welcome dp

DP/FibonacciClimbingStairs.java

@@ -0,0 +1,77 @@
+public class Main {
+
+    static class FibonacciClimbingStairs {
+        static int[] memo = new int[46];
+
+        public int climbStairs(int n) {
+            return climbTabularizedSpaceOptimized(n, 2);
+        }
+
+        private int climbMemoized(int n, int k) {
+            if (n == 0) return 1;
+
+            if (memo[n] != 0) return memo[n];
+
+            int ways = 0;
+
+            for (int jump = 1; jump <= k; jump++) {
+                if (n - jump >= 0) {
+                    ways += climbMemoized(n - jump, k);
+                }
+            }
+
+            memo[n] = ways;
+            return ways;
+        }
+
+        private int climbTabularized(int n, int k) {
+            int[] tab = new int[n + 1];
+            tab[0] = 1;
+
+            for (int i = 1; i <= n; i++) {
+                for (int j = 1; j <= k; j++) {
+                    if (i - j >= 0) {
+                        tab[i] += tab[i - j];
+                    }
+                }
+            }
+            return tab[n];
+        }
+
+        private int climbTabularizedSpaceOptimized(int n, int k) {
+            int[] dp = new int[k];
+            dp[0] = 1;
+
+            for (int i = 1; i <= n; i++) {
+                int sum = 0;
+
+                for (int j = 1; j <= k; j++) {
+                    if (i - j >= 0) {
+                        sum += dp[(i - j) % k];
+                    }
+                }
+
+                dp[i % k] = sum;
+            }
+
+            return dp[n % k];
+        }
+    }
+
+    public static void main(String[] args) {
+        FibonacciClimbingStairs sol = new FibonacciClimbingStairs();
+
+        // basic tests
+        for (int n = 0; n <= 10; n++) {
+            System.out.println("n = " + n + " -> " + sol.climbStairs(n));
+        }
+
+        // expected:
+        // 0 -> 1
+        // 1 -> 1
+        // 2 -> 2
+        // 3 -> 3
+        // 4 -> 5
+        // 5 -> 8
+    }
+}