{"id":775,"date":"2023-08-10T09:59:15","date_gmt":"2023-08-10T01:59:15","guid":{"rendered":"https:\/\/zhaocunwei.co.uk\/?p=775"},"modified":"2023-08-10T10:22:12","modified_gmt":"2023-08-10T02:22:12","slug":"treap","status":"publish","type":"post","link":"https:\/\/zhaocunwei.co.uk\/index.php\/2023\/08\/10\/treap\/","title":{"rendered":"Treap\u7684\u7406\u8bba\u4e0eJava\u4ee3\u7801\u5b9e\u73b0"},"content":{"rendered":"

\u524d\u8a00<\/h1>\n

Treap\uff08\u6811\u5806\uff09\u662f\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u540c\u65f6\u5177\u6709\u4e8c\u53c9\u641c\u7d22\u6811\uff08BST\uff09\u548c\u6700\u5c0f\u5806\u7684\u7279\u6027\u3002\u5b83\u7684\u5b9e\u73b0\u76f8\u5bf9\u7b80\u5355\uff0c\u901a\u5e38\u7528\u4e8e\u9700\u8981\u540c\u65f6\u7ef4\u62a4\u5143\u7d20\u987a\u5e8f\u548c\u4f18\u5148\u7ea7\u7684\u60c5\u51b5\u3002<\/p>\n

Treap\u7684\u7406\u8bba\u89e3\u91ca<\/h1>\n

Treap\u7684\u6bcf\u4e2a\u8282\u70b9\u5305\u542b\u4e24\u4e2a\u5c5e\u6027\uff1a\u4e00\u4e2a\u952e\u503c\u548c\u4e00\u4e2a\u968f\u673a\u4f18\u5148\u7ea7\u3002\u5b83\u6ee1\u8db3\u4ee5\u4e0b\u4e24\u4e2a\u6027\u8d28\uff1a
\nBST\u6027\u8d28\uff1a \u6bcf\u4e2a\u8282\u70b9\u7684\u5de6\u5b50\u6811\u4e2d\u7684\u952e\u503c\u5c0f\u4e8e\u8be5\u8282\u70b9\u7684\u952e\u503c\uff0c\u53f3\u5b50\u6811\u4e2d\u7684\u952e\u503c\u5927\u4e8e\u8be5\u8282\u70b9\u7684\u952e\u503c\u3002
\n\u5806\u6027\u8d28\uff1a \u6bcf\u4e2a\u8282\u70b9\u7684\u4f18\u5148\u7ea7\u5927\u4e8e\u5176\u5b50\u8282\u70b9\u7684\u4f18\u5148\u7ea7\u3002
\n\u8fd9\u4e24\u4e2a\u6027\u8d28\u5171\u540c\u786e\u4fdd\u4e86Treap\u7684\u6709\u5e8f\u6027\u548c\u4f18\u5148\u7ea7\u6027\u3002<\/p>\n

Java\u4ee3\u7801\u5b9e\u73b0<\/h1>\n
import java.util.Random;\nclass Node {\n    int key, priority;\n    Node left, right;\n    Node(int key) {\n        this.key = key;\n        this.priority = new Random().nextInt(); \/\/ Assign random priority\n    }\n}\npublic class Treap {\n    Node root;\n    private Node leftRotate(Node node) {\n        Node newRoot = node.right;\n        node.right = newRoot.left;\n        newRoot.left = node;\n        return newRoot;\n    }\n    private Node rightRotate(Node node) {\n        Node newRoot = node.left;\n        node.left = newRoot.right;\n        newRoot.right = node;\n        return newRoot;\n    }\n    public Node insert(Node root, int key) {\n        if (root == null)\n            return new Node(key);\n        if (key <= root.key) {\n            root.left = insert(root.left, key);\n            if (root.left.priority > root.priority)\n                root = rightRotate(root);\n        } else {\n            root.right = insert(root.right, key);\n            if (root.right.priority > root.priority)\n                root = leftRotate(root);\n        }\n        return root;\n    }\n    public void insert(int key) {\n        root = insert(root, key);\n    }\n    \/\/ In-order traversal for testing\n    private void inOrderTraversal(Node node) {\n        if (node != null) {\n            inOrderTraversal(node.left);\n            System.out.print(node.key + " ");\n            inOrderTraversal(node.right);\n        }\n    }\n    public void inOrderTraversal() {\n        inOrderTraversal(root);\n    }\n    public static void main(String[] args) {\n        Treap treap = new Treap();\n        int[] testData = {5, 3, 7, 2, 4, 6, 8};\n        for (int key : testData)\n            treap.insert(key);\n        treap.inOrderTraversal();\n    }\n}<\/code><\/pre>\n
\u4f7f\u7528\u573a\u666f<\/h1>\n
\u4f18\u5148\u7ea7\u961f\u5217\uff1a Treap\u53ef\u4ee5\u7528\u4f5c\u4f18\u5148\u7ea7\u961f\u5217\uff0c\u5141\u8bb8\u4f60\u4ee5\u4e00\u79cd\u9ad8\u6548\u7684\u65b9\u5f0f\u63d2\u5165\u548c\u5220\u9664\u5177\u6709\u4e0d\u540c\u4f18\u5148\u7ea7\u7684\u5143\u7d20\u3002<\/p>\n
\u52a8\u6001\u4e2d\u4f4d\u6570\u67e5\u627e\uff1a \u5728\u4e00\u4e2a\u6570\u636e\u6d41\u4e2d\uff0cTreap\u53ef\u4ee5\u7528\u6765\u5b9e\u65f6\u67e5\u627e\u4e2d\u4f4d\u6570\uff0c\u56e0\u4e3a\u5b83\u7ef4\u62a4\u4e86\u6709\u5e8f\u6027\u548c\u4f18\u5148\u7ea7\u6027\u3002<\/p>\n
\u8303\u56f4\u67e5\u8be2\uff1a Treap\u5141\u8bb8\u9ad8\u6548\u5730\u6267\u884c\u8303\u56f4\u67e5\u8be2\uff0c\u5982\u67e5\u627e\u6240\u6709\u5728\u7ed9\u5b9a\u8303\u56f4\u5185\u7684\u5143\u7d20\u3002<\/p>\n
\u5e73\u8861\u6811\u66ff\u4ee3\uff1a \u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0cTreap\u53ef\u4ee5\u4f5c\u4e3a\u5e73\u8861\u6811\uff08\u5982AVL\u6811\u3001\u7ea2\u9ed1\u6811\uff09\u7684\u66ff\u4ee3\uff0c\u63d0\u4f9b\u8f83\u597d\u7684\u5e73\u8861\u6027\u80fd\u3002<\/p>\n
\u968f\u673a\u5316\u7b97\u6cd5\uff1a \u7531\u4e8eTreap\u7684\u4f18\u5148\u7ea7\u968f\u673a\u6027\uff0c\u5b83\u53ef\u4ee5\u7528\u4e8e\u8bbe\u8ba1\u968f\u673a\u5316\u7b97\u6cd5\u3002<\/p>\n
\u4f18\u5148\u7ea7\u961f\u5217<\/h1>\n
import java.util.Random;\nclass Node {\n    int key, priority;\n    Node left, right;\n    Node(int key) {\n        this.key = key;\n        this.priority = new Random().nextInt(); \/\/ Assign random priority\n    }\n}\npublic class TreapPriorityQueue {\n    Node root;\n    \/\/ ...\uff08\u7701\u7565\u63d2\u5165\u3001\u65cb\u8f6c\u7b49\u65b9\u6cd5\uff0c\u4e0e\u524d\u9762\u7684\u4ee3\u7801\u76f8\u540c\uff09\n    public int extractMax() {\n        if (root == null)\n            throw new IllegalStateException("Priority queue is empty");\n        int maxKey = root.key;\n        root = merge(root.left, root.right);\n        return maxKey;\n    }\n    public static void main(String[] args) {\n        TreapPriorityQueue pq = new TreapPriorityQueue();\n        pq.insert(5);\n        pq.insert(3);\n        pq.insert(7);\n        pq.insert(2);\n        pq.insert(4);\n        while (!pq.isEmpty()) {\n            System.out.println("Extracted max: " + pq.extractMax());\n        }\n    }\n}<\/code><\/pre>\n
\u52a8\u6001\u4e2d\u4f4d\u6570\u67e5\u627e<\/h1>\n
\/\/ \u5728 TreapPriorityQueue \u7c7b\u4e2d\u6dfb\u52a0\u4ee5\u4e0b\u65b9\u6cd5\npublic int findMedian() {\n    if (root == null)\n        throw new IllegalStateException("Treap is empty");\n    int size = size(root.left) + 1;\n    if (size == (size(root) + 1) \/ 2)\n        return root.key;\n    else if (size > (size(root) + 1) \/ 2)\n        return findMedian(root.left);\n    else\n        return findMedian(root.right);\n}\npublic static void main(String[] args) {\n    TreapPriorityQueue pq = new TreapPriorityQueue();\n    pq.insert(5);\n    pq.insert(3);\n    pq.insert(7);\n    pq.insert(2);\n    pq.insert(4);\n    pq.insert(6);\n    pq.insert(8);\n    System.out.println("Median: " + pq.findMedian()); \/\/ Should output 5\n}<\/code><\/pre>\n
\u8303\u56f4\u67e5\u8be2<\/h1>\n
\/\/ \u5728 TreapPriorityQueue \u7c7b\u4e2d\u6dfb\u52a0\u4ee5\u4e0b\u65b9\u6cd5\npublic void rangeQuery(Node node, int low, int high) {\n    if (node == null)\n        return;\n    if (node.key >= low && node.key <= high) {\n        System.out.print(node.key + " ");\n        rangeQuery(node.left, low, high);\n        rangeQuery(node.right, low, high);\n    } else if (node.key < low)\n        rangeQuery(node.right, low, high);\n    else\n        rangeQuery(node.left, low, high);\n}\npublic void rangeQuery(int low, int high) {\n    rangeQuery(root, low, high);\n}\npublic static void main(String[] args) {\n    TreapPriorityQueue pq = new TreapPriorityQueue();\n    pq.insert(5);\n    pq.insert(3);\n    pq.insert(7);\n    pq.insert(2);\n    pq.insert(4);\n    pq.insert(6);\n    pq.insert(8);\n    System.out.print("Elements in range [4, 7]: ");\n    pq.rangeQuery(4, 7); \/\/ Should output 5 4 6 7\n}<\/code><\/pre>\n
\u5e73\u8861\u6811\u66ff\u4ee3<\/h1>\n
\/\/ \u5728 TreapPriorityQueue \u7c7b\u4e2d\u6dfb\u52a0\u4ee5\u4e0b\u65b9\u6cd5\npublic int getHeight(Node node) {\n    if (node == null)\n        return 0;\n    return Math.max(getHeight(node.left), getHeight(node.right)) + 1;\n}\npublic boolean isBalanced() {\n    return isBalanced(root);\n}\nprivate boolean isBalanced(Node node) {\n    if (node == null)\n        return true;\n    int balanceFactor = getHeight(node.left) - getHeight(node.right);\n    return Math.abs(balanceFactor) <= 1 && isBalanced(node.left) && isBalanced(node.right);\n}\npublic static void main(String[] args) {\n    TreapPriorityQueue pq = new TreapPriorityQueue();\n    pq.insert(5);\n    pq.insert(3);\n    pq.insert(7);\n    pq.insert(2);\n    pq.insert(4);\n    pq.insert(6);\n    pq.insert(8);\n    System.out.println("Is the Treap balanced? " + pq.isBalanced()); \/\/ Should output true\n}<\/code><\/pre>\n
\u968f\u673a\u5316\u7b97\u6cd5<\/h1>\n
\/\/ \u5728 TreapPriorityQueue \u7c7b\u4e2d\u6dfb\u52a0\u4ee5\u4e0b\u65b9\u6cd5\npublic void shuffle() {\n    List<Integer> keys = new ArrayList<>();\n    inOrderTraversalToList(root, keys);\n    Collections.shuffle(keys);\n    root = null;\n    for (int key : keys) {\n        insert(key);\n    }\n}\nprivate void inOrderTraversalToList(Node node, List<Integer> list) {\n    if (node != null) {\n        inOrderTraversalToList(node.left, list);\n        list.add(node.key);\n        inOrderTraversalToList(node.right, list);\n    }\n}\npublic static void main(String[] args) {\n    TreapPriorityQueue pq = new TreapPriorityQueue();\n    pq.insert(5);\n    pq.insert(3);\n    pq.insert(7);\n    pq.insert(2);\n    pq.insert(4);\n    pq.insert(6);\n    pq.insert(8);\n    System.out.print("Original order: ");\n    pq.inOrderTraversal(); \/\/ Should output ordered elements\n    pq.shuffle();\n    System.out.print("\\nShuffled order: ");\n    pq.inOrderTraversal(); \/\/ Should output shuffled elements\n}\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u524d\u8a00 Treap\uff08\u6811\u5806\uff09\u662f\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u540c\u65f6\u5177\u6709\u4e8c\u53c9\u641c\u7d22\u6811\uff08BST\uff09\u548c\u6700\u5c0f\u5806\u7684\u7279\u6027\u3002\u5b83\u7684\u5b9e\u73b0\u76f8\u5bf9\u7b80\u5355\uff0c\u901a\u5e38\u7528\u4e8e […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false},"categories":[1],"tags":[],"aioseo_notices":[],"yoast_head":"\nTreap\u7684\u7406\u8bba\u4e0eJava\u4ee3\u7801\u5b9e\u73b0 - \u672c\u7f51\u7ad9\u5206\u4eab\u7f16\u7a0b\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u7684bug<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/zhaocunwei.co.uk\/index.php\/2023\/08\/10\/treap\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Treap\u7684\u7406\u8bba\u4e0eJava\u4ee3\u7801\u5b9e\u73b0 - \u672c\u7f51\u7ad9\u5206\u4eab\u7f16\u7a0b\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u7684bug\" \/>\n<meta property=\"og:description\" content=\"\u524d\u8a00 Treap\uff08\u6811\u5806\uff09\u662f\u4e00\u79cd\u6570\u636e\u7ed3\u6784\uff0c\u540c\u65f6\u5177\u6709\u4e8c\u53c9\u641c\u7d22\u6811\uff08BST\uff09\u548c\u6700\u5c0f\u5806\u7684\u7279\u6027\u3002\u5b83\u7684\u5b9e\u73b0\u76f8\u5bf9\u7b80\u5355\uff0c\u901a\u5e38\u7528\u4e8e […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/zhaocunwei.co.uk\/index.php\/2023\/08\/10\/treap\/\" \/>\n<meta property=\"og:site_name\" content=\"\u672c\u7f51\u7ad9\u5206\u4eab\u7f16\u7a0b\u8fc7\u7a0b\u4e2d\u51fa\u73b0\u7684bug\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-10T01:59:15+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-08-10T02:22:12+00:00\" \/>\n<meta name=\"author\" content=\"\u603b\u662f\u5e78\u798f\u7684\u8001\u8c4c\u8c46\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u603b\u662f\u5e78\u798f\u7684\u8001\u8c4c\u8c46\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3\u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/zhaocunwei.co.uk\/index.php\/2023\/08\/10\/treap\/\",\"url\":\"https:\/\/zhaocunwei.co.uk\/index.php\/2023\/08\/10\/treap\/\",\"name\":\"Treap\u7684\u7406\u8bba\u4e0eJava\u4ee3\u7801\u5b9e\u73b0 - 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