added very easy, short, super fast method

chapter-8-recursion-and-Dynamic-Programming/8-5-Recursive-Multiply.cpp

@@ -1,40 +1,27 @@
+/*
+* Author: Madhur Chauhan
+* A simple log(min(a,b)) solution, but does not take more than 96 instructions
+* Similar to binary exponentiation by exploiting bit pattern of multiplicand
+*/
 #include <vector>
 #include <iostream>
 using namespace std;
 
-int multiply(int a, int b, vector<int>& dp)
-{
-	int bigger = a < b ? b:a;
-	int smaller = a <b ? a:b;
-
-	if (smaller==0)
-		return 0;
-
-	if (smaller==1)
-		return bigger;
-
-	if (dp[smaller]!=-1)
-		return dp[smaller];
-
-	int s = smaller >> 1; //divide by 2
-
-	int side1 = multiply(s,bigger,dp);
-	int side2 = 0;
-	if (smaller%2)
-		side2 = side1+bigger;
-	else
-	    side2 = side1;
-
-	dp[smaller] = side2 +side1;
-	return side1+side2;
-}
+auto multiply=[](int a, int b){
+  int big=a>b?a:b, small=a<b?a:b, res=0;
+  while(small){
+    if(small&1) res+=big;
+    big<<=1, small>>=1;
+  }
+  return res;
+};
 
 int main()
 {	
 	int m = 7, n = 6;
 	int smaller = m>n?n:m;
 	int bigger = m>n?m:n;
-	std::vector<int> dp(smaller+1,-1);
+
 	cout<<multiply(smaller,bigger,dp)<<endl;
 	return 0;
 }