Added Fast Power in Number Theory

NumberTheory/FastPower.cpp

@@ -0,0 +1,47 @@
+/*
+<Fast Power>
+--------------
+Fast Power is an optimized algorithm to compute exponentiation in a short time.
+
+
+Time Complexity
+-----------------
+O(log(N)) where N is the power the number is raised to.
+
+Space Complexity
+------------------
+O(log(N)) where N is the power the number is raised to.
+
+*/
+#include <iostream>
+
+using namespace std;
+typedef long long ll;
+
+//Function that returns x raised to the power of y
+ll fastPower (ll x,ll y)
+{
+    if (y==0) return 1;
+
+    if (y%2==1)
+    {
+        return fastPower(x,y-1) * x;
+    }
+    else
+    {
+        x = fastPower(x,y/2);
+        return (x*x);
+    }
+}
+
+//Testing the function
+int main()
+{
+    int base,power;
+    cout<<"Enter the number and the power it's raised to:"<<endl;
+
+    cin>>base>>power;
+
+    cout<<fastPower(base,power);
+    return 0;
+}