8.01 Triple step

chapter08/8.01 - Triple Step/tripleStep.js

@@ -1,20 +1,65 @@
-var numWays = function(N) {
-  var answer = 0;
-  var recurse = function(number) {
-    if (number === 0) {
-      answer++;
-    } else if (number > 0) {
-      recurse(number - 1);
-      recurse(number - 2);
-      recurse(number - 3);
-    }
-  };
-  recurse(N);
-  return answer;
-};
+/*
+Recursion and Dynamic Programming (4 steps)
+1. Start with the recursive backtracking solution (Brute Force)
+2. Optimize by using a memoization table (top-down dynamic programming)
+3. Remove the need for recursion (bottom-up dynamic programming)
+4. Apply final tricks to reduce the time / memory complexity
+*/
+
+// Recursive BackTracking 
+// Time & Space O(n!)
+var tripleStep = function(n, res=0) {
+  if (n < 0) return 0
+  if (n === 0) return 1 
+  return tripleStep(n - 1) + tripleStep(n - 2) + tripleStep(n - 3)
+}
+
+// Top Down Memoization
+// Time & Space O(n)
+var tripleStep = function(n, i=3, memo = [1, 1, 2, 4]) {
+  if (n < 0) return memo[0]
+  if (n === 1) return memo[n]
+  if (i > n ) return memo[memo.length - 1]
+
+  memo[i] = memo[i - 1] + memo[i - 2] + memo[i - 3]
+  return tripleStep(n, i+1, memo)
+}
+
+// Bottom Up memoization
+// Time & Space O(n) 
+var tripleStep = function(n, memo=[1,1,2,4]) {
+  for (let i = 3; i <= n; i++) {
+    memo[i] = memo[i - 1] + memo[i - 2] + memo[i - 3]
+  }
+
+  return memo[memo.length - 1]
+}
+
+// Constant Space 
+// Time O(n) & Space O(1)
+var tripleStep = function(n) {
+  if (n <= 0) return 0
+  if (n === 1) return 1
+  if (n === 2) return 2
+
+  let a = 1
+  let b = 1
+  let c = 2
+
+  for (let i = 3; i < n; i++) {
+    let d = a + b + c
+    a = b
+    b = c
+    c = d
+  }
+  return a + b + c
+}
 
 /* TEST */
+console.log(tripleStep(1), 1);
+console.log(tripleStep(2), 2);
+console.log(tripleStep(3), 4);
+console.log(tripleStep(5), 13)
+console.log(tripleStep(7), 44)
+console.log(tripleStep(10), 274);
 
-console.log(numWays(1), 1);
-console.log(numWays(2), 2);
-console.log(numWays(3), 4);