Add climbing-stairs solution

Author: Jeehay28

climbing-stairs/Jeehay28.js

@@ -0,0 +1,40 @@
+/**
+ * @param {number} n
+ * @return {number}
+ */
+
+// Time Complexity: O(n^2)
+// First O(n): From the loop that runs up to n times.
+// Second O(n): From the factorial calculations in each iteration.
+// overall time complexity is O(n^2).
+
+// Space Complexity: O(n)
+// the factorial function's recursion has a space complexity of O(n)
+// O(1) means constant space complexity. It implies that the amount of memory used does not grow with the size of the input.
+// The other variables in the function only use a constant amount of space, resulting in an O(1) space usage.
+
+var climbStairs = function (n) {
+  let ways = 0;
+
+  let maxStepTwo = Math.floor(n / 2);
+
+  const factorial = (num) => {
+    if (num === 0 || num === 1) {
+      return 1;
+    }
+
+    for (let i = 2; i <= num; i++) {
+      return num * factorial(num - 1);
+    }
+  };
+
+  for (let i = 0; i <= maxStepTwo; i++) {
+    const stepTwo = i;
+    const stepOne = n - 2 * i;
+    const steps = stepTwo + stepOne;
+
+    ways += factorial(steps) / (factorial(stepTwo) * factorial(stepOne));
+  }
+
+  return ways;
+};