feat: add solutions to lc problem: No.1257

solution/1200-1299/1257.Smallest Common Region/README.md

@@ -75,7 +75,11 @@ region2 = "New York"
 
 <!-- solution:start -->
 
-### 方法一
+### 方法一：哈希表
+
+我们可以用一个哈希表 $\textit{g}$ 来存储每个区域的父区域，然后从 $\textit{region1}$ 开始，不断向上找到所有的父区域，直到根区域，将这些区域放入集合 $\textit{s}$ 中。然后从 $\textit{region2}$ 开始，不断向上找到第一个在 $\textit{s}$ 中的区域，即为最小公共区域。
+
+时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为区域列表 $\textit{regions}$ 的长度。
 
 <!-- tabs:start -->
 
@@ -86,44 +90,43 @@ class Solution:
     def findSmallestRegion(
         self, regions: List[List[str]], region1: str, region2: str
     ) -> str:
-        m = {}
-        for region in regions:
-            for r in region[1:]:
-                m[r] = region[0]
+        g = {}
+        for r in regions:
+            x = r[0]
+            for y in r[1:]:
+                g[y] = x
         s = set()
-        while m.get(region1):
-            s.add(region1)
-            region1 = m[region1]
-        while m.get(region2):
-            if region2 in s:
-                return region2
-            region2 = m[region2]
-        return region1
+        x = region1
+        while x in g:
+            s.add(x)
+            x = g[x]
+        x = region2
+        while x in g and x not in s:
+            x = g[x]
+        return x
 ```
 
 #### Java
 
 ```java
 class Solution {
     public String findSmallestRegion(List<List<String>> regions, String region1, String region2) {
-        Map<String, String> m = new HashMap<>();
-        for (List<String> region : regions) {
-            for (int i = 1; i < region.size(); ++i) {
-                m.put(region.get(i), region.get(0));
+        Map<String, String> g = new HashMap<>();
+        for (var r : regions) {
+            String x = r.get(0);
+            for (String y : r.subList(1, r.size())) {
+                g.put(y, x);
             }
         }
         Set<String> s = new HashSet<>();
-        while (m.containsKey(region1)) {
-            s.add(region1);
-            region1 = m.get(region1);
+        for (String x = region1; x != null; x = g.get(x)) {
+            s.add(x);
         }
-        while (m.containsKey(region2)) {
-            if (s.contains(region2)) {
-                return region2;
-            }
-            region2 = m.get(region2);
+        String x = region2;
+        while (g.get(x) != null && !s.contains(x)) {
+            x = g.get(x);
         }
-        return region1;
+        return x;
     }
 }
 ```
@@ -134,20 +137,22 @@ class Solution {
 class Solution {
 public:
     string findSmallestRegion(vector<vector<string>>& regions, string region1, string region2) {
-        unordered_map<string, string> m;
-        for (auto& region : regions)
-            for (int i = 1; i < region.size(); ++i)
-                m[region[i]] = region[0];
+        unordered_map<string, string> g;
+        for (const auto& r : regions) {
+            string x = r[0];
+            for (size_t i = 1; i < r.size(); ++i) {
+                g[r[i]] = x;
+            }
+        }
         unordered_set<string> s;
-        while (m.count(region1)) {
-            s.insert(region1);
-            region1 = m[region1];
+        for (string x = region1; !x.empty(); x = g[x]) {
+            s.insert(x);
         }
-        while (m.count(region2)) {
-            if (s.count(region2)) return region2;
-            region2 = m[region2];
+        string x = region2;
+        while (!g[x].empty() && s.find(x) == s.end()) {
+            x = g[x];
         }
-        return region1;
+        return x;
     }
 };
 ```
@@ -156,24 +161,89 @@ public:
 
 ```go
 func findSmallestRegion(regions [][]string, region1 string, region2 string) string {
-	m := make(map[string]string)
-	for _, region := range regions {
-		for i := 1; i < len(region); i++ {
-			m[region[i]] = region[0]
+	g := make(map[string]string)
+
+	for _, r := range regions {
+		x := r[0]
+		for _, y := range r[1:] {
+			g[y] = x
 		}
 	}
+
 	s := make(map[string]bool)
-	for region1 != "" {
-		s[region1] = true
-		region1 = m[region1]
+	for x := region1; x != ""; x = g[x] {
+		s[x] = true
 	}
-	for region2 != "" {
-		if s[region2] {
-			return region2
-		}
-		region2 = m[region2]
+
+	x := region2
+	for g[x] != "" && !s[x] {
+		x = g[x]
 	}
-	return region1
+
+	return x
+}
+```
+
+#### TypeScript
+
+```ts
+function findSmallestRegion(regions: string[][], region1: string, region2: string): string {
+    const g: Record<string, string> = {};
+
+    for (const r of regions) {
+        const x = r[0];
+        for (const y of r.slice(1)) {
+            g[y] = x;
+        }
+    }
+
+    const s: Set<string> = new Set();
+    for (let x: string = region1; x !== undefined; x = g[x]) {
+        s.add(x);
+    }
+
+    let x: string = region2;
+    while (g[x] !== undefined && !s.has(x)) {
+        x = g[x];
+    }
+
+    return x;
+}
+```
+
+#### Rust
+
+```rust
+use std::collections::{HashMap, HashSet};
+
+impl Solution {
+    pub fn find_smallest_region(regions: Vec<Vec<String>>, region1: String, region2: String) -> String {
+        let mut g: HashMap<String, String> = HashMap::new();
+
+        for r in &regions {
+            let x = &r[0];
+            for y in &r[1..] {
+                g.insert(y.clone(), x.clone());
+            }
+        }
+
+        let mut s: HashSet<String> = HashSet::new();
+        let mut x = Some(region1);
+        while let Some(region) = x {
+            s.insert(region.clone());
+            x = g.get(&region).cloned();
+        }
+
+        let mut x = Some(region2);
+        while let Some(region) = x {
+            if s.contains(&region) {
+                return region;
+            }
+            x = g.get(&region).cloned();
+        }
+
+        String::new()
+    }
 }
 ```