{"id":679,"date":"2022-12-13T09:11:07","date_gmt":"2023-05-15T04:25:38","guid":{"rendered":"https:\/\/www.silicloud.com\/zh\/blog\/index.php\/2023\/11\/30\/%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91%ef%bc%88bst%ef%bc%89-%e6%90%9c%e7%b4%a2%e3%80%81%e6%8f%92%e5%85%a5%e5%92%8c%e5%88%a0%e9%99%a4%e6%93%8d%e4%bd%9c%e3%80%82\/"},"modified":"2025-08-03T02:48:11","modified_gmt":"2025-08-02T18:48:11","slug":"%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91%ef%bc%88bst%ef%bc%89-%e6%90%9c%e7%b4%a2%e3%80%81%e6%8f%92%e5%85%a5%e5%92%8c%e5%88%a0%e9%99%a4%e6%93%8d%e4%bd%9c%e3%80%82","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/zh\/blog\/%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91%ef%bc%88bst%ef%bc%89-%e6%90%9c%e7%b4%a2%e3%80%81%e6%8f%92%e5%85%a5%e5%92%8c%e5%88%a0%e9%99%a4%e6%93%8d%e4%bd%9c%e3%80%82\/","title":{"rendered":"\u4e8c\u53c9\u641c\u7d22\u6811(BST)\u5b8c\u5168\u6307\u5357\uff1a\u8be6\u89e3\u641c\u7d22\u3001\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c | \u7b97\u6cd5\u5165\u95e8\u5fc5\u5907"},"content":{"rendered":"<p>\u5728\u672c\u6559\u7a0b\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u4e8c\u53c9\u641c\u7d22\u6811\u6570\u636e\u7ed3\u6784\u3002\u6211\u4eec\u5c06\u5b9e\u73b0\u4ece\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u641c\u7d22\u3001\u63d2\u5165\u548c\u5220\u9664\u503c\u7684\u51fd\u6570\u3002\u6211\u4eec\u5c06\u9012\u5f52\u548c\u8fed\u4ee3\u5730\u5b9e\u73b0\u8fd9\u4e9b\u64cd\u4f5c\u3002<\/p>\n<h2>\u4e8c\u53c9\u641c\u7d22\u6811<\/h2>\n<p>\u4e8c\u53c9\u641c\u7d22\u6811\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/p>\n<ul class=\"post-ul\">\n<li>\u6240\u6709\u8282\u70b9\u7684\u5de6\u5b50\u8282\u70b9\u7684\u503c\u603b\u662f\u5c0f\u4e8e\u7236\u8282\u70b9\u3002<\/li>\n<li>\u6240\u6709\u8282\u70b9\u7684\u53f3\u5b50\u8282\u70b9\u7684\u503c\u603b\u662f\u5927\u4e8e\u7236\u8282\u70b9\u3002<\/li>\n<\/ul>\n<p>\u5728\u63a5\u4e0b\u6765\u7684\u7ae0\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u5b66\u4e60\u5982\u4f55\u9012\u5f52\u548c\u8fed\u4ee3\u5730\u641c\u7d22\u3001\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u641c\u7d22\u6811\u3002\u8ba9\u6211\u4eec\u9996\u5148\u521b\u5efa\u6211\u4eec\u7684\u4e8c\u53c9\u6811\u6570\u636e\u7ed3\u6784\u3002<\/p>\n<pre class=\"post-pre\"><code>public class BinaryTree {\r\n\r\n\tpublic TreeNode root;\r\n\r\n\tpublic static class TreeNode {\r\n\r\n\t\tpublic TreeNode left;\r\n\t\tpublic TreeNode right;\r\n\t\tpublic Object data;\r\n\r\n\t\tpublic TreeNode(Object data) {\r\n\t\t\tthis.data = data;\r\n\t\t\tleft = right = null;\r\n\t\t}\r\n\t}\r\n}\r\n<\/code><\/pre>\n<p>\u8bf7\u6ce8\u610f\uff0c\u4e0a\u8ff0\u5b9e\u73b0\u4e0d\u662f\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u56e0\u4e3a\u5728\u5411\u6811\u4e2d\u63d2\u5165\u5143\u7d20\u65f6\u6ca1\u6709\u4efb\u4f55\u9650\u5236\u3002<\/p>\n<h3>\u4ee5\u9012\u5f52\u65b9\u5f0f\u8fdb\u884c\u4e8c\u53c9\u641c\u7d22\u6811\u641c\u7d22<\/h3>\n<p>\u4ee5\u4e0b\u7684Java\u7a0b\u5e8f\u5305\u542b\u4e86\u4e00\u4e2a\u7528\u9012\u5f52\u65b9\u5f0f\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u67e5\u627e\u503c\u7684\u51fd\u6570\u3002<\/p>\n<pre class=\"post-pre\"><code>public class SearchInsertRemoveFromTree {\r\n\r\n    public static void main(String[] args) {\r\n\r\n\t\/**\r\n\t *   \u6211\u4eec\u7684\u793a\u4f8b\u4e8c\u53c9\u641c\u7d22\u6811\r\n\t *       10\r\n\t *     5    20\r\n\t *   4  8  15 25\r\n\t *\/\r\n\r\n        BinaryTree tree = new BinaryTree();\r\n        tree.root = new TreeNode(10);\r\n        tree.root.left = new TreeNode(5);\r\n        tree.root.right = new TreeNode(20);\r\n        tree.root.left.left = new TreeNode(4);\r\n        tree.root.left.right = new TreeNode(8);\r\n        tree.root.right.left = new TreeNode(15);\r\n        tree.root.right.right = new TreeNode(25);\r\n\r\n        System.out.println(\"\u641c\u7d22\u503c2\u662f\u5426\u5728\u6811\u4e2d\uff1f \" + searchRecursively(tree.root, 2));\r\n        System.out.println(\"\u641c\u7d22\u503c10\u662f\u5426\u5728\u6811\u4e2d\uff1f \" + searchRecursively(tree.root, 10));\r\n    }\r\n\r\n    public static boolean searchRecursively(TreeNode root, int value) {\r\n\r\n\r\n        if (root == null)\r\n            return false;\r\n\r\n\r\n        if ((int) root.data == value)\r\n            return true;\r\n\r\n        if (value &lt; (int) root.data)\r\n            return searchRecursively(root.left, value);\r\n\r\n        else if (value &gt; (int) root.data)\r\n            return searchRecursively(root.right, value);\r\n\r\n\r\n        return false;\r\n    }\r\n}\r\n<\/code><\/pre>\n<p>\u8f93\u51fa\u662f\uff1a<\/p>\n<h3>\u4ee5\u8fed\u4ee3\u65b9\u5f0f\u8fdb\u884c\u4e8c\u53c9\u641c\u7d22\u6811\u641c\u7d22<\/h3>\n<p>\u4e3a\u4e86\u9010\u6b65\u641c\u7d22\uff0c\u8bf7\u4f7f\u7528\u4ee5\u4e0b\u65b9\u6cd5\u66ff\u4ee3\uff1a<\/p>\n<pre class=\"post-pre\"><code>public static boolean searchIteratively(TreeNode root, int value) {\r\n\r\n        while (root != null) {\r\n            if ((int) root.data == value)\r\n                return true;\r\n\r\n            if (value &lt; (int) root.data)\r\n                root = root.left;\r\n\r\n            else\r\n                root = root.right;\r\n        }\r\n\r\n        return false;\r\n    }\r\n<\/code><\/pre>\n<p>\u8ba9\u6211\u4eec\u6765\u770b\u4e00\u4e0b\u5982\u4f55\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u63d2\u5165\u4e00\u4e2a\u65b0\u8282\u70b9\u3002<\/p>\n<h3>\u9012\u5f52\u5730\u8fdb\u884c\u4e8c\u53c9\u641c\u7d22\u6811\u63d2\u5165<\/h3>\n<pre class=\"post-pre\"><code>public static TreeNode insertionRecursive(TreeNode root, int value) {\r\n\r\n        if (root == null)\r\n            return new TreeNode(value);\r\n\r\n        if (value &lt; (int) root.data) {\r\n            root.left = insertionRecursive(root.left, value);\r\n        } else if (value &gt; (int) root.data) {\r\n            root.right = insertionRecursive(root.right, value);\r\n        }\r\n\r\n        return root;\r\n\r\n    }\r\n\r\npublic static void printInorderTraversal(TreeNode root) {\r\n        if (root != null) {\r\n            printInorderTraversal(root.left);\r\n            System.out.print(root.data + \" \");\r\n            printInorderTraversal(root.right);\r\n        }\r\n    }\r\n\r\n<\/code><\/pre>\n<p>\u5728\u4e3b\u65b9\u6cd5\u4e2d\u8c03\u7528\u4e0a\u8ff0\u65b9\u6cd5\u3002<\/p>\n<pre class=\"post-pre\"><code>tree.root = insertionRecursive(tree.root, 24);\r\ntree.root = insertionRecursive(tree.root, 2);\r\nprintInorderTraversal(tree.root);\r\n<\/code><\/pre>\n<p>\u8fd9\u68f5\u6811\u4ee5\u4e2d\u5e8f\u904d\u5386\u7684\u5f62\u5f0f\u6253\u5370\u51fa\u6765\u3002<\/p>\n<h3>\u4e8c\u53c9\u641c\u7d22\u6811\u8fed\u4ee3\u5f0f\u63d2\u5165<\/h3>\n<p>\u4e3a\u4e86\u5728\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u8fed\u4ee3\u5730\u63d2\u5165\u4e00\u4e2a\u8282\u70b9\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u4e24\u4e2a\u6307\u9488\u904d\u5386\u6811\u3002<\/p>\n<pre class=\"post-pre\"><code>public static TreeNode insertionIterative(TreeNode root, int value) {\r\n\r\n        TreeNode current, parent;\r\n\r\n        TreeNode tempNode = new TreeNode(value);\r\n\r\n        if (root == null) {\r\n            root = tempNode;\r\n            return root;\r\n        } else {\r\n            current = root;\r\n        }\r\n\r\n        while (true) {\r\n            parent = current;\r\n\r\n            if (value &lt; (int) current.data) {\r\n                current = current.left;\r\n                if (current == null) {\r\n                    parent.left = tempNode;\r\n                    return root;\r\n                }\r\n\r\n            } else if (value &gt; (int) current.data) {\r\n                current = current.right;\r\n\r\n                if (current == null) {\r\n                    parent.right = tempNode;\r\n                    return root;\r\n                }\r\n            }\r\n\r\n        }\r\n    }\r\n<\/code><\/pre>\n<h3>\u9012\u5f52\u5220\u9664\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u7684\u5143\u7d20<\/h3>\n<p>\u4ece\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u79fb\u9664\u4e00\u4e2a\u5143\u7d20\u6bd4\u641c\u7d22\u548c\u63d2\u5165\u590d\u6742\u4e00\u4e9b\uff0c\u56e0\u4e3a\u6211\u4eec\u5fc5\u987b\u786e\u4fdd\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\u5f97\u4ee5\u4fdd\u7559\u3002\u8981\u5220\u9664\u4e00\u4e2a\u8282\u70b9\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u641c\u7d22\u5b83\u3002\u7136\u540e\u6211\u4eec\u9700\u8981\u786e\u5b9a\u8be5\u8282\u70b9\u662f\u5426\u6709\u5b50\u8282\u70b9\u3002<\/p>\n<ul class=\"post-ul\">\n<li>\u5982\u679c\u6ca1\u6709\u5b50\u8282\u70b9 &#8211; \u76f4\u63a5\u5220\u9664\u3002<\/li>\n<li>\u5982\u679c\u53ea\u6709\u4e00\u4e2a\u5b50\u8282\u70b9 &#8211; \u5c06\u8be5\u5b50\u8282\u70b9\u590d\u5236\u5230\u8981\u5220\u9664\u7684\u8282\u70b9\u4f4d\u7f6e\u3002<\/li>\n<li>\u5982\u679c\u6709\u4e24\u4e2a\u5b50\u8282\u70b9 &#8211; \u786e\u5b9a\u53f3\u5b50\u6811\u4e2d\u7684\u4e0b\u4e00\u4e2a\u6700\u9ad8\u5143\u7d20\uff08\u4e2d\u5e8f\u540e\u7ee7\uff09\u3002\u7528\u4e2d\u5e8f\u540e\u7ee7\u66ff\u6362\u8981\u5220\u9664\u7684\u8282\u70b9\u3002\u5220\u9664\u4e2d\u5e8f\u540e\u7ee7\u7684\u91cd\u590d\u9879\u3002<\/li>\n<\/ul>\n<p>\u53ef\u4ee5\u901a\u8fc7\u627e\u5230\u8282\u70b9\u53f3\u5b50\u6811\u4e2d\u7684\u6700\u5c0f\u503c\u6765\u83b7\u5f97\u4e2d\u5e8f\u904d\u5386\u7684\u540e\u7ee7\u3002<\/p>\n<p>\u4e0b\u9762\u8fd9\u4e2aJava\u7a0b\u5e8f\u4ece\u4e8c\u53c9\u641c\u7d22\u6811\u4e2d\u5220\u9664\u5143\u7d20<\/p>\n<pre class=\"post-pre\"><code>public static TreeNode deleteRecursively(TreeNode root, int value) {\r\n\r\n        if (root == null)\r\n            return root;\r\n\r\n        if (value &lt; (int) root.data) {\r\n            root.left = deleteRecursively(root.left, value);\r\n        } else if (value &gt; (int) root.data) {\r\n            root.right = deleteRecursively(root.right, value);\r\n        } else {\r\n\r\n            if (root.left == null) {\r\n                return root.right;\r\n            } else if (root.right == null)\r\n                return root.left;\r\n\r\n            root.data = inOrderSuccessor(root.right);\r\n            root.right = deleteRecursively(root.right, (int) root.data);\r\n        }\r\n\r\n        return root;\r\n\r\n    }\r\n\r\n    public static int inOrderSuccessor(TreeNode root) {\r\n        int minimum = (int) root.data;\r\n        while (root.left != null) {\r\n            minimum = (int) root.left.data;\r\n            root = root.left;\r\n        }\r\n        return minimum;\r\n    }\r\n\r\n<\/code><\/pre>\n<p>\u5728\u4e3b\u65b9\u6cd5\u4e2d\u8c03\u7528\u4e0a\u9762\u7684\u5220\u9664\u65b9\u6cd5\u3002<\/p>\n<pre class=\"post-pre\"><code>tree.root = deleteRecursively(tree.root, 4);\r\ntree.root = deleteRecursively(tree.root, 20);\r\nprintInorderTraversal(tree.root);\r\n<\/code><\/pre>\n<p>\u8f93\u51fa\u7ed3\u679c\u662f\uff1a2 5 8 10 15 24 25 \u8ba9\u6211\u4eec\u7528\u8fed\u4ee3\u7684\u65b9\u5f0f\u505a\u540c\u6837\u7684\u4e8b\u60c5\u3002<\/p>\n<h3>\u4e8c\u53c9\u641c\u7d22\u6811\u8fed\u4ee3\u5f0f\u5220\u9664\u5143\u7d20<\/h3>\n<pre class=\"post-pre\"><code>public static TreeNode deleteNodeIteratively(TreeNode root, int value) {\r\n        TreeNode parent = null, current = root;\r\n        boolean hasLeft = false;\r\n\r\n        if (root == null)\r\n            return root;\r\n\r\n        while (current != null) {\r\n            if ((int) current.data == value) {\r\n                break;\r\n            }\r\n\r\n            parent = current;\r\n            if (value &lt; (int) current.data) {\r\n                hasLeft = true;\r\n                current = current.left;\r\n            } else {\r\n                hasLeft = false;\r\n                current = current.right;\r\n            }\r\n        }\r\n\r\n\r\n        if (parent == null) {\r\n            return deleteNodeIteratively(current);\r\n        }\r\n\r\n        if (hasLeft) {\r\n            parent.left = deleteNodeIteratively(current);\r\n        } else {\r\n            parent.right = deleteNodeIteratively(current);\r\n        }\r\n\r\n        return root;\r\n    }\r\n\r\n    private static TreeNode deleteNodeIteratively(TreeNode node) {\r\n\r\n        if (node != null) {\r\n            if (node.left == null &amp;&amp; node.right == null) {\r\n                return null;\r\n            }\r\n\r\n            if (node.left != null &amp;&amp; node.right != null) {\r\n                TreeNode inOrderSuccessor = deleteInOrderSuccessorDuplicate(node);\r\n                node.data = inOrderSuccessor.data;\r\n            } else if (node.left != null) {\r\n                node = node.left;\r\n            } else {\r\n                node = node.right;\r\n            }\r\n        }\r\n\r\n        return node;\r\n    }\r\n\r\n    private static TreeNode deleteInOrderSuccessorDuplicate(TreeNode node) {\r\n        TreeNode parent = node;\r\n        node = node.right;\r\n        boolean rightChild = node.left == null;\r\n\r\n        while (node.left != null) {\r\n            parent = node;\r\n            node = node.left;\r\n        }\r\n\r\n        if (rightChild) {\r\n            parent.right = node.right;\r\n        } else {\r\n            parent.left = node.right;\r\n        }\r\n\r\n        node.right = null;\r\n        return node;\r\n    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[&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[1883,1882,1884,252,786],"class_list":["post-679","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-bst","tag-1882","tag-1884","tag-252","tag-786"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.5 (Yoast SEO v21.5) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u4e8c\u53c9\u641c\u7d22\u6811(BST)\u5b8c\u5168\u6307\u5357\uff1a\u8be6\u89e3\u641c\u7d22\u3001\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c | \u7b97\u6cd5\u5165\u95e8\u5fc5\u5907 - Blog - Silicon Cloud<\/title>\n<meta name=\"description\" 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