{"id":983,"date":"2023-02-01T06:24:08","date_gmt":"2023-05-05T11:54:48","guid":{"rendered":"https:\/\/www.silicloud.com\/ja\/blog\/index.php\/2023\/11\/30\/%e3%83%90%e3%82%a4%e3%83%8a%e3%83%aa%e3%83%bc%e3%82%b5%e3%83%bc%e3%83%81%e3%83%84%e3%83%aa%e3%83%bc%ef%bc%88bst%ef%bc%89-%e6%a4%9c%e7%b4%a2%e3%80%81%e6%8c%bf%e5%85%a5%e3%80%81%e5%89%8a%e9%99%a4\/"},"modified":"2025-08-01T04:02:27","modified_gmt":"2025-07-31T19:02:27","slug":"%e3%83%90%e3%82%a4%e3%83%8a%e3%83%aa%e3%83%bc%e3%82%b5%e3%83%bc%e3%83%81%e3%83%84%e3%83%aa%e3%83%bc%ef%bc%88bst%ef%bc%89-%e6%a4%9c%e7%b4%a2%e3%80%81%e6%8c%bf%e5%85%a5%e3%80%81%e5%89%8a%e9%99%a4","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/ja\/blog\/%e3%83%90%e3%82%a4%e3%83%8a%e3%83%aa%e3%83%bc%e3%82%b5%e3%83%bc%e3%83%81%e3%83%84%e3%83%aa%e3%83%bc%ef%bc%88bst%ef%bc%89-%e6%a4%9c%e7%b4%a2%e3%80%81%e6%8c%bf%e5%85%a5%e3%80%81%e5%89%8a%e9%99%a4\/","title":{"rendered":"\u30d0\u30a4\u30ca\u30ea\u30fc\u30b5\u30fc\u30c1\u30c4\u30ea\u30fc\uff08BST\uff09- \u691c\u7d22\u3001\u633f\u5165\u3001\u524a\u9664"},"content":{"rendered":"<p>\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001\u30d0\u30a4\u30ca\u30ea\u30b5\u30fc\u30c1\u30c4\u30ea\u30fc\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u3064\u3044\u3066\u8a71\u3057\u5408\u3044\u307e\u3059\u3002\u30d0\u30a4\u30ca\u30ea\u30b5\u30fc\u30c1\u30c4\u30ea\u30fc\u304b\u3089\u5024\u3092\u691c\u7d22\u3001\u633f\u5165\u3001\u524a\u9664\u3059\u308b\u305f\u3081\u306e\u95a2\u6570\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u308c\u3089\u306e\u64cd\u4f5c\u3092\u518d\u5e30\u7684\u306b\u304a\u3088\u3073\u53cd\u5fa9\u7684\u306b\u5b9f\u88c5\u3057\u307e\u3059\u3002<\/p>\n<h2>\u30d0\u30a4\u30ca\u30ea\u30fc\u30c4\u30ea\u30fc<\/h2>\n<p>\u30d0\u30a4\u30ca\u30ea\u30b5\u30fc\u30c1\u30c4\u30ea\u30fc\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul class=\"post-ul\">\n<li>All nodes should be such that the left child is always less than the parent node.<\/li>\n<li>The right child is always greater than the parent node.<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u518d\u5e30\u7684\u304a\u3088\u3073\u53cd\u5fa9\u7684\u306bBST\uff08\u4e8c\u5206\u63a2\u7d22\u6728\uff09\u3067\u306e\u691c\u7d22\u3001\u633f\u5165\u3001\u304a\u3088\u3073\u524a\u9664\u65b9\u6cd5\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002\u307e\u305a\u3001\u4e8c\u5206\u6728\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u4f5c\u6210\u3057\u307e\u3057\u3087\u3046\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>\u4e0a\u8a18\u306e\u5b9f\u88c5\u306f\u3001\u8981\u7d20\u3092\u6728\u306b\u633f\u5165\u3059\u308b\u5236\u9650\u304c\u306a\u3044\u305f\u3081\u3001\u30d0\u30a4\u30ca\u30ea\u30b5\u30fc\u30c1\u30c4\u30ea\u30fc\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<h3>\u518d\u5e30\u7684\u306bBST\u63a2\u7d22<\/h3>\n<p>\u4ee5\u4e0b\u306eJava\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u306f\u3001\u518d\u5e30\u7684\u306bBST\u5185\u306e\u5024\u3092\u691c\u7d22\u3059\u308b\u305f\u3081\u306e\u95a2\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\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 *   Our Example Binary Search Tree\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(\"Search Value 2 is in tree? \" + searchRecursively(tree.root, 2));\r\n        System.out.println(\"Search Value 10 in tree? \" + 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>\u51fa\u529b\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>BST\u3092\u53cd\u5fa9\u7684\u306b\u691c\u7d22\u3059\u308b<\/h3>\n<p>\u53cd\u5fa9\u51e6\u7406\u3067\u691c\u7d22\u3059\u308b\u5834\u5408\u306f\u3001\u4ee3\u308f\u308a\u306b\u6b21\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/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>\u4e8c\u5206\u63a2\u7d22\u6728\u306b\u65b0\u3057\u3044\u30ce\u30fc\u30c9\u3092\u633f\u5165\u3059\u308b\u65b9\u6cd5\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u518d\u5e30\u7684\u306bBST\u306b\u8981\u7d20\u3092\u633f\u5165\u3059\u308b\u3002<\/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>\u30e1\u30a4\u30f3\u30e1\u30bd\u30c3\u30c9\u3067\u4e0a\u8a18\u306e\u30e1\u30bd\u30c3\u30c9\u3092\u547c\u3073\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\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>\u305d\u306e\u6728\u306f\u4e2d\u9593\u9806\u5e8f\u306e\u5f62\u5f0f\u3067\u51fa\u529b\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3>BST\uff08Binary Search Tree\uff09\u306e\u633f\u5165\u3092\u53cd\u5fa9\u7684\u306a\u65b9\u6cd5\u3067\u884c\u3046\u3002<\/h3>\n<p>BST\u306e\u6728\u306b\u30ce\u30fc\u30c9\u3092\u53cd\u5fa9\u7684\u306b\u633f\u5165\u3059\u308b\u306b\u306f\u30012\u3064\u306e\u30dd\u30a4\u30f3\u30bf\u3092\u4f7f\u7528\u3057\u3066\u6728\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\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>\u8981\u7d20\u3092\u518d\u5e30\u7684\u306b\u524a\u9664\u3059\u308bBST<\/h3>\n<p>BST\u304b\u3089\u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u3053\u3068\u306f\u3001\u691c\u7d22\u3084\u633f\u5165\u3088\u308a\u3082\u3084\u3084\u8907\u96d1\u3067\u3059\u3002\u306a\u305c\u306a\u3089\u3001BST\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u4fdd\u6301\u3055\u308c\u308b\u3088\u3046\u306b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u304b\u3089\u3067\u3059\u3002\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u307e\u305a\u691c\u7d22\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6b21\u306b\u3001\u305d\u306e\u30ce\u30fc\u30c9\u304c\u5b50\u3092\u6301\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul class=\"post-ul\">\n<li>If no children &#8211; Just delete.<\/li>\n<li>If a single child &#8211; Copy that child to the node.<\/li>\n<li>If two children &#8211; Determine the next highest element (inorder successor) in the right subtree. Replace the node to be removed with the inorder successor. Delete the inorder successor duplicate.<\/li>\n<\/ul>\n<p>\u30ce\u30fc\u30c9\u306e\u53f3\u5074\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u4e2d\u3067\u6700\u5c0f\u5024\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u4e2d\u9593\u6b21\u7bc0\u70b9\u3092\u53d6\u5f97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306eJava\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3001BST\u304b\u3089\u8981\u7d20\u3092\u524a\u9664\u3057\u307e\u3059\u3002<\/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>\u30e1\u30a4\u30f3\u30e1\u30bd\u30c3\u30c9\u3067\u4e0a\u8a18\u306e\u524a\u9664\u30e1\u30bd\u30c3\u30c9\u3092\u547c\u3073\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\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>\u51fa\u529b\u306f\uff1a2 5 8 10 15 24 25 \u3067\u3059\u3002\u540c\u3058\u624b\u9806\u3092\u53cd\u5fa9\u3057\u3066\u884c\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>BST\u3092\u8981\u7d20\u3092\u53cd\u5fa9\u7684\u306b\u524a\u9664\u3059\u308b<\/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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