8.01 Triple step

chapter08/8.01 - Triple Step/tripleStepv2.js

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+/*
+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!)
+function tripleStep(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)
+function tripleStep(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)
+function tripleStep(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)
+function tripleStep(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);