{"id":200,"date":"2021-09-27T19:24:02","date_gmt":"2021-09-27T11:24:02","guid":{"rendered":"http:\/\/www.gislxz.top\/?p=200"},"modified":"2022-08-20T16:39:08","modified_gmt":"2022-08-20T08:39:08","slug":"%e4%bc%98%e5%85%88%e7%ba%a7%e9%98%9f%e5%88%97","status":"publish","type":"post","link":"https:\/\/www.gislxz.com\/index.php\/2021\/09\/27\/%e4%bc%98%e5%85%88%e7%ba%a7%e9%98%9f%e5%88%97\/","title":{"rendered":"\u6570\u636e\u7ed3\u6784\uff088\uff09\u4f18\u5148\u7ea7\u961f\u5217"},"content":{"rendered":"\n

\u961f\u5217\u662f\u4e00\u79cd\u7279\u5f81\u4e3aFIFO\u7684\u6570\u636e\u7ed3\u6784\uff0c\u6bcf\u6b21\u4ece\u961f\u5217\u4e2d\u53d6\u51fa\u7684\u662f\u6700\u65e9\u52a0\u5165\u961f\u5217\u4e2d\u7684\u5143\u7d20\u3002\u4f46\u662f\uff0c\u8bb8\u591a\u5e94\u7528\u9700\u8981\u53e6\u4e00\u79cd\u961f\u5217\uff0c\u6bcf\u6b21\u4ece\u961f\u5217\u4e2d\u53d6\u51fa\u7684\u5e94\u662f\u5177\u6709\u6700\u9ad8\u4f18\u5148\u6743\u7684\u5143\u7d20\uff0c\u8fd9\u79cd\u961f\u5217\u5c31\u662f\u4f18\u5148\u7ea7\u961f\u5217(Priority Queue)\uff0c\u4e5f\u79f0\u4e3a\u4f18\u5148\u6743\u961f\u5217\u3002<\/strong><\/p>\n\n\n\n

\u4f18\u5148\u7ea7\u961f\u5217\u6709\u5f88\u591a\u5b9e\u73b0\u65b9\u6848\uff0c\u6700\u5e38\u7528\u7684\u662f\u5806\uff0c\u5206\u4e3a\u5927\u9876\u5806\/\u5c0f\u9876\u5806\uff08\u5927\u6839\u5806\/\u5c0f\u6839\u5806\uff09\uff0c\u7b80\u5355\u6765\u8bf4\u5c31\u662f\u8282\u70b9\u7684\u503c\u5927\u4e8e\/\u5c0f\u4e8e\u5b50\u8282\u70b9\u7684\u503c\u3002<\/p>\n\n\n\n

\u7279\u522b\u6ce8\u610f\u5806\u5fc5\u987b\u662f\u5b8c\u5168\u4e8c\u53c9\u6811\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u56e0\u4e3a\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u7279\u6b8a\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u6570\u7ec4\u6765\u5b58\u50a8\u5806\uff0c\u4ee5\u6b64\u4e3a\u57fa\u7840\u6765\u5199\u5927\u9876\u5806\u7684class\u3002<\/p>\n\n\n\n

\u9996\u5148\u5728\u5934\u6587\u4ef6\u91cc\u5b9a\u4e49maxHeap\u7c7b\uff0c\u6ce8\u610f\u6570\u7ec4\u4ece\u30101\u3011\u5f00\u59cb\u5b58\u50a8\uff0c\u30100\u3011\u7a7a\u7740\uff0c\u56e0\u4e3a\u8fd9\u6837\u5de6\u5b50\u8282\u70b9\u4e0e\u7236\u8282\u70b9\u5728\u5e8f\u53f7\u4e0a\u521a\u597d\u5c31\u662f\u4e24\u500d\u5173\u7cfb<\/p>\n\n\n\n

template<class T>\nclass maxHeap\n{\npublic:\n    maxHeap(int initialCapacity = 10);\/\/\u6784\u9020\u51fd\u6570\uff0c\u9ed8\u8ba4\u5143\u7d20\u4e2a\u6570\u4e3a10\n    ~maxHeap() { delete[] heap; }\/\/\u6790\u6784\u51fd\u6570\uff0c\u628a\u5b58\u50a8\u5143\u7d20\u7684\u6570\u7ec4\u5220\u9664\n    bool empty() const { return heapSize == 0; }\/\/\u5224\u65ad\u662f\u5426\u4e3a\u7a7a\n    int size() const\/\/\u8fd4\u56de\u5143\u7d20\u4e2a\u6570\n    {\n        return heapSize;\n    }\n    const T& top()\/\/\u8fd4\u56de\u6700\u5927\u7684\u5143\u7d20\uff08\u7b2c\u4e00\u4e2a\u5143\u7d20\uff09\n    {\/\/ return max element\n        if (heapSize == 0)\n            throw queueEmpty();\n        return heap[1];\/\/\u6570\u7ec4\u9996\u5143\u7d20\u4e3a\u7a7a\n    }\n    void pop();\/\/\u5220\u9664\u6700\u5927\u5143\u7d20\n    void push(const T&);\/\/\u63d2\u5165\u5143\u7d20\n    void initialize(T*, int);\/\/\u521d\u59cb\u5316\uff08\u63a5\u53d7\u4e00\u4e2a\u6570\u7ec4\uff0c\u5e76\u5c06\u5176\u521d\u59cb\u5316\u4e3a\u5927\u9876\u5806\uff09\n    void deactivateArray()\/\/\u91cd\u7f6e\n    {\n        heap = NULL; arrayLength = heapSize = 0;\n    }\n    void output(ostream& out) const;\/\/\u8f93\u51fa\nprivate:\n    int heapSize;       \/\/ \u5143\u7d20\u4e2a\u6570\n    int arrayLength;    \/\/ \u957f\u5ea6\uff08\u5bb9\u91cf+1\uff09\n    T* heap;            \/\/ \u5b58\u50a8\u5143\u7d20\u7684\u6570\u7ec4\n};\n\n\/*-----------------\u6784\u9020\u51fd\u6570------------------*\/\ntemplate<class T>\nmaxHeap<T>::maxHeap(int initialCapacity)\n{\/\/ Constructor.\n    if (initialCapacity < 1)\n    {\n        ostringstream s;\n        s << \"Initial capacity = \" << initialCapacity << \" Must be > 0\";\n        throw illegalParameterValue(s.str());\n    }\n    arrayLength = initialCapacity + 1;\n    heap = new T[arrayLength];\n    heapSize = 0;\n}\n\n<\/code><\/pre>\n\n\n\n
 \u4e0b\u9762\u6765\u5177\u4f53\u5b9e\u73b0\u5404\u4e2a\u529f\u80fd\uff0c\u5305\u62ec\u63d2\u5165\uff0c\u5220\u9664\uff0c\u521d\u59cb\u5316\u3002<\/p>\n\n\n\n
\u4e2a\u4eba\u7406\u89e3\uff1a\u5806\u7684\u64cd\u4f5c\u5c31\u662f\u57fa\u4e8e\u5b8c\u5168\u4e8c\u53c9\u6811\u4e3a\u57fa\u7840\u7684\uff0c\u4e0d\u7ba1\u63d2\u5165\u8fd8\u662f\u5220\u9664\u90fd\u8981\u4fdd\u91cd\u6811\u59cb\u7ec8\u6ee1\u8db3\u5b8c\u5168\u4e8c\u53c9\u6811\u7684\u6761\u4ef6<\/p>\n\n\n\n
\u63d2\u5165\u64cd\u4f5c\u76f8\u5bf9\u7b80\u5355\uff0c\u5c31\u662f\u4ece\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u540e\u9762\u65b0\u5efa\u4e00\u4e2a\u8282\u70b9\uff0c\u7136\u540e\u548c\u7236\u8282\u70b9\u6bd4\u8f83\u662f\u5426\u9700\u8981\u4ea4\u6362\uff0c\u4ea4\u6362\u540e\u518d\u6b21\u5224\u65ad\u76f4\u5230\u5c0f\u4e8e\u7236\u8282\u70b9\u6216\u8005\u5230\u9876\u4e3a\u6b62\u3002<\/p>\n\n\n\n
template<class T>\nvoid maxHeap<T>::push(const T& theElement)\/\/\u63d2\u5165\u5143\u7d20\n{\n\n   \/\/ \u9996\u5148\u5224\u65ad\u6570\u7ec4\u957f\u5ea6\u662f\u5426\u8db3\u591f\n    if (heapSize == arrayLength - 1)\n    {\n        changeLength1D(heap, arrayLength, 2 * arrayLength);\/\/\u8be5\u51fd\u6570\u89c1\u300a\u7ebf\u6027\u8868-\u6570\u7ec4\u5b9e\u73b0\u300b\n        arrayLength *= 2;\n    }\n\n    \/\/\u67e5\u627e\u5e94\u8be5\u63d2\u5165\u7684\u4f4d\u7f6e\n    int currentNode = ++heapSize;\/\/\u5148\u7ed9\u5143\u7d20\u4e2a\u6570+1\uff0c\u7136\u540e\u4ece\u6700\u540e\u4e00\u4f4d\u5f00\u59cb\u67e5\n    while (currentNode != 1 && heap[currentNode \/ 2] < theElement)\/\/\u5982\u679c\u6ca1\u5230\u9876\u4e14\u6bd4\u7236\u8282\u70b9\u7684\u5143\u7d20\u5927\n    {\n        heap[currentNode] = heap[currentNode \/ 2]; \/\/ \u628a\u7236\u8282\u70b9\u7684\u5143\u7d20\u79fb\u4e0b\u6765\n        currentNode \/= 2;                          \/\/\u5f53\u524d\u5143\u7d20\u5e8f\u53f7\u79fb\u5230\u7236\u8282\u70b9\n    }\n\n    heap[currentNode] = theElement;\n}<\/code><\/pre>\n\n\n\n
\u5220\u9664\u64cd\u4f5c\u590d\u6742\u4e00\u70b9\u3002\u5220\u9664\u64cd\u4f5c\u5c31\u662f\u5220\u9664\u9996\u4e2a\u5143\u7d20\uff0c\u5373\u6700\u5927\u7684\u5143\u7d20\u3002<\/p>\n\n\n\n
\u5177\u4f53\u6b65\u9aa4\u4e3a\uff1a <\/p>\n\n\n\n
1.\u5220\u9664\u9996\u8282\u70b9\u7684\u503c <\/p>\n\n\n\n
2.\u63d0\u53d6\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7684\u503c\u518d\u5220\u9664\u6700\u540e\u7684\u8282\u70b9\uff0c\u5143\u7d20\u4e2a\u6570-1 <\/p>\n\n\n\n
3.\u4ece\u6839\u8282\u70b9\u5f00\u59cb\uff0c\u9009\u51fa\u8f83\u5927\u7684\u5b50\u8282\u70b9\uff0c\u5c06\u503c\u8d4b\u4e88\u7236\u8282\u70b9\uff08\u7236\u8282\u70b9\u73b0\u5728\u6ca1\u6709\u503c\uff09\uff0c\u5c06\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7684\u503c\u4e0e\u5f53\u524d\u8282\u70b9\uff08\u9009\u51fa\u7684\u8f83\u5927\u5b50\u8282\u70b9\uff09\u7684\u8f83\u5927\u5b50\u8282\u70b9\u6bd4\u8f83\u5927\u5c0f\uff0c\u5982\u679c\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5927\u5c31\u76f4\u63a5\u586b\u5728\u8fd9\u4e2a\u8282\u70b9\u4e0a\uff0c\u5982\u679c\u5b50\u8282\u70b9\u5927\u5c31\u91cd\u590d\u64cd\u4f5c\u518d\u5411\u4e0b\u4e00\u5c42\u6bd4\u8f83\uff0c\u76f4\u5230\u6bd4\u5b50\u8282\u70b9\u5927\u6216\u8005\u5230\u8fbe\u6700\u540e\u4e00\u5c42\u3002 <\/p>\n\n\n\n
template<class T>\nvoid maxHeap<T>::pop()\/\/\u5220\u9664\u5143\u7d20\n{\n   \/\/\u68c0\u67e5\u6570\u7ec4\u662f\u5426\u4e3a\u7a7a\n    if (heapSize == 0)\n        throw queueEmpty();\n\n    \/\/\u628a\u9996\u5143\u7d20\u6790\u6784\n    heap[1].~T();\n\n    \/\/ \u53d6\u51fa\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u5e76\u4f7f\u5143\u7d20\u4e2a\u6570-1\n    T lastElement = heap[heapSize--];\n\n    \/\/ \n    int currentNode = 1,\/\/\u5f53\u524d\u7236\u8282\u70b9\n        child = 2;     \/\/ \u5f53\u524d\u5b50\u8282\u70b9\uff08\u9ed8\u8ba4\u5de6\u8282\u70b9\uff09\n    while (child <= heapSize)\/\/\u5982\u679c\u5b50\u8282\u70b9\u5e8f\u53f7\u5927\u4e8e\u5143\u7d20\u4e2a\u6570\uff0c\u8bf4\u660e\u5230\u5e95\u4e86\uff0c\u9000\u51fa\n    {\n        \/\/ \u5224\u65ad\u5de6\u53f3\u8282\u70b9\u54ea\u4e2a\u5927\n        if (child < heapSize && heap[child] < heap[child + 1])\n            child++;\/\/\u5982\u679c\u53f3\u5b50\u8282\u70b9\u5927\u5c31\u5207\u6362\u5230\u53f3\u5b50\u8282\u70b9\n\n        \/\/ \u6700\u540e\u4e00\u4e2a\u5143\u7d20\u662f\u5426\u6bd4\u5f53\u524d\u5b50\u8282\u70b9\u5927\n        if (lastElement >= heap[child])\n            break;   \/\/\u6bd4\u5f53\u524d\u5b50\u8282\u70b9\u5927\u5c31\u76f4\u63a5\u9000\u51fa\u5faa\u73af\n\n        heap[currentNode] = heap[child]; \/\/ \u4ea4\u6362\u7236\u5b50\u8282\u70b9\n        currentNode = child;             \/\/ \u5f53\u524d\u7236\u8282\u70b9\u5e8f\u53f7\u5207\u6362\u5230\u5b50\u8282\u70b9\n        child *= 2;                      \/\/ \u5b50\u8282\u70b9\u5e8f\u53f7\u5207\u6362\u5230\u5de6\u5b50\u8282\u70b9\n    }\n    heap[currentNode] = lastElement;\n}<\/code><\/pre>\n\n\n\n
\u6700\u540e\u662f\u521d\u59cb\u5316\u51fd\u6570\uff0c\u8bfb\u53d6\u4e00\u4e2a\u6570\u7ec4\uff0c\u5e76\u5c06\u5176\u8f6c\u5316\u6210\u5927\u9876\u5806\u6761\u4ef6\u7684\u6570\u7ec4<\/p>\n\n\n\n
\u539f\u7406\u4e5f\u4e0d\u590d\u6742\uff0c\u4ece\u6700\u540e\u4e00\u4e2a\u6709\u5b50\u8282\u70b9\uff08heapsize\/2\u53d6\u6574\uff09\u7684\u8282\u70b9\u5f00\u59cb\u68c0\u67e5\u662f\u5426\u6bd4\u5b50\u8282\u70b9\u5927\uff0c\u7136\u540e\u4f9d\u6b21\u68c0\u67e5\u524d\u4e00\u4e2a\u8282\u70b9\uff0c\u76f4\u5230\u6839\u8282\u70b9<\/p>\n\n\n\n
template<class T>\nvoid maxHeap<T>::initialize(T* theHeap, int theSize)\/\/\u521d\u59cb\u5316\n{\/\/ \u8bfb\u53d6\u6570\u7ec4theHeap[1:theSize]\u5e76\u6309\u7167\u5927\u9876\u5806\u7684\u8981\u6c42\u8fdb\u884c\u6392\u5e8f\n    delete[] heap;\/\/\u5220\u9664\u539f\u5b58\u50a8\u6570\u7ec4\n    heap = theHeap;\/\/\u590d\u5236\u8f93\u5165\u6570\u7ec4\u81f3\u5806\u7684\u5b58\u50a8\u6570\u7ec4\n    heapSize = theSize;\n\n    \/\/ \u4ece\u6700\u540e\u4e00\u4e2a\u6709\u5b69\u5b50\u7684\u8282\u70b9\u5f00\u59cb\u68c0\u67e5\n    for (int root = heapSize \/ 2; root >= 1; root--)\n    {\n        T rootElement = heap[root];\n\n        \/\/ \u5b69\u5b50\u7684\u5e8f\u53f7\u662f\u8282\u70b9\u7684\u4e24\u500d\n        int child = 2 * root; \n        while (child <= heapSize)\/\/\u662f\u5426\u5b58\u5728\u5b57\u8282\u70b9\n        {\n            \/\/ \u5982\u679c\u6709\u53f3\u5b50\u8282\u70b9\uff0c\u90a3\u4e48\u6bd4\u8f83\u5927\u5c0f\u5224\u65ad\u8c01\u5927\n            if (child < heapSize && heap[child] < heap[child + 1])\n                child++;\n\n            \/\/ \u662f\u5426\u6bd4\u8f83\u5927\u7684\u5b69\u5b50\u8282\u70b9\u5927\n            if (rootElement >= heap[child])\n                break;  \/\/\u662f\u5c31\u9000\u51fa\uff0c\u4e0d\u9700\u8981\u64cd\u4f5c\n\n             \/\/ \u4e0d\u662f\u5c31\u4ea4\u6362\n            heap[child \/ 2] = heap[child]; \n            child *= 2;                    \n        }\n        heap[child \/ 2] = rootElement;\n    }\n}<\/code><\/pre>\n\n\n\n
\u5927\u9876\u5806\u7ed3\u6784\u7b80\u5355\uff0c\u6548\u7387\u5f88\u9ad8\uff0c\u5c5e\u4e8e\u9690\u5f0f\u6570\u636e\u7ed3\u6784\uff0c\u4f46\u662f\u5f53\u9762\u5bf9\u5408\u5e76\u64cd\u4f5c\u65f6\u663e\u5f97\u5c31\u4e0d\u662f\u5f88\u65b9\u4fbf\uff0c\u5f53\u5bf9\u8c61\u7ecf\u5e38\u9700\u8981\u5408\u5e76\u64cd\u4f5c\u65f6\u53ef\u4ee5\u4f7f\u7528\u5de6\u9ad8\u6811\u8fd9\u79cd\u7ed3\u6784\u3002<\/p>\n\n\n\n
\u9996\u5148\u5b9a\u4e49\u5916\u90e8\u8282\u70b9\uff0c\u5373\u5728\u73b0\u6709\u7684\u4e8c\u53c9\u6811\u6240\u6709\u7a7a\u4f4d\u4e0a\u6302\u4e00\u5c42\u5916\u90e8\u8282\u70b9\u3002<\/p>\n\n\n\n
s(x)\u662f\u4e00\u4e2a\u51fd\u6570\uff0c\u4ee3\u8868\u4e86\u5185\u90e8\u8282\u70b9x\u5230\u5176\u5b50\u6811\u5916\u90e8\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u3002<\/strong><\/p>\n\n\n\n
\u5982\u679cx\u662f\u5916\u90e8\u8282\u70b9\uff0c\u90a3\u4e48s(x\uff09= 0\u3002<\/p>\n\n\n\n
\u5982\u679cx\u662f\u5185\u90e8\u8282\u70b9 ,\u90a3\u4e48s(x) >= 1.<\/p>\n\n\n\n
\u5982\u679cx\u7684\u4e00\u4e2a\u5b69\u5b50s(x1) = 1,\u53e6\u4e00\u4e2a\u5b69\u5b50s(x2) = 2,\u90a3\u4e48s(x) = 2<\/p>\n\n\n\n
\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u5199\u51fas\uff08x\uff09\u7684\u89e3\u6cd5<\/p>\n\n\n\n
s(x)=min(s(L)+s(R))+1<\/p>\n\n\n\n
\u4e00\u9897\u4e8c\u53c9\u6811\u79f0\u4e3a\u9ad8\u5ea6\u4f18\u5148\u5de6\u9ad8\u6811\uff08height-biased leftist tree,HBLT\uff09\u3002\u5f53\u4e14\u4ec5\u5f53\u5176\u4efb\u4f55\u4e00\u4e2a\u5185\u90e8\u8282\u70b9\u7684\u5de6\u5b69\u5b50\u7684s(x) \u503c\u90fd\u5927\u4e8e\u6216\u7b49\u4e8e\u53f3\u5b69\u5b50\u7684s\u503c\u3002<\/p>\n\n\n\n
\u5de6\u9ad8\u6570\u7684\u4e3b\u8981\u64cd\u4f5c\u5c31\u662f\u5408\u5e76\uff0c\u5c31\u662f\u4e00\u4e2a\u9012\u5f52\u7684\u64cd\u4f5c\uff0c\u5177\u4f53\u4e0d\u5199\u4e86\uff0c\u53c2\u89c1https:\/\/blog.csdn.net\/qq_41882686\/article\/details\/107423918<\/p>\n\n\n\n
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