feat: add solutions to lc problem: No.0248

No.0248.Strobogrammatic Number III

Author: yanglbme

solution/0200-0299/0247.Strobogrammatic Number II/README.md

@@ -51,7 +51,9 @@
 
 最终，我们将所有长度为 $n$ 的中心对称数返回即可。
 
-时间复杂度为 $O(4\times 2^ n)$。
+时间复杂度为 $O(2^{n+2})$。
+
+相似题目：[248. 中心对称数 III](/solution/0200-0299/0248.Strobogrammatic%20Number%20III/README.md)
 
 <!-- tabs:start -->
 

solution/0200-0299/0248.Strobogrammatic Number III/README.md

@@ -43,22 +43,180 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
+**方法一：递归**
+
+若长度为 $1$，则中心对称数只有 $0, 1, 8$；若长度为 $2$，则中心对称数只有 $11, 69, 88, 96$。
+
+我们设计递归函数 $dfs(u)$，其返回长度为 $u$ 的中心对称数。
+
+若 $u$ 为 $0$，返回包含一个空串的列表，即 `[""]`；若 $u$ 为 $1$，返回列表 `["0", "1", "8"]`。
+
+若 $u$ 大于 $1$，我们对长度为 $u - 2$ 的所有中心对称数进行遍历，对于每个中心对称数 $v$，在其左右两侧分别添加 $1, 8, 6, 9$，即可得到长度为 $u$ 的中心对称数。
+
+注意，如果 $u\neq n$，我们还可以在中心对称数的左右两侧分别添加 $0$。
+
+设 $low$ 和 $high$ 的长度分别为 $a$ 和 $b$。
+
+接下来，我们在 $[a,..b]$ 范围内遍历所有长度，对于每个长度 $n$，我们获取所有中心对称数 $dfs(n)$，然后判断是否在 $[low, high]$ 范围内，若在，答案加一。
+
+时间复杂度为 $O(2^{n+2}\times \log n)$。
+
+相似题目：[247. 中心对称数 II](/solution/0200-0299/0247.Strobogrammatic%20Number%20II/README.md)
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```python
-
+class Solution:
+    def strobogrammaticInRange(self, low: str, high: str) -> int:
+        def dfs(u):
+            if u == 0:
+                return ['']
+            if u == 1:
+                return ['0', '1', '8']
+            ans = []
+            for v in dfs(u - 2):
+                for l, r in ('11', '88', '69', '96'):
+                    ans.append(l + v + r)
+                if u != n:
+                    ans.append('0' + v + '0')
+            return ans
+
+        a, b = len(low), len(high)
+        low, high = int(low), int(high)
+        ans = 0
+        for n in range(a, b + 1):
+            for s in dfs(n):
+                if low <= int(s) <= high:
+                    ans += 1
+        return ans
 ```
 
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```java
+class Solution {
+    private static final int[][] PAIRS = {{1, 1}, {8, 8}, {6, 9}, {9, 6}};
+    private int n;
+
+    public int strobogrammaticInRange(String low, String high) {
+        int a = low.length(), b = high.length();
+        long l = Long.parseLong(low), r = Long.parseLong(high);
+        int ans = 0;
+        for (n = a; n <= b; ++n) {
+            for (String s : dfs(n)) {
+                long v = Long.parseLong(s);
+                if (l <= v && v <= r) {
+                    ++ans;
+                }
+            }
+        }
+        return ans;
+    }
+
+    private List<String> dfs(int u) {
+        if (u == 0) {
+            return Collections.singletonList("");
+        }
+        if (u == 1) {
+            return Arrays.asList("0", "1", "8");
+        }
+        List<String> ans = new ArrayList<>();
+        for (String v : dfs(u - 2)) {
+            for (var p : PAIRS) {
+                ans.add(p[0] + v + p[1]);
+            }
+            if (u != n) {
+                ans.add(0 + v + 0);
+            }
+        }
+        return ans;
+    }
+}
+```
+
+### **C++**
+
+```cpp
+using ll = long long;
+
+class Solution {
+public:
+    const vector<pair<char, char>> pairs = {{'1', '1'}, {'8', '8'}, {'6', '9'}, {'9', '6'}};
+
+    int strobogrammaticInRange(string low, string high) {
+        int n;
+        function<vector<string>(int)> dfs = [&](int u) {
+            if (u == 0) return vector<string>{""};
+            if (u == 1) return vector<string>{"0", "1", "8"};
+            vector<string> ans;
+            for (auto& v : dfs(u - 2)) {
+                for (auto& [l, r] : pairs) ans.push_back(l + v + r);
+                if (u != n) ans.push_back('0' + v + '0');
+            }
+            return ans;
+        };
+
+        int a = low.size(), b = high.size();
+        int ans = 0;
+        ll l = stoll(low), r = stoll(high);
+        for (n = a; n <= b; ++n) {
+            for (auto& s : dfs(n)) {
+                ll v = stoll(s);
+                if (l <= v && v <= r) {
+                    ++ans;
+                }
+            }
+        }
+        return ans;
+    }
+};
+```
 
+### **Go**
+
+```go
+func strobogrammaticInRange(low string, high string) int {
+	n := 0
+	var dfs func(int) []string
+	dfs = func(u int) []string {
+		if u == 0 {
+			return []string{""}
+		}
+		if u == 1 {
+			return []string{"0", "1", "8"}
+		}
+		var ans []string
+		pairs := [][]string{{"1", "1"}, {"8", "8"}, {"6", "9"}, {"9", "6"}}
+		for _, v := range dfs(u - 2) {
+			for _, p := range pairs {
+				ans = append(ans, p[0]+v+p[1])
+			}
+			if u != n {
+				ans = append(ans, "0"+v+"0")
+			}
+		}
+		return ans
+	}
+	a, b := len(low), len(high)
+	l, _ := strconv.Atoi(low)
+	r, _ := strconv.Atoi(high)
+	ans := 0
+	for n = a; n <= b; n++ {
+		for _, s := range dfs(n) {
+			v, _ := strconv.Atoi(s)
+			if l <= v && v <= r {
+				ans++
+			}
+		}
+	}
+	return ans
+}
 ```
 
 ### **...**

solution/0200-0299/0248.Strobogrammatic Number III/README_EN.md

@@ -33,13 +33,151 @@
 ### **Python3**
 
 ```python
-
+class Solution:
+    def strobogrammaticInRange(self, low: str, high: str) -> int:
+        def dfs(u):
+            if u == 0:
+                return ['']
+            if u == 1:
+                return ['0', '1', '8']
+            ans = []
+            for v in dfs(u - 2):
+                for l, r in ('11', '88', '69', '96'):
+                    ans.append(l + v + r)
+                if u != n:
+                    ans.append('0' + v + '0')
+            return ans
+
+        a, b = len(low), len(high)
+        low, high = int(low), int(high)
+        ans = 0
+        for n in range(a, b + 1):
+            for s in dfs(n):
+                if low <= int(s) <= high:
+                    ans += 1
+        return ans
 ```
 
 ### **Java**
 
 ```java
+class Solution {
+    private static final int[][] PAIRS = {{1, 1}, {8, 8}, {6, 9}, {9, 6}};
+    private int n;
+
+    public int strobogrammaticInRange(String low, String high) {
+        int a = low.length(), b = high.length();
+        long l = Long.parseLong(low), r = Long.parseLong(high);
+        int ans = 0;
+        for (n = a; n <= b; ++n) {
+            for (String s : dfs(n)) {
+                long v = Long.parseLong(s);
+                if (l <= v && v <= r) {
+                    ++ans;
+                }
+            }
+        }
+        return ans;
+    }
+
+    private List<String> dfs(int u) {
+        if (u == 0) {
+            return Collections.singletonList("");
+        }
+        if (u == 1) {
+            return Arrays.asList("0", "1", "8");
+        }
+        List<String> ans = new ArrayList<>();
+        for (String v : dfs(u - 2)) {
+            for (var p : PAIRS) {
+                ans.add(p[0] + v + p[1]);
+            }
+            if (u != n) {
+                ans.add(0 + v + 0);
+            }
+        }
+        return ans;
+    }
+}
+```
+
+### **C++**
+
+```cpp
+using ll = long long;
+
+class Solution {
+public:
+    const vector<pair<char, char>> pairs = {{'1', '1'}, {'8', '8'}, {'6', '9'}, {'9', '6'}};
+
+    int strobogrammaticInRange(string low, string high) {
+        int n;
+        function<vector<string>(int)> dfs = [&](int u) {
+            if (u == 0) return vector<string>{""};
+            if (u == 1) return vector<string>{"0", "1", "8"};
+            vector<string> ans;
+            for (auto& v : dfs(u - 2)) {
+                for (auto& [l, r] : pairs) ans.push_back(l + v + r);
+                if (u != n) ans.push_back('0' + v + '0');
+            }
+            return ans;
+        };
+
+        int a = low.size(), b = high.size();
+        int ans = 0;
+        ll l = stoll(low), r = stoll(high);
+        for (n = a; n <= b; ++n) {
+            for (auto& s : dfs(n)) {
+                ll v = stoll(s);
+                if (l <= v && v <= r) {
+                    ++ans;
+                }
+            }
+        }
+        return ans;
+    }
+};
+```
 
+### **Go**
+
+```go
+func strobogrammaticInRange(low string, high string) int {
+	n := 0
+	var dfs func(int) []string
+	dfs = func(u int) []string {
+		if u == 0 {
+			return []string{""}
+		}
+		if u == 1 {
+			return []string{"0", "1", "8"}
+		}
+		var ans []string
+		pairs := [][]string{{"1", "1"}, {"8", "8"}, {"6", "9"}, {"9", "6"}}
+		for _, v := range dfs(u - 2) {
+			for _, p := range pairs {
+				ans = append(ans, p[0]+v+p[1])
+			}
+			if u != n {
+				ans = append(ans, "0"+v+"0")
+			}
+		}
+		return ans
+	}
+	a, b := len(low), len(high)
+	l, _ := strconv.Atoi(low)
+	r, _ := strconv.Atoi(high)
+	ans := 0
+	for n = a; n <= b; n++ {
+		for _, s := range dfs(n) {
+			v, _ := strconv.Atoi(s)
+			if l <= v && v <= r {
+				ans++
+			}
+		}
+	}
+	return ans
+}
 ```
 
 ### **...**

solution/0200-0299/0248.Strobogrammatic Number III/Solution.cpp

@@ -0,0 +1,33 @@
+using ll = long long;
+
+class Solution {
+public:
+    const vector<pair<char, char>> pairs = {{'1', '1'}, {'8', '8'}, {'6', '9'}, {'9', '6'}};
+
+    int strobogrammaticInRange(string low, string high) {
+        int n;
+        function<vector<string>(int)> dfs = [&](int u) {
+            if (u == 0) return vector<string>{""};
+            if (u == 1) return vector<string>{"0", "1", "8"};
+            vector<string> ans;
+            for (auto& v : dfs(u - 2)) {
+                for (auto& [l, r] : pairs) ans.push_back(l + v + r);
+                if (u != n) ans.push_back('0' + v + '0');
+            }
+            return ans;
+        };
+
+        int a = low.size(), b = high.size();
+        int ans = 0;
+        ll l = stoll(low), r = stoll(high);
+        for (n = a; n <= b; ++n) {
+            for (auto& s : dfs(n)) {
+                ll v = stoll(s);
+                if (l <= v && v <= r) {
+                    ++ans;
+                }
+            }
+        }
+        return ans;
+    }
+};