tripleStep Backtracking, Top Down and Bottom up memoization implement…

…ation

chapter08/8.01 - Triple Step/tripleStep.js

@@ -1,4 +1,22 @@
-var numWays = function(N) {
+/*
+Recursion and Dynamic Programming (4 steps)
+1. Start with the recursive backtracking solution 
+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
+*/
+
+/*
+Triple Step: 
+A child is running up a staircase with n steps and 
+can hop either 1 step, 2 steps, or 3 steps at a time. 
+
+Implement a method to count how many possible ways 
+the child can run up the stairs.
+ */
+
+
+var numWays = function(N) { 
   var answer = 0;
   var recurse = function(number) {
     if (number === 0) {
@@ -13,8 +31,51 @@ var numWays = function(N) {
   return answer;
 };
 
+// Recursive BackTracking 
+// Time & Space O(n!)
+/*
+var numWays = function(n, res=0) {
+  if (n < 0) return 0
+  if (n === 0)  {
+    res++
+    return res
+  }
+  return numWays(n - 1) + numWays(n - 2) + numWays(n - 3)
+}
+*/
+
+// Top Down Memoization
+// Time & Space O(n)
+/*
+var numWays = 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 numWays(n, i+1, memo)
+}
+*/
+
+// Bottom Up memoization
+// Time & Space O(n) 
+/*
+var numWays = 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]
+}
+*/
+
+
 /* TEST */
 
 console.log(numWays(1), 1);
 console.log(numWays(2), 2);
 console.log(numWays(3), 4);
+console.log(numWays(5), 13)
+console.log(numWays(7), 44)
+console.log(numWays(10), 274);
+