memoize integer powers.

scratch/500/BigMultiply.java

@@ -3,6 +3,7 @@ import java.math.BigInteger;
 import java.util.List;
 import java.util.Map;
 import java.util.TreeMap;
+import java.util.HashMap;
 
 /**
  * Find the product of the first 500500 primes.
@@ -15,7 +16,7 @@ public class BigMultiply {
 	} 
 
 	public static void solve() {
-		int N1 = 500500;
+		int N1 = 100500;
 		int N2 = 500500507;
 		//int N2fac1 = 13;
 		//int N2fac2 = 38500039;
@@ -29,6 +30,11 @@ public class BigMultiply {
 		// This will store the number of times we have used each prime
 		TreeMap<Long,Integer> primeUsage = new TreeMap<Long,Integer>();
 
+		// This will memoize power of prime:
+		// each key is the prime, 
+		// each value is the prime to its power of occurrence
+		HashMap<Long,Long> primePower = new HashMap<Long,Long>();
+
 		BigInteger b = BigInteger.ONE;
 		BigInteger prime = BigInteger.ONE;
 
@@ -42,6 +48,9 @@ public class BigMultiply {
 			// - Multiply by a prime we have not used before
 			// - Multiply by a prime that we have used k times before, k+1 times
 			// Both of these will double the number of divisors.
+			if(i%1000==0) { 
+				System.out.println("On divisor 2^"+i);
+			}
 
 			// Get next prime
 			nextPrime = primesList.get(primeIndex);
@@ -51,7 +60,7 @@ public class BigMultiply {
 			boolean useOptionA = true;
 
 			for(Long primeSoFar : primeUsage.keySet()) { 
-				optionB = longpow( primeSoFar, primeUsage.get(primeSoFar)+1 );
+				optionB = primePower.get(primeSoFar);
 				//System.out.println("Checking option B: primeSoFar = "+primeSoFar+" current count = "+ (primeUsage.get(primeSoFar)) +" option B = "+optionB);
 				if(optionB<optionA) { 
 					// Use option B
@@ -61,6 +70,9 @@ public class BigMultiply {
 					//System.out.println("Incrementing value of prime "+primeSoFar+" by "+ (value+1) +" to "+ ((value+1)+value) );
 					value = value + (value+1);
 					primeUsage.put(primeSoFar,value);
+
+					// memoize the power we will see next time
+					primePower.put(primeSoFar, longpow(primeSoFar, value + (value+1) ) );
 					
 					// Multiply 
 					b = b.multiply( BigInteger.valueOf(optionB) ).mod(base);
@@ -74,6 +86,10 @@ public class BigMultiply {
 				primeUsage.put(optionA, new Integer(1));
 				//System.out.println("Initializing value of prime "+optionA+" to 1.");
 
+				// add a memoized version of what the power 
+				// will be next time (2)
+				primePower.put(optionA, optionA*optionA);
+
 				// Multiply 
 				b = b.multiply( BigInteger.valueOf(optionA) ).mod(base);
 				//System.out.println("A: Next factor is "+optionA);