chore(CPlusPlus): add binary power on maths algorithm (MakeContributi…

…ons#810)

Co-authored-by: angshudas <[email protected]>
Co-authored-by: Mohnish Deshpande <[email protected]>

algorithms/CPlusPlus/Maths/binary-power.cpp

@@ -0,0 +1,56 @@
+#include<iostream>
+using namespace std;
+
+/*
+The idea is to half the power on every iteration
+Computes the power in log(n) operations
+
+On every iteration:
+Square the base, half the power
+
+Special case - if power is odd:
+Multiply the ans with a
+Because the ODD-NUMBER % 2 == 1
+
+Note: There will always be one iteration where power is odd
+*/
+
+long binpow(long a, long b){
+	long ans=1;
+	// while b is greater than zero, we continue the binary exponentiation
+	while(b>0){
+		// if b is odd, multiply result with base 
+		if(b&1)
+			ans *= a;
+		// square the base
+		a *= a;
+		// half the power
+		b /= 2;
+	}
+	return ans;
+}
+
+// source: @angshudas
+long binpow_rec(long a, long b){
+	// a^0 = 1 [for any a]
+	if(b==0)
+		return 1;
+	// recursive call for a^(b/2)
+	long ans = binpow_rec(a, b/2);
+	// square the result
+	ans *= ans;
+	// if b is odd, times by a
+	// to cover for 
+	if(b&1)
+		ans *= a;
+
+	return ans;
+}
+
+int main(){
+	long base, power;
+	cout<<"Enter the base and power: "<<endl;
+	cin>>base>>power;
+	cout<<base<<" ^ "<<power<<" = "<<binpow(base, power)<<endl;
+	return 0;
+}

algorithms/CPlusPlus/README.md

@@ -169,6 +169,7 @@
 - [Power of two](Maths/power-of-two.cpp)
 - [Small numbers](Maths/small-numbers.cpp)
 - [Segmented Sieve](Maths/segmented-sieve-range.cpp)
+- [Binary Power](Maths/binary-power.cpp)
 
 # Recursion