feat: add solutions to lc problem: No.310 (#2451)

No.0310.Minimum Height Trees

Author: yanglbme

solution/0300-0399/0310.Minimum Height Trees/README.md

@@ -51,7 +51,13 @@
 
 ## 解法
 
-### 方法一
+### 方法一：拓扑排序
+
+如果这棵树只有一个节点，那么这个节点就是最小高度树的根节点，直接返回这个节点即可。
+
+如果这棵树有多个节点，那么一定存在叶子节点。叶子节点是只有一个相邻节点的节点。我们可以利用拓扑排序，从外向内剥离叶子节点，当我们到达最后一层的时候，剩下的节点就是最小高度树的根节点。
+
+时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为节点数。
 
 <!-- tabs:start -->
 
@@ -60,7 +66,7 @@ class Solution:
     def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]:
         if n == 1:
             return [0]
-        g = defaultdict(list)
+        g = [[] for _ in range(n)]
         degree = [0] * n
         for a, b in edges:
             g[a].append(b)
@@ -85,7 +91,7 @@ class Solution:
 class Solution {
     public List<Integer> findMinHeightTrees(int n, int[][] edges) {
         if (n == 1) {
-            return Collections.singletonList(0);
+            return List.of(0);
         }
         List<Integer>[] g = new List[n];
         Arrays.setAll(g, k -> new ArrayList<>());
@@ -97,7 +103,7 @@ class Solution {
             ++degree[a];
             ++degree[b];
         }
-        Queue<Integer> q = new LinkedList<>();
+        Deque<Integer> q = new ArrayDeque<>();
         for (int i = 0; i < n; ++i) {
             if (degree[i] == 1) {
                 q.offer(i);
@@ -125,7 +131,9 @@ class Solution {
 class Solution {
 public:
     vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
-        if (n == 1) return {0};
+        if (n == 1) {
+            return {0};
+        }
         vector<vector<int>> g(n);
         vector<int> degree(n);
         for (auto& e : edges) {
@@ -136,19 +144,23 @@ public:
             ++degree[b];
         }
         queue<int> q;
-        for (int i = 0; i < n; ++i)
-            if (degree[i] == 1)
+        for (int i = 0; i < n; ++i) {
+            if (degree[i] == 1) {
                 q.push(i);
+            }
+        }
         vector<int> ans;
         while (!q.empty()) {
             ans.clear();
             for (int i = q.size(); i > 0; --i) {
                 int a = q.front();
                 q.pop();
                 ans.push_back(a);
-                for (int b : g[a])
-                    if (--degree[b] == 1)
+                for (int b : g[a]) {
+                    if (--degree[b] == 1) {
                         q.push(b);
+                    }
+                }
             }
         }
         return ans;
@@ -157,7 +169,7 @@ public:
 ```
 
 ```go
-func findMinHeightTrees(n int, edges [][]int) []int {
+func findMinHeightTrees(n int, edges [][]int) (ans []int) {
 	if n == 1 {
 		return []int{0}
 	}
@@ -170,13 +182,12 @@ func findMinHeightTrees(n int, edges [][]int) []int {
 		degree[a]++
 		degree[b]++
 	}
-	var q []int
-	for i := 0; i < n; i++ {
-		if degree[i] == 1 {
+	q := []int{}
+	for i, d := range degree {
+		if d == 1 {
 			q = append(q, i)
 		}
 	}
-	var ans []int
 	for len(q) > 0 {
 		ans = []int{}
 		for i := len(q); i > 0; i-- {
@@ -191,7 +202,44 @@ func findMinHeightTrees(n int, edges [][]int) []int {
 			}
 		}
 	}
-	return ans
+	return
+}
+```
+
+```ts
+function findMinHeightTrees(n: number, edges: number[][]): number[] {
+    if (n === 1) {
+        return [0];
+    }
+    const g: number[][] = Array.from({ length: n }, () => []);
+    const degree: number[] = Array(n).fill(0);
+    for (const [a, b] of edges) {
+        g[a].push(b);
+        g[b].push(a);
+        ++degree[a];
+        ++degree[b];
+    }
+    const q: number[] = [];
+    for (let i = 0; i < n; ++i) {
+        if (degree[i] === 1) {
+            q.push(i);
+        }
+    }
+    const ans: number[] = [];
+    while (q.length > 0) {
+        ans.length = 0;
+        const t: number[] = [];
+        for (const a of q) {
+            ans.push(a);
+            for (const b of g[a]) {
+                if (--degree[b] === 1) {
+                    t.push(b);
+                }
+            }
+        }
+        q.splice(0, q.length, ...t);
+    }
+    return ans;
 }
 ```
 

solution/0300-0399/0310.Minimum Height Trees/README_EN.md

@@ -44,7 +44,13 @@
 
 ## Solutions
 
-### Solution 1
+### Solution 1: Topological Sorting
+
+If the tree only has one node, then this node is the root of the minimum height tree. We can directly return this node.
+
+If the tree has multiple nodes, there must be leaf nodes. A leaf node is a node that only has one adjacent node. We can use topological sorting to peel off the leaf nodes from the outside to the inside. When we reach the last layer, the remaining nodes are the root nodes of the minimum height tree.
+
+The time complexity is $O(n)$ and the space complexity is $O(n)$, where $n$ is the number of nodes.
 
 <!-- tabs:start -->
 
@@ -53,7 +59,7 @@ class Solution:
     def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]:
         if n == 1:
             return [0]
-        g = defaultdict(list)
+        g = [[] for _ in range(n)]
         degree = [0] * n
         for a, b in edges:
             g[a].append(b)
@@ -78,7 +84,7 @@ class Solution:
 class Solution {
     public List<Integer> findMinHeightTrees(int n, int[][] edges) {
         if (n == 1) {
-            return Collections.singletonList(0);
+            return List.of(0);
         }
         List<Integer>[] g = new List[n];
         Arrays.setAll(g, k -> new ArrayList<>());
@@ -90,7 +96,7 @@ class Solution {
             ++degree[a];
             ++degree[b];
         }
-        Queue<Integer> q = new LinkedList<>();
+        Deque<Integer> q = new ArrayDeque<>();
         for (int i = 0; i < n; ++i) {
             if (degree[i] == 1) {
                 q.offer(i);
@@ -118,7 +124,9 @@ class Solution {
 class Solution {
 public:
     vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
-        if (n == 1) return {0};
+        if (n == 1) {
+            return {0};
+        }
         vector<vector<int>> g(n);
         vector<int> degree(n);
         for (auto& e : edges) {
@@ -129,19 +137,23 @@ public:
             ++degree[b];
         }
         queue<int> q;
-        for (int i = 0; i < n; ++i)
-            if (degree[i] == 1)
+        for (int i = 0; i < n; ++i) {
+            if (degree[i] == 1) {
                 q.push(i);
+            }
+        }
         vector<int> ans;
         while (!q.empty()) {
             ans.clear();
             for (int i = q.size(); i > 0; --i) {
                 int a = q.front();
                 q.pop();
                 ans.push_back(a);
-                for (int b : g[a])
-                    if (--degree[b] == 1)
+                for (int b : g[a]) {
+                    if (--degree[b] == 1) {
                         q.push(b);
+                    }
+                }
             }
         }
         return ans;
@@ -150,7 +162,7 @@ public:
 ```
 
 ```go
-func findMinHeightTrees(n int, edges [][]int) []int {
+func findMinHeightTrees(n int, edges [][]int) (ans []int) {
 	if n == 1 {
 		return []int{0}
 	}
@@ -163,13 +175,12 @@ func findMinHeightTrees(n int, edges [][]int) []int {
 		degree[a]++
 		degree[b]++
 	}
-	var q []int
-	for i := 0; i < n; i++ {
-		if degree[i] == 1 {
+	q := []int{}
+	for i, d := range degree {
+		if d == 1 {
 			q = append(q, i)
 		}
 	}
-	var ans []int
 	for len(q) > 0 {
 		ans = []int{}
 		for i := len(q); i > 0; i-- {
@@ -184,7 +195,44 @@ func findMinHeightTrees(n int, edges [][]int) []int {
 			}
 		}
 	}
-	return ans
+	return
+}
+```
+
+```ts
+function findMinHeightTrees(n: number, edges: number[][]): number[] {
+    if (n === 1) {
+        return [0];
+    }
+    const g: number[][] = Array.from({ length: n }, () => []);
+    const degree: number[] = Array(n).fill(0);
+    for (const [a, b] of edges) {
+        g[a].push(b);
+        g[b].push(a);
+        ++degree[a];
+        ++degree[b];
+    }
+    const q: number[] = [];
+    for (let i = 0; i < n; ++i) {
+        if (degree[i] === 1) {
+            q.push(i);
+        }
+    }
+    const ans: number[] = [];
+    while (q.length > 0) {
+        ans.length = 0;
+        const t: number[] = [];
+        for (const a of q) {
+            ans.push(a);
+            for (const b of g[a]) {
+                if (--degree[b] === 1) {
+                    t.push(b);
+                }
+            }
+        }
+        q.splice(0, q.length, ...t);
+    }
+    return ans;
 }
 ```
 

solution/0300-0399/0310.Minimum Height Trees/Solution.cpp

@@ -1,7 +1,9 @@
 class Solution {
 public:
     vector<int> findMinHeightTrees(int n, vector<vector<int>>& edges) {
-        if (n == 1) return {0};
+        if (n == 1) {
+            return {0};
+        }
         vector<vector<int>> g(n);
         vector<int> degree(n);
         for (auto& e : edges) {
@@ -12,19 +14,23 @@ class Solution {
             ++degree[b];
         }
         queue<int> q;
-        for (int i = 0; i < n; ++i)
-            if (degree[i] == 1)
+        for (int i = 0; i < n; ++i) {
+            if (degree[i] == 1) {
                 q.push(i);
+            }
+        }
         vector<int> ans;
         while (!q.empty()) {
             ans.clear();
             for (int i = q.size(); i > 0; --i) {
                 int a = q.front();
                 q.pop();
                 ans.push_back(a);
-                for (int b : g[a])
-                    if (--degree[b] == 1)
+                for (int b : g[a]) {
+                    if (--degree[b] == 1) {
                         q.push(b);
+                    }
+                }
             }
         }
         return ans;

solution/0300-0399/0310.Minimum Height Trees/Solution.go

@@ -1,4 +1,4 @@
-func findMinHeightTrees(n int, edges [][]int) []int {
+func findMinHeightTrees(n int, edges [][]int) (ans []int) {
 	if n == 1 {
 		return []int{0}
 	}
@@ -11,13 +11,12 @@ func findMinHeightTrees(n int, edges [][]int) []int {
 		degree[a]++
 		degree[b]++
 	}
-	var q []int
-	for i := 0; i < n; i++ {
-		if degree[i] == 1 {
+	q := []int{}
+	for i, d := range degree {
+		if d == 1 {
 			q = append(q, i)
 		}
 	}
-	var ans []int
 	for len(q) > 0 {
 		ans = []int{}
 		for i := len(q); i > 0; i-- {
@@ -32,5 +31,5 @@ func findMinHeightTrees(n int, edges [][]int) []int {
 			}
 		}
 	}
-	return ans
+	return
 }

solution/0300-0399/0310.Minimum Height Trees/Solution.java

@@ -1,7 +1,7 @@
 class Solution {
     public List<Integer> findMinHeightTrees(int n, int[][] edges) {
         if (n == 1) {
-            return Collections.singletonList(0);
+            return List.of(0);
         }
         List<Integer>[] g = new List[n];
         Arrays.setAll(g, k -> new ArrayList<>());
@@ -13,7 +13,7 @@ public List<Integer> findMinHeightTrees(int n, int[][] edges) {
             ++degree[a];
             ++degree[b];
         }
-        Queue<Integer> q = new LinkedList<>();
+        Deque<Integer> q = new ArrayDeque<>();
         for (int i = 0; i < n; ++i) {
             if (degree[i] == 1) {
                 q.offer(i);