Added Fast Power in Number Theory

NumberTheory/FastPower.cpp

@@ -0,0 +1,54 @@
+/*
+    Fast Power
+    ----------------
+    Fast Power is an optimized algorithm to compute exponentiation in a short time.
+    It calculates the power by squaring, meaning we divide the power by 2 on each step and multiply
+    the base by itself. We keep doing this until the power is 0 where we return 1.
+
+
+    Time Complexity
+    -----------------
+    O(log(N)) where N is the exponent.
+
+    Space Complexity
+    -----------------
+    O(log(N)) where N is the exponent.
+
+*/
+#include <iostream>
+
+using namespace std;
+typedef unsigned long long ull;
+
+//Function that returns base raised to the exponent
+ull fast_power (ull base,ull exponent)
+{
+    if (exponent==0) return 1;
+
+    if (exponent%2==1)  //If the power is odd
+    {
+        return fast_power(base,exponent-1) * base;
+    }
+    else    //If the power is even
+    {
+        base = fast_power(base,exponent/2);
+        return (base*base);
+    }
+}
+
+#ifndef FAST_POWER_TEST
+
+int main()
+{
+    //Testing the function
+    int base,exponent;
+    cout<<"Enter the number and its exponent:"<<endl;
+
+    cin>>base>>exponent;
+
+    cout<<endl<<fast_power(base,exponent)<<endl;
+
+    return 0;
+}
+
+#endif

Test/NumberTheory/fastPower.test.cpp

@@ -0,0 +1,24 @@
+#define FAST_POWER_TEST
+#define CATCH_CONFIG_MAIN
+
+#include "../catch.hpp"
+#include "../../NumberTheory/FastPower.cpp"
+
+
+TEST_CASE("Base cases", "[fast_power]") {
+    REQUIRE(fast_power(2,2) == 4);
+    REQUIRE(fast_power(2,4) == 16);
+}
+
+TEST_CASE("Normal cases", "[fast_power]") {
+    REQUIRE(fast_power(3,4) == 81);
+    REQUIRE(fast_power(7,9) == 40353607);
+    REQUIRE(fast_power(15,10) == 576650390625);
+}
+
+TEST_CASE("Overflow cases", "[fast_power]") {
+    REQUIRE(fast_power(2,100) == 0);
+    REQUIRE(fast_power(10,99) == 0);
+}
+
+#undef FAST_POWER_TEST