{"id":209,"date":"2021-10-05T14:12:52","date_gmt":"2021-10-05T14:12:52","guid":{"rendered":"http:\/\/www.gislxz.top\/?p=209"},"modified":"2022-11-17T08:04:22","modified_gmt":"2022-11-17T08:04:22","slug":"%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84%ef%bc%889%ef%bc%89%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91","status":"publish","type":"post","link":"https:\/\/www.gislxz.com\/index.php\/2021\/10\/05\/%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84%ef%bc%889%ef%bc%89%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91\/","title":{"rendered":"\u6570\u636e\u7ed3\u6784\uff089\uff09\u4e8c\u53c9\u641c\u7d22\u6811"},"content":{"rendered":"\n

\u4e8c\u53c9\u67e5\u627e\u6811\uff08Binary Search Tree\uff09\uff0c\uff08\u53c8\uff1a\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u4e8c\u53c9\u6392\u5e8f\u6811\uff09\u5b83\u6216\u8005\u662f\u4e00\u68f5\u7a7a\u6811\uff0c\u6216\u8005\u662f\u5177\u6709\u4e0b\u5217\u6027\u8d28\u7684\u4e8c\u53c9\u6811\uff1a \u82e5\u5b83\u7684\u5de6\u5b50\u6811\u4e0d\u7a7a\uff0c\u5219\u5de6\u5b50\u6811\u4e0a\u6240\u6709\u7ed3\u70b9\u7684\u503c\u5747\u5c0f\u4e8e\u5b83\u7684\u6839\u7ed3\u70b9\u7684\u503c\uff1b \u82e5\u5b83\u7684\u53f3\u5b50\u6811\u4e0d\u7a7a\uff0c\u5219\u53f3\u5b50\u6811\u4e0a\u6240\u6709\u7ed3\u70b9\u7684\u503c\u5747\u5927\u4e8e\u5b83\u7684\u6839\u7ed3\u70b9\u7684\u503c\uff1b \u5b83\u7684\u5de6\u3001\u53f3\u5b50\u6811\u4e5f\u5206\u522b\u4e3a\u4e8c\u53c9\u6392\u5e8f\u6811\u3002\u4e8c\u53c9\u641c\u7d22\u6811\u4f5c\u4e3a\u4e00\u79cd\u7ecf\u5178\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u65e2\u6709\u94fe\u8868\u7684\u5feb\u901f\u63d2\u5165\u4e0e\u5220\u9664\u64cd\u4f5c\u7684\u7279\u70b9\uff0c\u53c8\u6709\u6570\u7ec4\u5feb\u901f\u67e5\u627e\u7684\u4f18\u52bf\uff1b\u6240\u4ee5\u5e94\u7528\u5341\u5206\u5e7f\u6cdb\uff0c\u4f8b\u5982\u5728\u6587\u4ef6\u7cfb\u7edf\u548c\u6570\u636e\u5e93\u7cfb\u7edf\u4e00\u822c\u4f1a\u91c7\u7528\u8fd9\u79cd\u6570\u636e\u7ed3\u6784\u8fdb\u884c\u9ad8\u6548\u7387\u7684\u6392\u5e8f\u4e0e\u68c0\u7d22\u64cd\u4f5c\u3002<\/p>\n\n\n\n

\u5982\u679c\u5728\u6bcf\u4e2a\u8282\u70b9\u6dfb\u52a0\u4e00\u4e2aleftSize\u57df\u8bb0\u5f55\u8be5\u8282\u70b9\u7684\u5de6\u5b50\u6811\u5143\u7d20\u4e2a\u6570\uff0c\u90a3\u4e48\u5c31\u5f97\u5230\u4e86\u7d22\u5f15\u4e8c\u53c9\u641c\u7d22\u6811\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e \u4e8c\u53c9\u641c\u7d22\u6811 \uff0c\u4e00\u822c\u9700\u8981\u5b9e\u73b0\u7684\u662f\u67e5\u627e\uff0c\u63d2\u5165\uff0c\u5220\u9664\u548c\u6309\u5e8f\u8f93\u51fa\u56db\u4e2a\u64cd\u4f5c\uff0c\u800c\u7d22\u5f15\u4e8c\u53c9\u641c\u7d22\u6811\u7531\u4e8eleftSize\u7684\u5b58\u5728\uff0c\u591a\u5177\u6709\u4e00\u4e2a\u8fd4\u56de\u7b2cindex\u7684\u6570\u5bf9\u529f\u80fd\u3002<\/p>\n\n\n\n

\u5728\u5b9e\u73b0\u4e8c\u53c9\u641c\u7d22\u6811\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u7ee7\u627f\u539f\u6709\u7684\u94fe\u8868\u63cf\u8ff0\u7684\u4e8c\u53c9\u6811\u7c7b\uff1alinkedBinaryTree\uff08\u6570\u636e\u7ed3\u6784\uff087\uff09\u4e8c\u53c9\u6811 \u2013 giser\u5431\u5431\u7684\u5c0f\u7ad9 (gislxz.top)<\/a>\uff09<\/p>\n\n\n\n

\u4f46\u662f\u539f\u6709\u7684\u4e8c\u53c9\u6811\u7c7b\u5b9a\u4e49\u65f6\u8282\u70b9\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\uff0c\u800c\u4e8c\u53c9\u641c\u7d22\u6811\u6bcf\u4e2a\u8282\u70b9\u662f\u5173\u952e\u5b57\u548c\u5143\u7d20\u503c\u3002\u4f46\u5e78\u597d\u6211\u4eec\u5e73\u65f6\u5b9a\u4e49\u65f6\u7528\u7684\u90fd\u662ftemplate\u6a21\u677f\u51fd\u6570\uff0c\u4f7f\u7528pair\u5076\u5bf9\u5373\u53ef\u5c06\u539f\u6765\u5355\u4e00\u5143\u7d20\u6269\u5c55\u51fa\u4e24\u4e2a\u4f4d\u7f6e\u7ed9\u7d22\u5f15\u548c\u771f\u6b63\u7684\u5143\u7d20\u503c<\/p>\n\n\n\n

\/\/\u4e8c\u53c9\u6811\u8282\u70b9\u7684\u5b9a\u4e49\ntemplate <class T>\nstruct binaryTreeNode\n{\n    T element;\/\/\u641c\u7d22\u4e8c\u53c9\u6811\u7528pair\u6765\u5b58\u50a8\u5173\u952e\u5b57\u548c\u5143\u7d20\n    binaryTreeNode<T>* leftChild,   \/\/ left subtree\n        * rightChild;  \/\/ right subtree\n\n    binaryTreeNode() { leftChild = rightChild = NULL; }\n    binaryTreeNode(const T& theElement) :element(theElement)\n    {\n        leftChild = rightChild = NULL;\n    }\n    binaryTreeNode(const T& theElement,\n        binaryTreeNode* theLeftChild,\n        binaryTreeNode* theRightChild)\n        :element(theElement)\n    {\n        leftChild = theLeftChild;\n        rightChild = theRightChild;\n    }\n};\n<\/code><\/pre>\n\n\n\n
\/\/\u641c\u7d22\u4e8c\u53c9\u6811\u7684\u5b9a\u4e49\ntemplate<class K, class E>\nclass binarySearchTree : public bsTree<K, E>,\/\/\u7ee7\u627f\u641c\u7d22\u4e8c\u53c9\u6811\u7684\u62bd\u8c61\u7c7b\uff0c\u4e0d\u7ee7\u627f\u4e5f\u53ef\u4ee5\u8fd0\u884c\n    public linkedBinaryTree<pair<const K, E> >\/\/\u7ee7\u627f\u94fe\u8868\u5b9e\u73b0\u7684\u4e8c\u53c9\u6811\u7c7b\npublic:\n    \/\/ methods of dictionary\n    bool empty() const { return treeSize == 0; }\n    int size() const { return treeSize; }\n    pair<const K, E>* find(const K& theKey) const;\n    void insert(const pair<const K, E>& thePair);\n    void erase(const K& theKey);\n\n    \/\/ additional method of bsTree\n    void ascend() { inOrderOutput(); }\n};\n<\/code><\/pre>\n\n\n\n
pair\u7ed3\u6784\u7684\u4ecb\u7ecd<\/p>\n\n\n\n
(11\u6761\u6d88\u606f) C++ pair\u7684\u57fa\u672c\u7528\u6cd5\u603b\u7ed3\uff08\u6574\u7406\uff09_sevenjoin\u7684\u535a\u5ba2-CSDN\u535a\u5ba2_c++ pair<\/a><\/p>\n\n\n\n
\u641c\u7d22\u4e8c\u53c9\u6811\u6700\u6838\u5fc3\u7684\u529f\u80fd\u4e00\u5b9a\u662f\u641c\u7d22\uff0c\u57fa\u4e8e\u641c\u7d22\u6811\u7684\u7279\u6027\uff0c\u6211\u4eec\u53ea\u8981\u6bd4\u8f83\u67e5\u627e\u7684\u5173\u952e\u5b57\u4e0e\u5f53\u524d\u8282\u70b9\u5173\u952e\u5b57\u7684\u5927\u5c0f\u5373\u53ef\uff0c\u5982\u679c\u76f8\u540c\u5c31\u627e\u5230\u4e86\uff0c\u5c0f\u5c31\u53bb\u5de6\u8282\u70b9\uff0c\u5927\u5c31\u53bb\u53f3\u8282\u70b9\uff0c\u76f4\u5230\u67e5\u5230\u6216\u8005\u5230\u5e95\u8fd4\u56de\u4e0d\u5b58\u5728\u8be5\u5143\u7d20\u3002\u6ce8\u610f\u8fd4\u56de\u7684\u662fpair\u6307\u9488<\/p>\n\n\n\n
template<class K, class E>\npair<const K, E>* binarySearchTree<K, E>::find(const K& theKey) const\n{\/\/ Return pointer to matching pair.\n \/\/ Return NULL if no matching pair.\n   \/\/ p starts at the root and moves through\n   \/\/ the tree looking for an element with key theKey\n    binaryTreeNode<pair<const K, E> >* p = root;\/\/\u590d\u5236\u6839\u8282\u70b9\n    while (p != NULL)\n        \/\/ examine p->element\n        if (theKey < p->element.first)\n            p = p->leftChild;\n        else\n            if (theKey > p->element.first)\n                p = p->rightChild;\n            else \/\/ found matching pair\n                return &p->element;\n\n    \/\/ no matching pair\n    return NULL;\n}<\/code><\/pre>\n\n\n\n
\u63d2\u5165\u64cd\u4f5c\u4e0e\u641c\u7d22\u76f8\u4f3c\uff0c\u901a\u8fc7\u6bd4\u8f83\u63d2\u5165\u5173\u952e\u5b57\u518d\u53bb\u5411\u5b50\u8282\u70b9\uff0c\u76f4\u5230\u4e0d\u5b58\u5728\u76f8\u5e94\u7684\u5b50\u8282\u70b9\u5c31\u5efa\u7acb\u5b50\u8282\u70b9\u63d2\u5165\uff0c\u5982\u679c\u8fc7\u7a0b\u4e2d\u53d1\u73b0\u5173\u952e\u5b57\u5df2\u5b58\u5728\u5c31\u4fee\u6539\u5bf9\u5e94\u5143\u7d20\u503c\u3002<\/p>\n\n\n\n
\u4ee3\u7801\u7ec6\u8282\u662f\u5efa\u7acb*p\u548c*pp\u4e24\u4e2apair\u6307\u9488\uff0c\u4e00\u4e2a\u6307\u5411\u5b50\u8282\u70b9\uff0c\u4e00\u4e2a\u6162\u4e00\u6b65\u7559\u5728\u7236\u8282\u70b9\u3002<\/p>\n\n\n\n
\u7279\u522b\u6ce8\u610f\u63d2\u5165\u65b0\u8282\u70b9\u65f6\u68c0\u67e5\u662f\u5426\u5b58\u5728\u6839\u8282\u70b9<\/p>\n\n\n\n
template<class K, class E>\nvoid binarySearchTree<K, E>::insert(const pair<const K, E>& thePair)\n{\/\/ Insert thePair into the tree. Overwrite existing\n \/\/ pair, if any, with same key.\n   \/\/ find place to insert\n    binaryTreeNode<pair<const K, E> >* p = root,\/\/p\u5148\u590d\u5236\u6839\u8282\u70b9\n        * pp = NULL;\n    while (p != NULL)\n    {\/\/ examine p->element\n        pp = p;\/\/pp\u6bd4p\u6162\u4e00\u6b65\uff0c\u505c\u7559\u5728\u7236\u8282\u70b9\n        \/\/ move p to a child\n        if (thePair.first < p->element.first)\n            p = p->leftChild;\n        else\n            if (thePair.first > p->element.first)\n                p = p->rightChild;\n            else\n            {\/\/ replace old value\n                p->element.second = thePair.second;\n                return;\n            }\n    }\n\n    \/\/ get a node for thePair and attach to pp\n    binaryTreeNode<pair<const K, E> >* newNode\n        = new binaryTreeNode<pair<const K, E> >(thePair);\n    if (root != NULL) \/\/ the tree is not empty\n        if (thePair.first < pp->element.first)\n            pp->leftChild = newNode;\n        else\n            pp->rightChild = newNode;\n    else\n        root = newNode; \/\/ insertion into empty tree\n    treeSize++;\n}<\/code><\/pre>\n\n\n\n
\u5220\u9664\u64cd\u4f5c\u7a0d\u590d\u6742\uff0c\u5982\u679c\u5220\u9664\u7684\u8282\u70b9\u53ea\u662f\u6811\u53f6\u6216\u8005\u53ea\u6709\u4e00\u9897\u5b50\u6811\u90a3\u4e48\u5f88\u7b80\u5355\uff0c\u5982\u679c\u6709\u4e24\u68f5\u5b50\u6811\u5c31\u590d\u6742\u4e00\u4e9b\u3002\u4e0b\u9762\u5206\u522b\u8ba8\u8bba<\/p>\n\n\n\n
1.\u662f\u6811\u53f6\uff0c\u5c31\u5c06\u7236\u8282\u70b9\u6307\u5411\u8be5\u8282\u70b9\u8bbe\u4e3aNULL\u518d\u91ca\u653e\u6b64\u8282\u70b9\u3002\u5982\u679c\u8be5\u8282\u70b9\u662f\u6839\u8282\u70b9\u5c31\u8bbe\u8be5\u6811\u7684\u6839\u8282\u70b9\u4e3aNULL\u7136\u540e\u91ca\u653e\u8be5\u8282\u70b9\u3002<\/p>\n\n\n\n
2.\u4ec5\u6709\u4e00\u4e2a\u5b50\u6811\u3002\u5982\u679c\u662f\u6839\u8282\u70b9\u5c31\u8bbe\u5176\u5b50\u6811\u4e3a\u6839\u8282\u70b9\uff0c\u5982\u679c\u4e0d\u662f\u6839\u8282\u70b9\u5219\u4fee\u6539\u5176\u7236\u8282\u70b9\u7684\u6307\u9488\u6307\u5411\u8be5\u8282\u70b9\u7684\u5b50\u6811\u3002<\/p>\n\n\n\n
3.\u5982\u679c\u6709\u4e24\u4e2a\u5b50\u6811\uff0c\u5c31\u5c06\u8be5\u8282\u70b9\u7684\u5143\u7d20\u66ff\u6362\u6210\u5de6\u5b50\u6811\u6700\u5927\u7684\u5143\u7d20\u6216\u53f3\u5b50\u6811\u6700\u5c0f\u7684\u5143\u7d20\uff0c\u7136\u540e\u628a\u88ab\u66ff\u6362\u7684\u5143\u7d20\u8282\u70b9\u5220\u9664\u3002\u81f3\u4e8e\u67e5\u627e\u6700\u5927\u5143\u7d20\u6216\u6700\u5c0f\u5143\u7d20\u5f88\u7b80\u5355\uff0c\u6bd4\u5982\u67e5\u627e\u5de6\u5b50\u6811\u6700\u5927\u7684\u5143\u7d20\u5c31\u5148\u8ba9\u5f53\u524d\u6307\u9488\u5230\u5230\u5de6\u5b69\u5b50\uff0c\u7136\u540e\u518d\u5bf9\u7740\u53f3\u5b69\u5b50\u4e00\u8def\u67e5\u4e0b\u53bb\u76f4\u5230\u6ca1\u6709\u53f3\u5b69\u5b50\u4e3a\u6b62\u3002 <\/p>\n\n\n\n
\u5b9e\u9645\u5b9e\u73b0\u8fc7\u7a0b\u548c\u63d2\u5165\u7c7b\u4f3c\uff0c*p\u548c*pp\u4e24\u4e2apair\u6307\u9488\uff0c\u4e00\u4e2a\u6307\u5411\u5b50\u8282\u70b9\uff0c\u4e00\u4e2a\u6162\u4e00\u6b65\u7559\u5728\u5f53\u524d\u8282\u70b9\u3002<\/p>\n\n\n\n
template<class K, class E>\nvoid binarySearchTree<K, E>::erase(const K& theKey)\n{\/\/ Delete the pair, if any, whose key equals theKey.\n\n   \/\/ \u5148\u79fb\u52a8\u5230\u9700\u88ab\u5220\u9664\u7684\u8282\u70b9\n    binaryTreeNode<pair<const K, E> >* p = root,\n        * pp = NULL;\n    while (p != NULL && p->element.first != theKey)\n    {\/\/ move to a child of p\n        pp = p;\n        if (theKey < p->element.first)\n            p = p->leftChild;\n        else\n            p = p->rightChild;\n    }\n    if (p == NULL)\n        return; \/\/ no pair with key theKey\n\n     \/\/ restructure tree\n     \/\/ \u5904\u7406\u4e24\u68f5\u5b50\u6811\u5747\u4e0d\u4e3a\u7a7a\u7684\u60c5\u51b5\n    if (p->leftChild != NULL && p->rightChild != NULL)\n    {\/\/ two children\n       \/\/ convert to zero or one child case\n       \/\/ find largest element in left subtree of p\n        binaryTreeNode<pair<const K, E> >* s = p->leftChild,\n            * ps = p;  \/\/ parent of s\n        while (s->rightChild != NULL)\n        {\/\/ move to larger element\n            ps = s;\n            s = s->rightChild;\n        }\n\n        \/\/ move largest from s to p, can't do a simple move\n        \/\/ p->element = s->element as key is const\n        binaryTreeNode<pair<const K, E> >* q =\n            new binaryTreeNode<pair<const K, E> >\n            (s->element, p->leftChild, p->rightChild);\n        if (pp == NULL)\n            root = q;\n        else if (p == pp->leftChild)\n            pp->leftChild = q;\n        else\n            pp->rightChild = q;\n        if (ps == p) pp = q;\n        else pp = ps;\n        delete p;\n        p = s;\n    }\n\n    \/\/ p has at most one child\n    \/\/ save child pointer in c\n    binaryTreeNode<pair<const K, E> >* c;\n    if (p->leftChild != NULL)\n        c = p->leftChild;\n    else\n        c = p->rightChild;\n\n    \/\/ delete p\n    if (p == root)\n        root = c;\n    else\n    {\/\/ is p left or right child of pp?\n        if (p == pp->leftChild)\n            pp->leftChild = c;\n        else pp->rightChild = c;\n    }\n    treeSize--;\n    delete p;\n}<\/code><\/pre>\n\n\n\n
\u8fd9\u6bb5\u4ee3\u7801\u5199\u7684\u975e\u5e38\u5999\uff0c\u4f46\u6709\u4e00\u90e8\u5206\u4e5f\u6709\u4e9b\u96be\u61c2\u3002<\/p>\n\n\n\n
 if (pp == NULL)\n            root = q;\n        else if (p == pp->leftChild)\n            pp->leftChild = q;\n        else\n            pp->rightChild = q;\n        if (ps == p) pp = q;\n        else pp = ps;\n        delete p;\n        p = s;<\/code><\/pre>\n\n\n\n
\u8fd9\u4e00\u90e8\u5206\u4e4d\u770b\u5b8c\u5168\u770b\u4e0d\u61c2\u5728\u5e72\u561b\uff0c\u5176\u5b9e\u662f\u4e3a\u4e86\u548c\u540e\u9762\u8ba8\u8bba\u5355\u5b50\u8282\u70b9\u6216\u65e0\u5b50\u8282\u70b9\u65f6\u4e00\u5e76\u5904\u7406\u3002\u65b0\u624b\u5206\u7c7b\u8ba8\u8bba\u65f6\u4e00\u5b9a\u662fif\uff08\u65e0\u5b50\u8282\u70b9\uff09\uff0celse if\uff08\u5355\u5b50\u7ed3\u70b9\uff09\uff0celse\uff08\u53cc\u5b50\u8282\u70b9\uff09\u4e09\u5927\u6bb5\u5199\u5b8c\uff0c\u4f46\u662f\u4e66\u4e0a\u8fd9\u6837\u5199\u9996\u5148\u628a\u5355\u5b50\u7ed3\u70b9\u548c\u65e0\u5b50\u8282\u70b9\u7edf\u4e00\u5904\u7406\uff0c\u5728\u901a\u8fc7\u4e0a\u9762\u8fd9\u6bb5\u4ee3\u7801\u628a\u539f\u6765\u53cc\u5b50\u8282\u70b9\u540e\u534a\u6bb5\u7684\u5220\u9664\u64cd\u4f5c\u4ea4\u7531\u5355\u5b50\u8282\u70b9\u548c\u65e0\u5b50\u8282\u70b9\u4ee3\u7801\u6bb5\u4e00\u5e76\u5904\u7406\u3002 <\/p>\n\n\n\n
\"\"
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