Update 0070.爬楼梯.md

problems/0070.爬楼梯.md

@@ -251,32 +251,66 @@ class Solution {
 ```
 
 ### Python
-
+动态规划（版本一）
 ```python
 # 空间复杂度为O(n)版本
 class Solution:
     def climbStairs(self, n: int) -> int:
-        # dp[i] 为第 i 阶楼梯有多少种方法爬到楼顶
-        dp = [0]*(n+1)
-        dp[0] = 1
+        if n <= 1:
+            return n
+        
+        dp = [0] * (n + 1)
         dp[1] = 1
-        for i in range(2, n+1):
-            dp[i] = dp[i-1] + dp[i-2]
+        dp[2] = 2
+        
+        for i in range(3, n + 1):
+            dp[i] = dp[i - 1] + dp[i - 2]
+        
         return dp[n]
 
+```
+动态规划（版本二）
+```python
+
+# 空间复杂度为O(3)版本
+class Solution:
+    def climbStairs(self, n: int) -> int:
+        if n <= 1:
+            return n
+        
+        dp = [0] * 3
+        dp[1] = 1
+        dp[2] = 2
+        
+        for i in range(3, n + 1):
+            total = dp[1] + dp[2]
+            dp[1] = dp[2]
+            dp[2] = total
+        
+        return dp[2]
+
+```
+动态规划（版本三）
+```python
+
 # 空间复杂度为O(1)版本
 class Solution:
     def climbStairs(self, n: int) -> int:
-        dp = [0]*(n+1)
-        dp[0] = 1
-        dp[1] = 1
-        for i in range(2,n+1):
-            tmp = dp[0] + dp[1]
-            dp[0] = dp[1]
-            dp[1] = tmp
-        return dp[1]
-```
+        if n <= 1:
+            return n
+        
+        prev1 = 1
+        prev2 = 2
+        
+        for i in range(3, n + 1):
+            total = prev1 + prev2
+            prev1 = prev2
+            prev2 = total
+        
+        return prev2
 
+
+```
 ### Go
 ```Go
 func climbStairs(n int) int {