Add files via upload

Author: assassint2017

Climbing Stairs/Climbing_Stairs.cpp

@@ -0,0 +1,76 @@
+// 最基础版，自顶向下的动态规划
+
+// 超时了 21 / 45 test cases passed.
+class Solution 
+{
+public:
+    int climbStairs(int n) 
+    {
+        if (n <= 2)    
+            return n;
+        else
+            return climbStairs(n - 1) + climbStairs(n - 2);
+    }
+};
+
+// 第二个版本，自顶向下的动态规划+备忘录，可以看到加速效果非常明显
+// Runtime: 0 ms, faster than 100.00% of C++ online submissions for Climbing Stairs.
+// Memory Usage: 9.1 MB, less than 5.02% of C++ online submissions for Climbing Stairs.
+class Solution 
+{
+public:
+    int climbStairs(int n) 
+    {
+        unordered_map<int, int> hashmap;
+        return n <= 2 ? n : dp(hashmap, n);
+    }
+private:
+    int dp(unordered_map<int, int>& hashmap, int n)
+    {
+        if (hashmap.find(n) == hashmap.end())
+        {
+            int res = n <= 2 ? n : dp(hashmap, n - 1) + dp(hashmap, n - 2);
+            hashmap.insert(pair<int, int>(n, res));
+        }
+        return hashmap.at(n);
+    }
+};
+
+// 第三个版本，自底向上的动态规划，使用递推而不是递归
+// Runtime: 0 ms, faster than 100.00% of C++ online submissions for Climbing Stairs.
+// Memory Usage: 8.5 MB, less than 23.91% of C++ online submissions for Climbing Stairs.
+class Solution 
+{
+public:
+    int climbStairs(int n) 
+    {
+        if (n <= 2) return n;
+
+        vector<int> res(n);
+        res[0] = 1; res[1] = 2;
+        for (int i = 2; i < n; ++i)
+            res[i] = res[i - 1] + res[i - 2];
+        
+        return res[n];
+    }
+};
+
+
+// 第四个版本，自底向上的动态规划，常数级的空间复杂度
+class Solution 
+{
+public:
+    int climbStairs(int n) 
+    {
+        if (n <= 2) return n;
+
+        int res, lres = 2, llres = 1;
+        for (int i = 2; i < n; ++i)
+        {
+            res = lres + llres;
+            llres = lres;
+            lres = res;
+        }
+        return res; 
+    }
+};