1, 2):
+        temp = 1
+        while n % i == 0:
+            temp += 1
+            n = int(n / i)
+        div = div * (temp)
+    
+    return div
+
+def sumOfDivisors(n):
+    s = 1
+    
+    temp = 1
+    while n % 2 == 0:
+        temp += 1
+        n = int(n / 2)
+    if temp > 1:
+        s *= (2**temp - 1) / (2 - 1) 
+    
+    for i in range(3, int(math.sqrt(n))+1, 2):
+        temp = 1
+        while n % i == 0:
+            temp += 1
+            n = int(n / i)
+        if temp > 1:
+            s *= (i**temp - 1) / (i - 1)
+    
+    return s
+
+def eulerPhi(n):
+    l = primeFactors(n)
+    l = set(l)
+    s = n
+    for x in l:
+        s *= (x - 1)/x 
+    return s   
+
+print(primeFactors(100))
+print(numberOfDivisors(100))
+print(sumOfDivisors(100))
+print(eulerPhi(100))
+    
+    

Maths/SegmentedSieve.py

@@ -0,0 +1,46 @@
+import math
+
+def sieve(n):
+    in_prime = []
+    start = 2
+    end   = int(math.sqrt(n)) # Size of every segment
+    temp = [True] * (end + 1)
+    prime = []
+    
+    while(start <= end):
+        if temp[start] == True:
+            in_prime.append(start)
+            for i in range(start*start, end+1, start):
+                if temp[i] == True:
+                    temp[i] = False
+        start += 1
+    prime += in_prime
+    
+    low = end + 1
+    high = low + end - 1
+    if high > n:
+        high = n
+    
+    while(low <= n):
+        temp = [True] * (high-low+1)
+        for each in in_prime:
+            
+            t = math.floor(low / each) * each
+            if t < low:
+                t += each
+            
+            for j in range(t, high+1, each):
+                temp[j - low] = False
+                
+        for j in range(len(temp)):
+            if temp[j] == True:
+                prime.append(j+low)
+        
+        low = high + 1
+        high = low + end - 1
+        if high > n:
+            high = n
+            
+    return prime
+
+print(sieve(10**6))

Maths/SieveOfEratosthenes.py

@@ -0,0 +1,24 @@
+import math
+n = int(input("Enter n: "))
+
+def sieve(n):
+    l = [True] * (n+1)
+    prime = []
+    start = 2
+    end   = int(math.sqrt(n))
+    while(start <= end):
+        if l[start] == True:
+            prime.append(start)
+            for i in range(start*start, n+1, start):
+                if l[i] == True:
+                    l[i] = False
+        start += 1
+    
+    for j in range(end+1,n+1):
+        if l[j] == True:
+            prime.append(j)
+    
+    return prime
+
+print(sieve(n))
+