先要理解 BFS 廣度優先收尋

二元樹 5 階圖

      static void Main(string[] args)
      {
        MinDepthCalculate();
      }
      
      public class TreeNode
       {
           public int val;
           public TreeNode left;
           public TreeNode right;

           public TreeNode(int val = 0, TreeNode left = null, TreeNode right = null)
           {
               this.val = val;
               this.left = left;
               this.right = right;
           }
       }

       /// <summary>
       /// 計算二元樹最小深度
       /// </summary>
       /// <exception cref="NotImplementedException"></exception>
       private static void MinDepthCalculate()
       {
           //宣告一個 5 階 二元樹
           TreeNode root = new TreeNode(1,
            new TreeNode(2,
                new TreeNode(4,
                    new TreeNode(8, new TreeNode(16), new TreeNode(17)),
                    new TreeNode(9, new TreeNode(18), new TreeNode(19))),
                new TreeNode(5,
                    new TreeNode(10, new TreeNode(20), new TreeNode(21)),
                    new TreeNode(11, new TreeNode(22), new TreeNode(23)))),
            new TreeNode(3,
                new TreeNode(6,
                    new TreeNode(12, new TreeNode(24), new TreeNode(25)),
                    new TreeNode(13, new TreeNode(26), new TreeNode(27))),
                new TreeNode(7,
                    new TreeNode(14, new TreeNode(28), new TreeNode(29)),
                    new TreeNode(15, new TreeNode(30), new TreeNode(31))))
        );
           int height = MinDepth(root);
           Console.WriteLine(height);
       }

       private static int MinDepth(TreeNode root)
       {
           if (root == null)
           {
               return 0;
           }

           Queue<TreeNode> queue = new Queue<TreeNode>();
           queue.Enqueue(root);
           int depth = 1;

           while (queue.Count > 0)
           {
               // 捕獲當前層的節點數量
               int levelSize = queue.Count; 

               for (int i = 0; i < levelSize; i++)
               {                    
                   // 僅迭代當前層的節點
                   TreeNode currentNode = queue.Dequeue();

                   // 檢查當前節點是否為葉節點
                   if (currentNode.left == null && currentNode.right == null)
                   {
                       return depth;
                   }

                   if (currentNode.left != null)
                   {
                       queue.Enqueue(currentNode.left);
                   }
                   if (currentNode.right != null)
                   {
                       queue.Enqueue(currentNode.right);
                   }
               }

               // 完成當前層的處理後，增加深度
               depth++; 
           }

           return depth;
       }