count total possible board path using recursive & iterative DP approach

Author: NirmalSilwal

Interview Prep/section19_DynamicProgramming/CountBoardPathDP.java

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+package section19_DynamicProgramming;
+
+public class CountBoardPathDP {
+
+	public static void main(String[] args) {
+
+		int n = 10;
+		System.out.println(countBoardPath(n, 0, new int[n + 1])); // 492
+		System.out.println(countBoardPathIterative(n)); // 492
+	}
+
+	// O(N) Time - recursive storage
+	public static int countBoardPath(int end, int current, int[] storage) {
+		if (current == end)
+			return 1;
+		if (current > end)
+			return 0;
+
+		if (storage[current] != 0)
+			return storage[current];
+
+		int count = 0;
+		for (int dice = 1; dice <= 6; dice++) {
+			count = count + countBoardPath(end, current + dice, storage);
+		}
+		storage[current] = count;
+
+		return count;
+	}
+
+	// iterative storage
+	// O(6N) ~ O(N) Time | O(N) Space
+	public static int countBoardPathIterative(int n) {
+		int[] storage = new int[n + 1];
+
+		// seed
+		storage[n] = 1;
+
+		for (int index = n - 1; index >= 0; index--) {
+			int currSum = 0;
+			for (int dice = index + 1; dice <= index + 6 && dice <= n; dice++) {
+				currSum = currSum + storage[dice];
+			}
+			storage[index] = currSum;
+		}
+
+		return storage[0];
+	}
+}