8.11: Removing assumption that final denomination is a penny and othe…

…r code cleanup

Java/Ch 08. Recursion and Dynamic Programming/Q8_11_Coins/Question.java

@@ -1,24 +1,27 @@
 package Q8_11_Coins;
 
 public class Question {	
-	public static int makeChange(int amount, int[] denoms, int index) {
-		if (index >= denoms.length - 1) return 1; // one denom remaining -> one way to do it
-		int denomAmount = denoms[index];
+	public static int makeChangeHelper(int total, int[] denoms, int index) {
+		int coin = denoms[index];
+		if (index == denoms.length - 1) { // One denom left, either you can do it or not
+			int remaining = total % coin; 
+			return remaining == 0 ? 1 : 0;
+		}
 		int ways = 0;
-		for (int i = 0; i * denomAmount <= amount; i++) {
-			int amountRemaining = amount - i * denomAmount;
-			ways += makeChange(amountRemaining, denoms, index + 1); // go to next denom
+		/* Try 1 coin, then 2 coins, 3 three, ... (recursing each time on rest). */
+		for (int amount = 0; amount <= total; amount += coin) { 
+			ways += makeChangeHelper(total - amount, denoms, index + 1); // go to next denom
 		}
 		return ways;
 	}
 
 	public static int makeChange(int amount, int[] denoms) {
-		return makeChange(amount, denoms, 0);
+		return makeChangeHelper(amount, denoms, 0);
 	}
 
 	public static void main(String[] args) {
 		int[] denoms = {25, 10, 5, 1};
-		int ways = makeChange(300322, denoms);
+		int ways = makeChange(10, denoms);
 		System.out.println(ways);
 	}
 

Java/Ch 08. Recursion and Dynamic Programming/Q8_11_Coins/QuestionB.java

@@ -4,28 +4,35 @@ public class QuestionB {
 
 	public static int makeChange(int n, int[] denoms) {
 		int[][] map = new int[n + 1][denoms.length];
-		return makeChange(n, denoms, 0, map);
+		return makeChangeHelper(n, denoms, 0, map);
 	}
 
-	public static int makeChange(int amount, int[] denoms, int index, int[][] map) {
-		if (map[amount][index] > 0) { // retrieve value
-			return map[amount][index];
+	public static int makeChangeHelper(int total, int[] denoms, int index, int[][] map) {
+		/* Check cache for prior result. */
+		if (map[total][index] > 0) { // retrieve value
+			return map[total][index];
 		}
-		if (index >= denoms.length - 1) return 1; // one denom remaining -> one way to do it
-		int denomAmount = denoms[index];
-		int ways = 0;
-		for (int i = 0; i * denomAmount <= amount; i++) {
-			// go to next denom, assuming i coins of denomAmount
-			int amountRemaining = amount - i * denomAmount;
-			ways += makeChange(amountRemaining, denoms, index + 1, map);
+
+		int coin = denoms[index];
+		if (index == denoms.length - 1) {
+			int remaining = total % coin; 
+			return remaining == 0 ? 1 : 0;
 		}
-		map[amount][index] = ways;
-		return ways;
+		int numberOfWays = 0;
+		/* Try 1 coin, then 2 coins, 3 three, ... (recursing each time on rest). */
+		for (int amount = 0; amount <= total; amount += coin) { 
+			numberOfWays += makeChangeHelper(total - amount, denoms, index + 1, map); // go to next denom
+		}
+
+		/* Update cache with current result. */
+		map[total][index] = numberOfWays;
+
+		return numberOfWays;
 	}	
 
 	public static void main(String[] args) {
 		int[] denoms = {25, 10, 5, 1};
-		int ways = makeChange(100000, denoms);
+		int ways = makeChange(10, denoms);
 		System.out.println(ways);
 	}