feat: update leetcode solutions: No.0091. Decode Ways

Author: yanglbme

README.md

@@ -156,6 +156,7 @@
 - [接雨水](/solution/0000-0099/0042.Trapping%20Rain%20Water/README.md)
 - [最大子序和](/solution/0000-0099/0053.Maximum%20Subarray/README.md)
 - [礼物的最大价值](/lcof/面试题47.%20礼物的最大价值/README.md)
+- [解码方法](/solution/0000-0099/0091.Decode%20Ways/README.md)
 - [乘积最大子序列](/solution/0100-0199/0152.Maximum%20Product%20Subarray/README.md)
 - [打家劫舍](/solution/0100-0199/0198.House%20Robber/README.md)
 - [打家劫舍 II](/solution/0200-0299/0213.House%20Robber%20II/README.md)

README_EN.md

@@ -149,6 +149,7 @@ Complete solutions to [LeetCode](https://leetcode-cn.com/problemset/all/), [LCOF
 - [Climbing Stairs](/solution/0000-0099/0070.Climbing%20Stairs/README_EN.md)
 - [Trapping Rain Water](/solution/0000-0099/0042.Trapping%20Rain%20Water/README_EN.md)
 - [Maximum Subarray](/solution/0000-0099/0053.Maximum%20Subarray/README_EN.md)
+- [Decode Ways](/solution/0000-0099/0091.Decode%20Ways/README_EN.md)
 - [Maximum Product Subarray](/solution/0100-0199/0152.Maximum%20Product%20Subarray/README_EN.md)
 - [House Robber](/solution/0100-0199/0198.House%20Robber/README_EN.md)
 - [House Robber II](/solution/0200-0299/0213.House%20Robber%20II/README_EN.md)

solution/0000-0099/0091.Decode Ways/README.md

@@ -33,22 +33,100 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
+动态规划法。
+
+假设 `dp[i]` 表示字符串 s 的前 i 个字符 `s[1..i]` 的解码方法数。
+
+考虑最后一次解码中使用了 s 中的哪些字符：
+
+- 第一种情况是我们使用了一个字符，即 `s[i]` 进行解码，那么只要 `s[i]≠0`，它就可以被解码成 `A∼I` 中的某个字母。由于剩余的前 `i-1` 个字符的解码方法数为 `dp[i-1]`，所以 `dp[i] = dp[i-1]`。
+- 第二种情况是我们使用了两个字符，即 `s[i-1]` 和 `s[i]` 进行编码。与第一种情况类似，`s[i-1]` 不能等于 0，并且 `s[i-1]` 和 `s[i]` 组成的整数必须小于等于 26，这样它们就可以被解码成 `J∼Z` 中的某个字母。由于剩余的前 `i-2` 个字符的解码方法数为 `dp[i-2]`，所以 `dp[i] = dp[i-2]`。
+
+将上面的两种状态转移方程在对应的条件满足时进行累加，即可得到 `dp[i]`的值。在动态规划完成后，最终的答案即为 `dp[n]`。
+
+由于 `dp[i]` 的值仅与 `dp[i-1]` 和 `dp[i-2]` 有关，因此可以不定义 dp 数组，可以仅使用三个变量进行状态转移。
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```python
+class Solution:
+    def numDecodings(self, s: str) -> int:
+        n = len(s)
+        dp = [0] * (n + 1)
+        dp[0] = 1
+        for i in range(1, n + 1):
+            if s[i - 1] != '0':
+                dp[i] += dp[i - 1]
+            if i > 1 and s[i - 2] != '0' and (int(s[i - 2]) * 10 + int(s[i - 1]) <= 26):
+                dp[i] += dp[i - 2]
+        return dp[n]
+```
+
+优化空间：
 
+```python
+class Solution:
+    def numDecodings(self, s: str) -> int:
+        n = len(s)
+        a, b, c = 0, 1, 0
+        for i in range(1, n + 1):
+            c = 0
+            if s[i - 1] != '0':
+                c += b
+            if i > 1 and s[i - 2] != '0' and (int(s[i - 2]) * 10 + int(s[i - 1]) <= 26):
+                c += a
+            a, b = b, c
+        return c
 ```
 
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```java
+class Solution {
+    public int numDecodings(String s) {
+        int n = s.length();
+        int[] dp = new int[n + 1];
+        dp[0] = 1;
+        for (int i = 1; i <= n; ++i) {
+            if (s.charAt(i - 1) != '0') {
+                dp[i] += dp[i - 1];
+            }
+            if (i > 1 && s.charAt(i - 2) != '0' && ((s.charAt(i - 2) - '0') * 10 + s.charAt(i - 1) - '0') <= 26) {
+                dp[i] += dp[i - 2];
+            }
+        }
+        return dp[n];
+    }
+}
+```
+
+优化空间：
 
+```java
+class Solution {
+    public int numDecodings(String s) {
+        int n = s.length();
+        int a = 0, b = 1, c = 0;
+        for (int i = 1; i <= n; ++i) {
+            c = 0;
+            if (s.charAt(i - 1) != '0') {
+                c += b;
+            }
+            if (i > 1 && s.charAt(i - 2) != '0' && ((s.charAt(i - 2) - '0') * 10 + s.charAt(i - 1) - '0') <= 26) {
+                c += a;
+            }
+            a = b;
+            b = c;
+        }
+        return c;
+    }
+}
 ```
 
 ### **...**

solution/0000-0099/0091.Decode Ways/README_EN.md

@@ -48,14 +48,83 @@
 
 ### **Python3**
 
+Solution1:
+
 ```python
+class Solution:
+    def numDecodings(self, s: str) -> int:
+        n = len(s)
+        dp = [0] * (n + 1)
+        dp[0] = 1
+        for i in range(1, n + 1):
+            if s[i - 1] != '0':
+                dp[i] += dp[i - 1]
+            if i > 1 and s[i - 2] != '0' and (int(s[i - 2]) * 10 + int(s[i - 1]) <= 26):
+                dp[i] += dp[i - 2]
+        return dp[n]
+```
 
+Solution2:
+
+```python
+class Solution:
+    def numDecodings(self, s: str) -> int:
+        n = len(s)
+        a, b, c = 0, 1, 0
+        for i in range(1, n + 1):
+            c = 0
+            if s[i - 1] != '0':
+                c += b
+            if i > 1 and s[i - 2] != '0' and (int(s[i - 2]) * 10 + int(s[i - 1]) <= 26):
+                c += a
+            a, b = b, c
+        return c
 ```
 
 ### **Java**
 
+Solution1:
+
 ```java
+class Solution {
+    public int numDecodings(String s) {
+        int n = s.length();
+        int[] dp = new int[n + 1];
+        dp[0] = 1;
+        for (int i = 1; i <= n; ++i) {
+            if (s.charAt(i - 1) != '0') {
+                dp[i] += dp[i - 1];
+            }
+            if (i > 1 && s.charAt(i - 2) != '0' && ((s.charAt(i - 2) - '0') * 10 + s.charAt(i - 1) - '0') <= 26) {
+                dp[i] += dp[i - 2];
+            }
+        }
+        return dp[n];
+    }
+}
+```
 
+Solution2:
+
+```java
+class Solution {
+    public int numDecodings(String s) {
+        int n = s.length();
+        int a = 0, b = 1, c = 0;
+        for (int i = 1; i <= n; ++i) {
+            c = 0;
+            if (s.charAt(i - 1) != '0') {
+                c += b;
+            }
+            if (i > 1 && s.charAt(i - 2) != '0' && ((s.charAt(i - 2) - '0') * 10 + s.charAt(i - 1) - '0') <= 26) {
+                c += a;
+            }
+            a = b;
+            b = c;
+        }
+        return c;
+    }
+}
 ```
 
 ### **...**

solution/0000-0099/0091.Decode Ways/Solution.java

@@ -1,19 +1,18 @@
 class Solution {
     public int numDecodings(String s) {
-        int len = s.length();
-        if (len == 0) return 0;
-        int current = s.charAt(0) == '0' ? 0 : 1;
-        int last = 1;
-        for (int i = 1; i < len; i++) {
-            int tmp = current;
-            if(s.charAt(i) == '0'){
-                if(s.charAt(i-1) == '1' || s.charAt(i-1) == '2') current = last;
-                else return 0;
-            }else if(s.charAt(i-1) == '1' || s.charAt(i-1) == '2' && s.charAt(i) <= '6') {
-                current += last;
+        int n = s.length();
+        int a = 0, b = 1, c = 0;
+        for (int i = 1; i <= n; ++i) {
+            c = 0;
+            if (s.charAt(i - 1) != '0') {
+                c += b;
             }
-            last = tmp;
+            if (i > 1 && s.charAt(i - 2) != '0' && ((s.charAt(i - 2) - '0') * 10 + s.charAt(i - 1) - '0') <= 26) {
+                c += a;
+            }
+            a = b;
+            b = c;
         }
-        return current;
+        return c;
     }
 }

solution/0000-0099/0091.Decode Ways/Solution.py

@@ -0,0 +1,12 @@
+class Solution:
+    def numDecodings(self, s: str) -> int:
+        n = len(s)
+        a, b, c = 0, 1, 0
+        for i in range(1, n + 1):
+            c = 0
+            if s[i - 1] != '0':
+                c += b
+            if i > 1 and s[i - 2] != '0' and (int(s[i - 2]) * 10 + int(s[i - 1]) <= 26):
+                c += a
+            a, b = b, c
+        return c