2. climbing stairs

Author: whewchews

climbing-stairs/whewchews.ts

@@ -0,0 +1,54 @@
+function climbStairs(n: number): number {
+  /*
+    * 아이디어 
+    * 층수 제한: 1 <= n <= 45
+    * 1 or 2 step 만 올라갈 수 있음
+    
+    * 1 -> [1]
+    * 2 -> [1,1]              [2]                                     
+    * 3 -> [1,1,1]            [2,1] [1,2]                             
+    * 4 -> [1,1,1,1]          [2,1,1] [1,2,1] [1,1,2]                      [2,2]     
+    * 5 -> [1,1,1,1,1]        [2,1,1,1] [1,2,1,1] [1,1,2,1] [1,1,1,2]      [2,2,1], [1,2,2], [2,1,2]
+    * 6 -> [1,1,1,1,1,1]      [2,1,1,1,1] [...] [1,1,1,1,2]                [2,2,1,1], [2,1,2,1], [2,1,1,2] [1,1,2,2], [1,2,1,2], [1,2,2,1]
+    =>     (1-n, 2-0) n가지   (1:n-2, 2:1) (n-1)*(n-2)/(n-2) 가지          (1: n-4, 2: n/2) (n-2)*(n-3)/2 가지   
+    */
+
+  // # solution 1
+  // TC: O(N)
+  // SC: O(N)
+  // const stair = {1: 1, 2:2}
+  // for(let i = 3; i<=n; i++){
+  //     stair[i] = stair[i-1] + stair[i-2]
+  // }
+
+  // # solution 2
+  // TC: O(N)
+  // SC: O(1)
+  //     if(n < 3) return n
+  //     let curr = 2
+  //     let prev = 1
+
+  //     for(let i=0; i<n-2; i++){
+  //         const next = prev + curr;
+  //         prev = curr;
+  //         curr = next;
+  //     }
+
+  //     return curr
+
+  // # Solution 3: 재귀
+  // TC: O(N)
+  // SC: O(N)
+  const memo = { 1: 1, 2: 2 };
+  function calculateClimbingWay(n, memo) {
+    if (!(n in memo)) {
+      if (n < 3) {
+        return n;
+      }
+      memo[n] =
+        calculateClimbingWay(n - 1, memo) + calculateClimbingWay(n - 2, memo);
+    }
+    return memo[n];
+  }
+  return calculateClimbingWay(n, memo);
+}