{"id":345,"date":"2023-11-17T09:57:49","date_gmt":"2023-07-28T05:49:53","guid":{"rendered":"https:\/\/www.silicloud.com\/zh\/blog\/index.php\/2023\/11\/30\/%e6%9c%80%e5%b0%8f%e5%a0%86%e4%ba%8c%e5%8f%89%e6%a0%91\/"},"modified":"2025-08-02T00:28:55","modified_gmt":"2025-08-01T16:28:55","slug":"%e6%9c%80%e5%b0%8f%e5%a0%86%e4%ba%8c%e5%8f%89%e6%a0%91","status":"publish","type":"post","link":"https:\/\/www.silicloud.com\/zh\/blog\/%e6%9c%80%e5%b0%8f%e5%a0%86%e4%ba%8c%e5%8f%89%e6%a0%91\/","title":{"rendered":"\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u6570\u636e\u7ed3\u6784\u8be6\u89e3\uff1a\u539f\u7406\u3001\u5b9e\u73b0\u4e0e\u5e94\u7528"},"content":{"rendered":"

\u8fd9\u662f\u6587\u7ae0\u300a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u300b\u7684\u7b2c1\u90e8\u5206\uff08\u51719\u90e8\u5206\uff09\u3002<\/p>\n

\u4e00\u4e2a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u662f\u4e00\u68f5\u4e8c\u53c9\u6811\uff0c\u5176\u4e2d\u6839\u8282\u70b9\u7684\u5173\u952e\u5b57\u662f\u6811\u4e2d\u7684\u6700\u5c0f\u503c\u3002<\/p>\n

\u4e0a\u8ff0\u5b9a\u4e49\u5bf9\u6811\u4e2d\u7684\u6240\u6709\u5b50\u6811\u90fd\u9002\u7528\uff0c\u8fd9\u88ab\u79f0\u4e3a\u6700\u5c0f\u5806\u5c5e\u6027\u3002<\/p>\n

\u9664\u4e86\u6700\u540e\u4e24\u5c42\u4ee5\u5916\uff0c\u51e0\u4e4e\u6bcf\u4e2a\u8282\u70b9\u5fc5\u987b\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u9664\u4e86\u6700\u540e\u4e24\u5c42\u4e4b\u5916\uff0c\u8fd9\u51e0\u4e4e\u662f\u4e00\u68f5\u5b8c\u5168\u4e8c\u53c9\u6811\u3002<\/p>\n

\u4ee5\u4e0b\u6811\u662f\u4e00\u4e2a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u7684\u793a\u4f8b\uff0c\u56e0\u4e3a\u4e0a\u8ff0\u4e24\u4e2a\u5c5e\u6027\u6210\u7acb\u3002<\/p>\n

\"\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\"<\/div>\n

\u65e2\u7136\u6211\u4eec\u5df2\u7ecf\u8bb2\u89e3\u4e86\u4ec0\u4e48\u662f\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\uff0c\u90a3\u4e48\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u770b\u5982\u4f55\u8868\u793a\u5b83\u3002<\/p>\n

\n

\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u7684\u8868\u793a<\/h2>\n

\u4e00\u4e2a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u901a\u5e38\u7528\u6570\u7ec4\u8868\u793a\uff0c\u6570\u7ec4\u7684\u7d22\u5f15\u6309\u4ee5\u4e0b\u683c\u5f0f\u6392\u5e8f\u3002<\/p>\n

\n
\n\n\n\n\n\n\n\n\n
\u8282\u70b9\u7c7b\u578b<\/th>\n\u6570\u7ec4\u7d22\u5f15<\/th>\n<\/tr>\n<\/thead>\n
\u5f53\u524d\u8282\u70b9<\/td>\narr[i]<\/code><\/td>\n<\/tr>\n
\u7236\u8282\u70b9<\/td>\narr[(i-1)\/2]<\/code><\/td>\n<\/tr>\n
\u5de6\u5b50\u8282\u70b9<\/td>\narr[(2*i) + 1]<\/code><\/td>\n<\/tr>\n
\u53f3\u5b50\u8282\u70b9<\/td>\narr[(2*i) + 2]<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

\u6574\u4e2a\u6811\u7684\u6839\u8282\u70b9\u662f arr[0]\u3002<\/p>\n

\u6211\u4eec\u5c06\u4f7f\u7528\u4e0b\u56fe\u6240\u793a\u7684\u7d22\u5f15\u3002\u5728\u8fd9\u91cc\u627e\u5230\u5339\u914d\u4e0a\u8868\u7684\u6a21\u5f0f\u5e76\u4e0d\u592a\u56f0\u96be\u3002<\/p>\n

\"\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u7d22\u5f15\"<\/div>\n

\u8fd9\u79cd\u7d22\u5f15\u65b9\u5f0f\u9075\u5faa\u4e8c\u53c9\u6811\u7684\u5c42\u5e8f\u904d\u5386\uff0c\u56e0\u6b64\u4e8c\u53c9\u5806\u6570\u7ec4\u662f\u4f7f\u7528\u5c42\u5e8f\u904d\u5386\u7684\u4e8c\u53c9\u6811\u3002<\/p>\n

\"\u6700\u5c0f\u5806\u6570\u7ec4\"<\/div>\n

\u4e0a\u56fe\u663e\u793a\u4e86\u6700\u5c0f\u5806\u6811\u7684\u6570\u7ec4\u8868\u793a\u3002<\/p>\n

\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u8fd9\u4e9b\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u5f00\u59cb\u5728C\u8bed\u8a00\u4e2d\u5b9e\u73b0\u5427\uff01<\/p>\n

\n

\u5b9e\u73b0\u4e00\u4e2a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811<\/h2>\n

\u8fd9\u662f\u6587\u7ae0\u300a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u300b\u7684\u7b2c2\u90e8\u5206\uff08\u51719\u90e8\u5206\uff09\u3002<\/p>\n

\u6211\u4eec\u5c06\u4f7f\u7528\u6570\u7ec4\u8868\u793a\u6765\u6784\u5efa\u6811\u3002\u8ba9\u6211\u4eec\u5f00\u59cb\u7f16\u5199\u6700\u5c0f\u5806\u7684\u7ed3\u6784\u3002<\/p>\n

typedef<\/span> struct<\/span> MinHeap<\/span> MinHeap;<\/span>\r\nstruct<\/span> MinHeap<\/span> {<\/span>\r\n    int<\/span>*<\/span> arr;<\/span>\r\n    \/\/ \u5806\u7684\u5f53\u524d\u5927\u5c0f<\/span>\r\n    int<\/span> size;<\/span>\r\n    \/\/ \u5806\u7684\u6700\u5927\u5bb9\u91cf<\/span>\r\n    int<\/span> capacity;<\/span>\r\n}<\/span>;<\/span>\r\n<\/code><\/pre>\n
\u6211\u4eec\u4f1a\u6709\u4e00\u4e2a\u5143\u7d20\u6570\u7ec4\u548c\u4e00\u4e2a\u5927\u5c0f\uff0c\u5927\u5c0f\u4f1a\u5728\u63d2\u5165\u6216\u5220\u9664\u5143\u7d20\u65f6\u8fdb\u884c\u66f4\u65b0\u3002<\/p>\n
\u6570\u7ec4\u8fd8\u6709\u4e00\u4e2a\u5bb9\u91cf\uff0c\u7528\u6765\u8868\u793a\u6570\u7ec4\u7684\u6700\u5927\u5c3a\u5bf8\u3002<\/p>\n
\u6211\u4eec\u9700\u8981\u5199\u51e0\u4e2a\u51fd\u6570\u6765\u8868\u793a\u6211\u4eec\u6b63\u5728\u8868\u793a\u4e00\u4e2a\u6700\u5c0f\u5806\uff0c\u6bd4\u5982\u627e\u5230\u7236\u8282\u70b9\u548c\u5b50\u8282\u70b9\u3002<\/p>\n
int<\/span> parent<\/span>(<\/span>int<\/span> i)<\/span> {<\/span>\r\n    \/\/ \u83b7\u53d6\u7236\u8282\u70b9\u7684\u7d22\u5f15<\/span>\r\n    return<\/span> (<\/span>i -<\/span> 1<\/span>)<\/span> \/<\/span> 2<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> left_child<\/span>(<\/span>int<\/span> i)<\/span> {<\/span>\r\n    return<\/span> (<\/span>2<\/span>*<\/span>i +<\/span> 1<\/span>)<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> right_child<\/span>(<\/span>int<\/span> i)<\/span> {<\/span>\r\n    return<\/span> (<\/span>2<\/span>*<\/span>i +<\/span> 2<\/span>)<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> get_min<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    \/\/ \u8fd4\u56de\u6839\u8282\u70b9\u5143\u7d20\uff0c<\/span>\r\n    \/\/ \u6839\u636e\u6700\u5c0f\u5806\u7684\u6027\u8d28\uff0c<\/span>\r\n    \/\/ \u8fd9\u5c31\u662f\u6700\u5c0f\u503c<\/span>\r\n    return<\/span> heap-><\/span>arr[<\/span>0<\/span>]<\/span>;<\/span>\r\n}<\/span>\r\n<\/code><\/pre>\n
\u6211\u4eec\u5c06\u7f16\u5199\u51fd\u6570\u6765\u521d\u59cb\u5316\u548c\u91ca\u653e\u5806\u5185\u5b58\u3002<\/p>\n
MinHeap*<\/span> init_minheap<\/span>(<\/span>int<\/span> capacity)<\/span> {<\/span>\r\n    MinHeap*<\/span> minheap =<\/span> (<\/span>MinHeap*<\/span>)<\/span> calloc<\/span> (<\/span>1<\/span>,<\/span> sizeof<\/span>(<\/span>MinHeap)<\/span>)<\/span>;<\/span>\r\n    minheap-><\/span>arr =<\/span> (<\/span>int<\/span>*<\/span>)<\/span> calloc<\/span> (<\/span>capacity,<\/span> sizeof<\/span>(<\/span>int<\/span>)<\/span>)<\/span>;<\/span>\r\n    minheap-><\/span>capacity =<\/span> capacity;<\/span>\r\n    minheap-><\/span>size =<\/span> 0<\/span>;<\/span>\r\n    return<\/span> minheap;<\/span>\r\n}<\/span>\r\n\r\nvoid<\/span> free_minheap<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    if<\/span> (<\/span>!<\/span>heap)<\/span>\r\n        return<\/span>;<\/span>\r\n    free<\/span>(<\/span>heap-><\/span>arr)<\/span>;<\/span>\r\n    free<\/span>(<\/span>heap)<\/span>;<\/span>\r\n}<\/span>\r\n<\/code><\/pre>\n
\u597d\u7684\uff0c\u65e2\u7136\u8fd9\u4e2a\u95ee\u9898\u89e3\u51b3\u4e86\uff0c\u73b0\u5728\u8ba9\u6211\u4eec\u6765\u8ba8\u8bba\u5982\u4f55\u63d2\u5165\u5143\u7d20\u5427\uff01<\/p>\n
\u63d2\u5165\u5230\u5c0f\u9876\u5806\u4e2d<\/h2>\n
\u8fd9\u662f\u6587\u7ae0\u300a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u300b\u7684\u7b2c3\u90e8\u5206\uff08\u51719\u90e8\u5206\uff09\u3002<\/p>\n
\u5185\u5bb9\u7247\u6bb5: \u63d2\u5165\u7b97\u6cd5\u5f88\u7b80\u5355\u3002\u5b83\u5c06\u4e00\u4e2a\u5143\u7d20\u63d2\u5165\u5230\u6811\u4e2d\u3002<\/p>\n
\u5206\u89e3\u7b97\u6cd5:<\/p>\n
    \n
  • \u9996\u5148\uff0c\u603b\u662f\u5728\u6811\u7684\u5e95\u90e8\u63d2\u5165\u3002\u63d2\u5165\u5143\u7d20\u7684\u521d\u59cb\u4f4d\u7f6e\u4f4d\u4e8e\u6700\u540e\u4e00\u5c42\u3002<\/li>\n
  • \u73b0\u5728\u6211\u4eec\u9700\u8981\u66f4\u65b0\u8fd9\u4e2a\u5143\u7d20\u7684\u4f4d\u7f6e\uff0c\u4ee5\u6ee1\u8db3\u6700\u5c0f\u5806\u7684\u6027\u8d28\u3002<\/li>\n
  • \u7531\u4e8e\u6bcf\u4e2a\u5b50\u6811\u7684\u6839\u8282\u70b9\u5fc5\u987b\u662f\u6700\u5c0f\u503c\uff0c\u56e0\u6b64\u68c0\u67e5\u5176\u76f4\u63a5\u7236\u8282\u70b9\u7684\u5b50\u6811\u3002<\/li>\n
  • \u5982\u679c\u7236\u8282\u70b9\u5927\u4e8e\u8fd9\u4e2a\u63d2\u5165\u7684\u5143\u7d20\uff0c\u6211\u4eec\u9700\u8981\u901a\u8fc7\u4ea4\u6362\u6765\u66f4\u65b0\u5b83\u7684\u4f4d\u7f6e\u3002<\/li>\n
  • \u4f46\u6211\u4eec\u8fd8\u6ca1\u6709\u5b8c\u6210\uff0c\u56e0\u4e3a\u66f4\u65b0\u8282\u70b9\u7684\u5b50\u6811\u53ef\u80fd\u8fdd\u53cd\u6700\u5c0f\u5806\u7684\u6027\u8d28\uff01<\/li>\n
  • \u6211\u4eec\u9700\u8981\u7ee7\u7eed\u4ea4\u6362\uff0c\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9\uff0c\u4e4b\u540e\u6211\u4eec\u5c31\u5b8c\u6210\u4e86\u3002<\/li>\n<\/ul>\n
    \u4e3a\u4e86\u7406\u89e3\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u8ba9\u6211\u4eec\u4e3e\u4e2a\u4f8b\u5b50\u6765\u8bf4\u660e\u3002<\/p>\n
    \u8003\u8651\u4e0b\u65b9\u4ec5\u542b\u6709\u4e00\u4e2a\u5143\u7d20\u7684\u6811\u3002<\/p>\n
    \"\u5355\u5143\u7d20\u6700\u5c0f\u5806\"<\/div>\n
    \u8ba9\u6211\u4eec\u63d2\u5165\u5143\u7d2040\u3002\u7531\u4e8e\u53ea\u6709\u4e00\u4e2a\u5143\u7d20\uff0c\u5b83\u88ab\u63d2\u5165\u5230\u5e95\u90e8\uff0c\u5e76\u4e14\u6211\u4eec\u89c2\u5bdf\u5230\u6700\u5c0f\u5806\u5c5e\u6027\u5f97\u5230\u6ee1\u8db3\uff0c\u56e0\u4e3a10 < 40\u3002\u6240\u4ee5\u4e0d\u9700\u8981\u8fdb\u884c\u4ea4\u6362\u3002<\/p>\n
    \"\u4e24\u5143\u7d20\u6700\u5c0f\u5806\"<\/div>\n
    \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u63d2\u516550\u3002\u968f\u540e\u8fdb\u884c\u7c7b\u4f3c\u7684\u6b65\u9aa4\u3002<\/p>\n
    \"\u4e09\u5143\u7d20\u6700\u5c0f\u5806\"<\/div>\n
    \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u63d2\u51655\u3002\u73b0\u5728\uff0c\u6211\u4eec\u9996\u5148\u5728\u6811\u7684\u5e95\u90e8\u63d2\u5165\uff0c\u5728\u7d22\u5f153\u5904\u3002<\/p>\n
    \"\u6700\u5c0f\u5806\u72b6\u60011\"<\/div>\n
    \u5b50\u68111-3\u8fdd\u53cd\u4e86\u6700\u5c0f\u5806\u7684\u5c5e\u6027\uff0c\u56e0\u6b64\u6574\u4e2a\u6811\u4e5f\u4f1a\u53d7\u5230\u5f71\u54cd\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u4e0d\u65ad\u4e0e\u7236\u8282\u70b9\u4ea4\u6362\uff0c\u76f4\u5230\u8fbe\u5230\u6839\u8282\u70b9\u4e3a\u6b62\u3002<\/p>\n
    \"\u7b2c\u4e00\u6b21\u4ea4\u6362\"<\/div>\n
    \u6240\u4ee5\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u8fdb\u884c\u4e00\u6b21\u4ea4\u6362\uff0c\u56e0\u4e3a\u5728\u4ee5\u8282\u70b90\u4e3a\u6839\u7684\u5b50\u6811\u4e2d\uff0c\u6700\u5c0f\u5806\u7684\u5c5e\u6027\u518d\u6b21\u88ab\u8fdd\u53cd\u4e86\u3002<\/p>\n
    \"\u4ea4\u6362\u540e\u7684\u6700\u5c0f\u5806\"<\/div>\n
    \u597d\u7684\uff0c\u65e2\u7136\u6211\u4eec\u5df2\u7ecf\u53ef\u89c6\u5316\u4e86\uff0c\u90a3\u5c31\u628a\u5b83\u5199\u4e0b\u6765\u5427\uff01<\/p>\n
    MinHeap*<\/span> insert_minheap<\/span>(<\/span>MinHeap*<\/span> heap,<\/span> int<\/span> element)<\/span> {<\/span>\r\n    \/\/ \u5411\u6700\u5c0f\u5806\u4e2d\u63d2\u5165\u4e00\u4e2a\u5143\u7d20<\/span>\r\n    \/\/ \u6211\u4eec\u9996\u5148\u5c06\u5143\u7d20\u6dfb\u52a0\u5230\u6811\u7684\u5e95\u90e8\uff08\u6700\u540e\u4e00\u5c42\uff09<\/span>\r\n    \/\/ \u5982\u679c\u5b83\u6bd4\u5176\u7236\u8282\u70b9\u5c0f\uff0c\u5219\u4e0d\u65ad\u4e0e\u7236\u8282\u70b9\u4ea4\u6362<\/span>\r\n    \/\/ \u6211\u4eec\u6301\u7eed\u8fd9\u4e2a\u8fc7\u7a0b\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9<\/span>\r\n    \/\/ \u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u5c06\u5143\u7d20\u63d2\u5165\u5230\u4e86\u9002\u5f53\u7684\u4f4d\u7f6e\uff0c\u4ee5\u4fdd\u6301\u6700\u5c0f\u5806\u7684\u6027\u8d28<\/span>\r\n    if<\/span> (<\/span>heap-><\/span>size ==<\/span> heap-><\/span>capacity)<\/span> {<\/span>\r\n        fprintf<\/span>(<\/span>stderr<\/span>,<\/span> \"\u65e0\u6cd5\u63d2\u5165 %d\u3002\u5806\u5df2\u6ee1\uff01\\n\"<\/span>,<\/span> element)<\/span>;<\/span>\r\n        return<\/span> heap;<\/span>\r\n    }<\/span>\r\n    \/\/ \u53ef\u4ee5\u6dfb\u52a0\u5143\u7d20\u3002\u589e\u52a0\u5806\u7684\u5927\u5c0f\u5e76\u5c06\u5143\u7d20\u6dfb\u52a0\u5230\u672b\u5c3e<\/span>\r\n    heap-><\/span>size++<\/span>;<\/span>\r\n    heap-><\/span>arr[<\/span>heap-><\/span>size -<\/span> 1<\/span>]<\/span> =<\/span> element;<\/span>\r\n\r\n    \/\/ \u6301\u7eed\u4ea4\u6362\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9<\/span>\r\n    int<\/span> curr =<\/span> heap-><\/span>size -<\/span> 1<\/span>;<\/span>\r\n    \/\/ \u53ea\u8981\u4e0d\u5728\u6839\u8282\u70b9\uff0c\u5e76\u4e14\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7684\u7236\u8282\u70b9\u5927\u4e8e\u5b83<\/span>\r\n    while<\/span> (<\/span>curr ><\/span> 0<\/span> &&<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> ><\/span> heap-><\/span>arr[<\/span>curr]<\/span>)<\/span> {<\/span>\r\n        \/\/ \u4ea4\u6362<\/span>\r\n        int<\/span> temp =<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> =<\/span> heap-><\/span>arr[<\/span>curr]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>curr]<\/span> =<\/span> temp;<\/span>\r\n        \/\/ \u66f4\u65b0\u5143\u7d20\u7684\u5f53\u524d\u7d22\u5f15<\/span>\r\n        curr =<\/span> parent<\/span>(<\/span>curr)<\/span>;<\/span>\r\n    }<\/span>\r\n    return<\/span> heap;<\/span> \r\n}<\/span>\r\n<\/code><\/pre>\n
    \u6211\u4eec\u73b0\u5728\u8981\u5b9e\u65bd\u5220\u9664\u65b9\u6cd5\u3002<\/p>\n
    \u4ece\u6700\u5c0f\u5806\u4e2d\u5220\u9664<\/h2>\n
    \u5728\u63a2\u8ba8\u5982\u4f55\u5220\u9664\u4efb\u610f\u7d22\u5f15\u4f4d\u7f6e\u7684\u5143\u7d20\u4e4b\u524d\uff0c\u7531\u4e8e\u6700\u5c0f\u5806\u7684\u7279\u6027\u4e0e\u6839\u8282\u70b9\u5bc6\u5207\u76f8\u5173\uff0c\u6211\u4eec\u5c06\u9996\u5148\u7814\u7a76\u5220\u9664\u6839\u8282\u70b9\u7684\u60c5\u51b5\u3002<\/p>\n
    \u8981\u5220\u9664\u6700\u5c0f\u5143\u7d20\uff08\u5373\u6839\u5143\u7d20\uff09\uff0c\u6211\u4eec\u5c06\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\uff1a<\/p>\n
      \n
    • \u5c06\u6839\u8282\u70b9\u66f4\u65b0\u4e3a\u6570\u7ec4\uff08\u6811\uff09\u7684\u6700\u540e\u4e00\u4e2a\u5143\u7d20<\/li>\n
    • \u73b0\u5728\u6211\u4eec\u5c06\u79fb\u9664\u5e95\u90e8\u7684\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u3002\u8fd9\u7c7b\u4f3c\u4e8e\u5728\u672b\u5c3e\u8fdb\u884c\u4ea4\u6362\u548c\u5220\u9664\uff01\u53ea\u662f\u56e0\u4e3a\u6211\u4eec\u4e0d\u518d\u5173\u5fc3\u6839\u8282\u70b9\u7684\u503c\uff0c\u6240\u4ee5\u76f4\u63a5\u66f4\u65b0\u5b83\u5373\u53ef\u3002<\/li>\n
    • \u95ee\u9898\u5728\u4e8e\u6211\u4eec\u9700\u8981\u7ef4\u62a4\u6700\u5c0f\u5806\u7684\u6027\u8d28\u3002<\/li>\n
    • \u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u786e\u4fdd\u6574\u4e2a\u6811\u90fd\u4fdd\u6301\u8fd9\u4e00\u6027\u8d28\u3002\u6211\u4eec\u5c06\u4f7f\u7528\u4e00\u4e2a\u540d\u4e3aheapify()\u7684\u51fd\u6570\u6765\u5b8c\u6210\u8fd9\u4e2a\u4efb\u52a1\u3002<\/li>\n<\/ul>\n
      \u56e0\u6b64\uff0c\u6211\u4eec\u77e5\u9053\u5728\u6267\u884cheapify()\u65b9\u6cd5\u4e4b\u540e\uff0c\u5220\u9664\u64cd\u4f5c\u5c31\u5b8c\u6210\u4e86\u3002<\/p>\n
      MinHeap*<\/span> delete_minimum<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    \/\/ \u5220\u9664\u6839\u8282\u70b9\u7684\u6700\u5c0f\u5143\u7d20<\/span>\r\n    if<\/span> (<\/span>!<\/span>heap ||<\/span> heap-><\/span>size ==<\/span> 0<\/span>)<\/span>\r\n        return<\/span> heap;<\/span>\r\n\r\n    int<\/span> size =<\/span> heap-><\/span>size;<\/span>\r\n    int<\/span> last_element =<\/span> heap-><\/span>arr[<\/span>size-<\/span>1<\/span>]<\/span>;<\/span>\r\n    \r\n    \/\/ \u7528\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u66f4\u65b0\u6839\u8282\u70b9\u503c<\/span>\r\n    heap-><\/span>arr[<\/span>0<\/span>]<\/span> =<\/span> last_element;<\/span>\r\n\r\n    \/\/ \u901a\u8fc7\u51cf\u5c0f\u5806\u7684\u5927\u5c0f\u6765\u79fb\u9664\u6700\u540e\u4e00\u4e2a\u5143\u7d20<\/span>\r\n    heap-><\/span>size--<\/span>;<\/span>\r\n    size--<\/span>;<\/span>\r\n\r\n    \/\/ \u6211\u4eec\u9700\u8981\u8c03\u7528heapify()\u6765\u7ef4\u62a4\u6700\u5c0f\u5806<\/span>\r\n    \/\/ \u7684\u6027\u8d28<\/span>\r\n    heap =<\/span> heapify<\/span>(<\/span>heap,<\/span> 0<\/span>)<\/span>;<\/span>\r\n    return<\/span> heap;<\/span>\r\n}<\/span>\r\n<\/code><\/pre>\n
      \u5806\u5316\uff08heapify()\uff09\u7684\u8fc7\u7a0b<\/h3>\n
      \u8fd9\u4e2a\u51fd\u6570\u63a5\u53d7\u4e00\u4e2a\u5143\u7d20\u7684\u7d22\u5f15index\uff0c\u5e76\u901a\u8fc7\u4e0e\u5176\u76f4\u63a5\u5b50\u6811\u4e2d\u6700\u5c0f\u7684\u5143\u7d20\u4ea4\u6362\u6765\u4fdd\u6301\u6700\u5c0f\u5806\u7684\u6027\u8d28\u3002<\/p>\n
      \u751f\u6210\u7684\u6811\u5c06\u6ee1\u8db3\u6700\u5c0f\u5806\u6027\u8d28\u3002<\/p>\n
      \u8fd9\u6d89\u53ca\u627e\u5230\u5b50\u6811\u4e2d\u7684\u6700\u5c0f\u5143\u7d20\uff0c\u5e76\u4e0e\u5f53\u524d\u5143\u7d20\u8fdb\u884c\u4ea4\u6362\u3002<\/p>\n
      \u5728\u8fd9\u4e4b\u540e\uff0c\u6211\u4eec\u8fd8\u9700\u8981\u786e\u4fdd\u6574\u4e2a\u6811\u6ee1\u8db3\u8fd9\u4e00\u6761\u4ef6\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u9700\u8981\u9012\u5f52\u5730\u5728\u6700\u5c0f\u5143\u7d20\u4e0a\u8c03\u7528\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u76f4\u5230\u8fbe\u5230\u6839\u8282\u70b9\u4e3a\u6b62\uff01<\/p>\n
      MinHeap*<\/span> heapify<\/span>(<\/span>MinHeap*<\/span> heap,<\/span> int<\/span> index)<\/span> {<\/span>\r\n    \/\/ \u91cd\u65b0\u6392\u5217\u5806\u4ee5\u7ef4\u62a4<\/span>\r\n    \/\/ \u6700\u5c0f\u5806\u6027\u8d28<\/span>\r\n    if<\/span> (<\/span>heap-><\/span>size <=<\/span> 1<\/span>)<\/span>\r\n        return<\/span> heap;<\/span>\r\n    \r\n    int<\/span> left =<\/span> left_child<\/span>(<\/span>index)<\/span>;<\/span> \r\n    int<\/span> right =<\/span> right_child<\/span>(<\/span>index)<\/span>;<\/span> \r\n\r\n    \/\/ \u7528\u4e8e\u83b7\u53d6\u5b50\u6811\u4e2d\u6700\u5c0f\u5143\u7d20\u7684\u53d8\u91cf<\/span>\r\n    \/\/ \u5728\u7ed9\u5b9a\u7d22\u5f15\u4f4d\u7f6e\u7684\u5143\u7d20<\/span>\r\n    int<\/span> smallest =<\/span> index;<\/span> \r\n    \r\n    \/\/ \u5982\u679c\u5de6\u5b50\u8282\u70b9\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\uff0c\u5219<\/span>\r\n    \/\/ \u5b83\u662f\u6700\u5c0f\u7684<\/span>\r\n    if<\/span> (<\/span>left <<\/span> heap-><\/span>size &&<\/span> heap-><\/span>arr[<\/span>left]<\/span> <<\/span> heap-><\/span>arr[<\/span>index]<\/span>)<\/span> \r\n        smallest =<\/span> left;<\/span> \r\n    \r\n    \/\/ \u7c7b\u4f3c\u5730\u5904\u7406\u53f3\u5b50\u8282\u70b9\uff0c\u4f46\u6211\u4eec\u66f4\u65b0\u6700\u5c0f\u5143\u7d20<\/span>\r\n    \/\/ \u4ee5\u786e\u4fdd\u4e00\u5b9a\u80fd\u5f97\u5230\u5b50\u6811\u4e2d\u7684\u6700\u5c0f\u5143\u7d20<\/span>\r\n    if<\/span> (<\/span>right <<\/span> heap-><\/span>size &&<\/span> heap-><\/span>arr[<\/span>right]<\/span> <<\/span> heap-><\/span>arr[<\/span>smallest]<\/span>)<\/span> \r\n        smallest =<\/span> right;<\/span> \r\n\r\n    \/\/ \u73b0\u5728\uff0c\u5982\u679c\u5f53\u524d\u5143\u7d20\u4e0d\u662f\u6700\u5c0f\u7684\uff0c<\/span>\r\n    \/\/ \u4e0e\u5f53\u524d\u5143\u7d20\u4ea4\u6362\u3002\u6700\u5c0f\u5806\u6027\u8d28<\/span>\r\n    \/\/ \u73b0\u5728\u5bf9\u4e8e\u8fd9\u4e2a\u5b50\u6811\u5df2\u7ecf\u6ee1\u8db3\u3002\u6211\u4eec\u73b0\u5728\u9700\u8981<\/span>\r\n    \/\/ \u9012\u5f52\u5730\u7ee7\u7eed\u6267\u884c\u6b64\u64cd\u4f5c\uff0c\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9\uff0c<\/span>\r\n    \/\/ \u90a3\u65f6\u5c06\u4e0d\u518d\u6709\u4efb\u4f55\u53d8\u5316\uff01<\/span>\r\n    if<\/span> (<\/span>smallest !=<\/span> index)<\/span> \r\n    {<\/span> \r\n        int<\/span> temp =<\/span> heap-><\/span>arr[<\/span>index]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>index]<\/span> =<\/span> heap-><\/span>arr[<\/span>smallest]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>smallest]<\/span> =<\/span> temp;<\/span>\r\n        heap =<\/span> heapify<\/span>(<\/span>heap,<\/span> smallest)<\/span>;<\/span> \r\n    }<\/span>\r\n\r\n    return<\/span> heap;<\/span>\r\n}<\/span>\r\n<\/code><\/pre>\n
      \u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u6269\u5c55\u8fd9\u4e2adelete_minimum()\u51fd\u6570\uff0c\u6765\u5220\u9664\u4efb\u4f55\u5143\u7d20\u3002<\/p>\n
      \u5220\u9664\u4e00\u4e2a\u4efb\u610f\u5143\u7d20<\/h2>\n
      \u8fd9\u662f\u6587\u7ae0\u300a\u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u300b\u7684\u7b2c7\u90e8\u5206\uff08\u51719\u90e8\u5206\uff09\u3002<\/p>\n
      \u8fd9\u4e00\u6b65\u9aa4\u4ec5\u6d89\u53ca\u5c06\u76ee\u6807\u5143\u7d20\u8bbe\u7f6e\u4e3a\u6700\u5c0f\u53ef\u80fd\u503c\uff0c\u5373get_min()-1\uff0c\u56e0\u4e3a\u5b83\u5fc5\u987b\u5c0f\u4e8e\u5f53\u524d\u6700\u5c0f\u503c\u3002<\/p>\n
      \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u7ee7\u7eed\u8fdb\u884c\u4ea4\u6362\u64cd\u4f5c\uff0c\u76f4\u5230\u66f4\u65b0\u5143\u7d20\u4f4d\u7f6e\uff0c\u4f7f\u8be5\u5143\u7d20\u6210\u4e3a\u65b0\u7684\u6839\u8282\u70b9\u3002<\/p>\n
      \u73b0\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e4b\u524d\u5b9a\u4e49\u7684delete_minimum()\u51fd\u6570\uff01\u8fd9\u6837\u6211\u4eec\u5c31\u80fd\u7b80\u5355\u5730\u5220\u9664\u65b0\u7684\u6839\u8282\u70b9\uff01<\/p>\n
      \u57fa\u4e8e\u4ee5\u4e0a\u6b65\u9aa4\uff0c\u6211\u4eec\u5b8c\u6574\u7684\u5143\u7d20\u5220\u9664\u8fc7\u7a0b\u5c06\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n
      MinHeap*<\/span> delete_element<\/span>(<\/span>MinHeap*<\/span> heap,<\/span> int<\/span> index)<\/span> {<\/span>\r\n    \/\/ \u5220\u9664\u6307\u5b9a\u7d22\u5f15\u4f4d\u7f6e\u7684\u5143\u7d20<\/span>\r\n    \/\/ \u786e\u4fdd\u8be5\u503c\u5c0f\u4e8e\u5f53\u524d\u6839\u8282\u70b9\u7684\u503c<\/span>\r\n    heap-><\/span>arr[<\/span>index]<\/span> =<\/span> get_min<\/span>(<\/span>heap)<\/span> -<\/span> 1<\/span>;<\/span>\r\n    \r\n    \/\/ \u6301\u7eed\u4ea4\u6362\uff0c\u76f4\u5230\u66f4\u65b0\u6574\u4e2a\u6811\u7ed3\u6784<\/span>\r\n    int<\/span> curr =<\/span> index;<\/span>\r\n    while<\/span> (<\/span>curr ><\/span> 0<\/span> &&<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> ><\/span> heap-><\/span>arr[<\/span>curr]<\/span>)<\/span> {<\/span>\r\n        int<\/span> temp =<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> =<\/span> heap-><\/span>arr[<\/span>curr]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>curr]<\/span> =<\/span> temp;<\/span>\r\n        curr =<\/span> parent<\/span>(<\/span>curr)<\/span>;<\/span>\r\n    }<\/span>\r\n\r\n    \/\/ \u73b0\u5728\u53ea\u9700\u5220\u9664\u6700\u5c0f\u5143\u7d20<\/span>\r\n    heap =<\/span> delete_minimum<\/span>(<\/span>heap)<\/span>;<\/span>\r\n    return<\/span> heap;<\/span>\r\n}<\/span>\r\n<\/code><\/pre>\n
      \u592a\u597d\u4e86\uff01\u6211\u4eec\u7ec8\u4e8e\u5b8c\u6210\u4e86\u6700\u5c0f\u5806\u4e2d\u5220\u9664\u4efb\u610f\u5143\u7d20\u7684\u5b9e\u73b0\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u5c06\u5c55\u793a\u5b8c\u6574\u7684\u4ee3\u7801\uff0c\u5305\u62ec\u7528\u4e8e\u53ef\u89c6\u5316\u6811\u7ed3\u6784\u7684print()\u51fd\u6570\u3002<\/p>\n
      \n
      \u5b8c\u6574\u7684\u4ee3\u7801\u5b9e\u73b0<\/h2>\n
      \u6700\u5c0f\u5806\u4e8c\u53c9\u6811\u7684C\u8bed\u8a00\u5b9e\u73b0<\/h2>\n
      #<\/span>include<\/span> <stdio.h><\/span><\/span>\r\n#<\/span>include<\/span> <stdlib.h><\/span><\/span>\r\n\r\ntypedef<\/span> struct<\/span> MinHeap<\/span> MinHeap;<\/span>\r\nstruct<\/span> MinHeap<\/span> {<\/span>\r\n    int<\/span>*<\/span> arr;<\/span>\r\n    \/\/ \u5806\u7684\u5f53\u524d\u5927\u5c0f<\/span>\r\n    int<\/span> size;<\/span>\r\n    \/\/ \u5806\u7684\u6700\u5927\u5bb9\u91cf<\/span>\r\n    int<\/span> capacity;<\/span>\r\n}<\/span>;<\/span>\r\n\r\nint<\/span> parent<\/span>(<\/span>int<\/span> i)<\/span> {<\/span>\r\n    \/\/ \u83b7\u53d6\u7236\u8282\u70b9\u7684\u7d22\u5f15<\/span>\r\n    return<\/span> (<\/span>i -<\/span> 1<\/span>)<\/span> \/<\/span> 2<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> left_child<\/span>(<\/span>int<\/span> i)<\/span> {<\/span>\r\n    return<\/span> (<\/span>2<\/span>*<\/span>i +<\/span> 1<\/span>)<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> right_child<\/span>(<\/span>int<\/span> i)<\/span> {<\/span>\r\n    return<\/span> (<\/span>2<\/span>*<\/span>i +<\/span> 2<\/span>)<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> get_min<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    \/\/ \u8fd4\u56de\u6839\u8282\u70b9\u5143\u7d20\uff0c\u56e0\u4e3a\u8fd9\u662f\u6700\u5c0f\u503c<\/span>\r\n    return<\/span> heap-><\/span>arr[<\/span>0<\/span>]<\/span>;<\/span>\r\n}<\/span>\r\n\r\nMinHeap*<\/span> init_minheap<\/span>(<\/span>int<\/span> capacity)<\/span> {<\/span>\r\n    MinHeap*<\/span> minheap =<\/span> (<\/span>MinHeap*<\/span>)<\/span> calloc<\/span> (<\/span>1<\/span>,<\/span> sizeof<\/span>(<\/span>MinHeap)<\/span>)<\/span>;<\/span>\r\n    minheap-><\/span>arr =<\/span> (<\/span>int<\/span>*<\/span>)<\/span> calloc<\/span> (<\/span>capacity,<\/span> sizeof<\/span>(<\/span>int<\/span>)<\/span>)<\/span>;<\/span>\r\n    minheap-><\/span>capacity =<\/span> capacity;<\/span>\r\n    minheap-><\/span>size =<\/span> 0<\/span>;<\/span>\r\n    return<\/span> minheap;<\/span>\r\n}<\/span>\r\n\r\nMinHeap*<\/span> insert_minheap<\/span>(<\/span>MinHeap*<\/span> heap,<\/span> int<\/span> element)<\/span> {<\/span>\r\n    \/\/ \u5411\u6700\u5c0f\u5806\u63d2\u5165\u5143\u7d20<\/span>\r\n    \/\/ \u6211\u4eec\u9996\u5148\u5c06\u5176\u6dfb\u52a0\u5230\u6811\u7684\u5e95\u90e8\uff08\u6700\u540e\u4e00\u5c42\uff09\uff0c<\/span>\r\n    \/\/ \u5982\u679c\u5b83\u6bd4\u7236\u8282\u70b9\u5c0f\uff0c\u5219\u4e0d\u65ad\u4e0e\u7236\u8282\u70b9\u4ea4\u6362\u3002<\/span>\r\n    \/\/ \u6211\u4eec\u4e00\u76f4\u8fd9\u6837\u505a\uff0c\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9\u3002<\/span>\r\n    \/\/ \u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u5c06\u5143\u7d20\u63d2\u5165\u5230\u4e86\u6b63\u786e\u7684\u4f4d\u7f6e\uff0c\u4ee5\u4fdd\u6301\u6700\u5c0f\u5806\u7684\u6027\u8d28<\/span>\r\n    if<\/span> (<\/span>heap-><\/span>size ==<\/span> heap-><\/span>capacity)<\/span> {<\/span>\r\n        fprintf<\/span>(<\/span>stderr<\/span>,<\/span> \"\u65e0\u6cd5\u63d2\u5165 %d\u3002\u5806\u5df2\u6ee1\uff01\\n\"<\/span>,<\/span> element)<\/span>;<\/span>\r\n        return<\/span> heap;<\/span>\r\n    }<\/span>\r\n    \/\/ \u53ef\u4ee5\u6dfb\u52a0\u3002\u589e\u52a0\u5927\u5c0f\u5e76\u5c06\u5176\u6dfb\u52a0\u5230\u672b\u5c3e<\/span>\r\n    heap-><\/span>size++<\/span>;<\/span>\r\n    heap-><\/span>arr[<\/span>heap-><\/span>size -<\/span> 1<\/span>]<\/span> =<\/span> element;<\/span>\r\n\r\n    \/\/ \u6301\u7eed\u4ea4\u6362\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9<\/span>\r\n    int<\/span> curr =<\/span> heap-><\/span>size -<\/span> 1<\/span>;<\/span>\r\n    \/\/ \u53ea\u8981\u4e0d\u5728\u6839\u8282\u70b9\uff0c\u5e76\u4e14\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7684\u7236\u8282\u70b9\u5927\u4e8e\u5b83<\/span>\r\n    while<\/span> (<\/span>curr ><\/span> 0<\/span> &&<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> ><\/span> heap-><\/span>arr[<\/span>curr]<\/span>)<\/span> {<\/span>\r\n        \/\/ \u4ea4\u6362<\/span>\r\n        int<\/span> temp =<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> =<\/span> heap-><\/span>arr[<\/span>curr]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>curr]<\/span> =<\/span> temp;<\/span>\r\n        \/\/ \u66f4\u65b0\u5143\u7d20\u7684\u5f53\u524d\u7d22\u5f15<\/span>\r\n        curr =<\/span> parent<\/span>(<\/span>curr)<\/span>;<\/span>\r\n    }<\/span>\r\n    return<\/span> heap;<\/span> \r\n}<\/span>\r\n\r\nMinHeap*<\/span> heapify<\/span>(<\/span>MinHeap*<\/span> heap,<\/span> int<\/span> index)<\/span> {<\/span>\r\n    \/\/ \u91cd\u65b0\u6392\u5217\u5806\u4ee5\u4fdd\u6301\u6700\u5c0f\u5806\u6027\u8d28<\/span>\r\n    if<\/span> (<\/span>heap-><\/span>size <=<\/span> 1<\/span>)<\/span>\r\n        return<\/span> heap;<\/span>\r\n    \r\n    int<\/span> left =<\/span> left_child<\/span>(<\/span>index)<\/span>;<\/span> \r\n    int<\/span> right =<\/span> right_child<\/span>(<\/span>index)<\/span>;<\/span> \r\n\r\n    \/\/ \u7528\u4e8e\u83b7\u53d6\u7d22\u5f15\u5904\u5143\u7d20\u5b50\u6811\u4e2d\u6700\u5c0f\u5143\u7d20\u7684\u53d8\u91cf<\/span>\r\n    int<\/span> smallest =<\/span> index;<\/span> \r\n    \r\n    \/\/ \u5982\u679c\u5de6\u5b50\u8282\u70b9\u5c0f\u4e8e\u6b64\u5143\u7d20\uff0c\u5219\u5b83\u662f\u6700\u5c0f\u7684<\/span>\r\n    if<\/span> (<\/span>left <<\/span> heap-><\/span>size &&<\/span> heap-><\/span>arr[<\/span>left]<\/span> <<\/span> heap-><\/span>arr[<\/span>index]<\/span>)<\/span> \r\n        smallest =<\/span> left;<\/span> \r\n    \r\n    \/\/ \u53f3\u5b50\u8282\u70b9\u540c\u7406\uff0c\u4f46\u6211\u4eec\u6b63\u5728\u66f4\u65b0\u6700\u5c0f\u5143\u7d20\uff0c<\/span>\r\n    \/\/ \u4ee5\u4fbf\u5b83\u4e00\u5b9a\u80fd\u7ed9\u51fa\u5b50\u6811\u4e2d\u7684\u6700\u5c0f\u5143\u7d20<\/span>\r\n    if<\/span> (<\/span>right <<\/span> heap-><\/span>size &&<\/span> heap-><\/span>arr[<\/span>right]<\/span> <<\/span> heap-><\/span>arr[<\/span>smallest]<\/span>)<\/span> \r\n        smallest =<\/span> right;<\/span> \r\n\r\n    \/\/ \u73b0\u5728\uff0c\u5982\u679c\u5f53\u524d\u5143\u7d20\u4e0d\u662f\u6700\u5c0f\u7684\uff0c\u5219\u4e0e\u5f53\u524d\u5143\u7d20\u4ea4\u6362\u3002<\/span>\r\n    \/\/ \u73b0\u5728\uff0c\u6b64\u5b50\u6811\u7684\u6700\u5c0f\u5806\u6027\u8d28\u5f97\u5230\u6ee1\u8db3\u3002<\/span>\r\n    \/\/ \u6211\u4eec\u73b0\u5728\u9700\u8981\u9012\u5f52\u5730\u7ee7\u7eed\u8fd9\u6837\u505a\uff0c\u76f4\u5230\u5230\u8fbe\u6839\u8282\u70b9\uff0c<\/span>\r\n    \/\/ \u6b64\u65f6\u5c06\u4e0d\u518d\u6709\u53d8\u5316\uff01<\/span>\r\n    if<\/span> (<\/span>smallest !=<\/span> index)<\/span> \r\n    {<\/span> \r\n        int<\/span> temp =<\/span> heap-><\/span>arr[<\/span>index]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>index]<\/span> =<\/span> heap-><\/span>arr[<\/span>smallest]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>smallest]<\/span> =<\/span> temp;<\/span>\r\n        heap =<\/span> heapify<\/span>(<\/span>heap,<\/span> smallest)<\/span>;<\/span> \r\n    }<\/span>\r\n\r\n    return<\/span> heap;<\/span>\r\n}<\/span>\r\n\r\nMinHeap*<\/span> delete_minimum<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    \/\/ \u5220\u9664\u6839\u8282\u70b9\u7684\u6700\u5c0f\u5143\u7d20<\/span>\r\n    if<\/span> (<\/span>!<\/span>heap ||<\/span> heap-><\/span>size ==<\/span> 0<\/span>)<\/span>\r\n        return<\/span> heap;<\/span>\r\n\r\n    int<\/span> size =<\/span> heap-><\/span>size;<\/span>\r\n    int<\/span> last_element =<\/span> heap-><\/span>arr[<\/span>size-<\/span>1<\/span>]<\/span>;<\/span>\r\n    \r\n    \/\/ \u7528\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u66f4\u65b0\u6839\u503c<\/span>\r\n    heap-><\/span>arr[<\/span>0<\/span>]<\/span> =<\/span> last_element;<\/span>\r\n\r\n    \/\/ \u73b0\u5728\u901a\u8fc7\u51cf\u5c0f\u5927\u5c0f\u6765\u79fb\u9664\u6700\u540e\u4e00\u4e2a\u5143\u7d20<\/span>\r\n    heap-><\/span>size--<\/span>;<\/span>\r\n    size--<\/span>;<\/span>\r\n\r\n    \/\/ \u6211\u4eec\u9700\u8981\u8c03\u7528heapify()\u6765\u4fdd\u6301\u6700\u5c0f\u5806\u6027\u8d28<\/span>\r\n    heap =<\/span> heapify<\/span>(<\/span>heap,<\/span> 0<\/span>)<\/span>;<\/span>\r\n    return<\/span> heap;<\/span>\r\n}<\/span>\r\n\r\nMinHeap*<\/span> delete_element<\/span>(<\/span>MinHeap*<\/span> heap,<\/span> int<\/span> index)<\/span> {<\/span>\r\n    \/\/ \u5220\u9664\u7d22\u5f15\u5904\u7684\u5143\u7d20<\/span>\r\n    \/\/ \u786e\u4fdd\u5b83\u5c0f\u4e8e\u5f53\u524d\u6839\u8282\u70b9<\/span>\r\n    heap-><\/span>arr[<\/span>index]<\/span> =<\/span> get_min<\/span>(<\/span>heap)<\/span> -<\/span> 1<\/span>;<\/span>\r\n    \r\n    \/\/ \u73b0\u5728\u6301\u7eed\u4ea4\u6362\uff0c\u76f4\u5230\u6211\u4eec\u66f4\u65b0\u6811<\/span>\r\n    int<\/span> curr =<\/span> index;<\/span>\r\n    while<\/span> (<\/span>curr ><\/span> 0<\/span> &&<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> ><\/span> heap-><\/span>arr[<\/span>curr]<\/span>)<\/span> {<\/span>\r\n        int<\/span> temp =<\/span> heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>parent<\/span>(<\/span>curr)<\/span>]<\/span> =<\/span> heap-><\/span>arr[<\/span>curr]<\/span>;<\/span>\r\n        heap-><\/span>arr[<\/span>curr]<\/span> =<\/span> temp;<\/span>\r\n        curr =<\/span> parent<\/span>(<\/span>curr)<\/span>;<\/span>\r\n    }<\/span>\r\n\r\n    \/\/ \u73b0\u5728\u53ea\u9700\u5220\u9664\u6700\u5c0f\u5143\u7d20<\/span>\r\n    heap =<\/span> delete_minimum<\/span>(<\/span>heap)<\/span>;<\/span>\r\n    return<\/span> heap;<\/span>\r\n}<\/span>\r\n\r\nvoid<\/span> print_heap<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    \/\/ \u7b80\u5355\u5730\u6253\u5370\u6570\u7ec4\u3002\u8fd9\u662f\u6811\u7684\u4e2d\u5e8f\u904d\u5386<\/span>\r\n    printf<\/span>(<\/span>\"\u6700\u5c0f\u5806\uff1a\\n\"<\/span>)<\/span>;<\/span>\r\n    for<\/span> (<\/span>int<\/span> i=<\/span>0<\/span>;<\/span> i<<\/span>heap-><\/span>size;<\/span> i++<\/span>)<\/span> {<\/span>\r\n        printf<\/span>(<\/span>\"%d -> \"<\/span>,<\/span> heap-><\/span>arr[<\/span>i]<\/span>)<\/span>;<\/span>\r\n    }<\/span>\r\n    printf<\/span>(<\/span>\"\\n\"<\/span>)<\/span>;<\/span>\r\n}<\/span>\r\n\r\nvoid<\/span> free_minheap<\/span>(<\/span>MinHeap*<\/span> heap)<\/span> {<\/span>\r\n    if<\/span> (<\/span>!<\/span>heap)<\/span>\r\n        return<\/span>;<\/span>\r\n    free<\/span>(<\/span>heap-><\/span>arr)<\/span>;<\/span>\r\n    free<\/span>(<\/span>heap)<\/span>;<\/span>\r\n}<\/span>\r\n\r\nint<\/span> main<\/span>(<\/span>)<\/span> {<\/span>\r\n    \/\/ \u5bb9\u91cf\u4e3a10\u4e2a\u5143\u7d20<\/span>\r\n    MinHeap*<\/span> heap =<\/span> init_minheap<\/span>(<\/span>10<\/span>)<\/span>;<\/span>\r\n\r\n    insert_minheap<\/span>(<\/span>heap,<\/span> 40<\/span>)<\/span>;<\/span>\r\n    insert_minheap<\/span>(<\/span>heap,<\/span> 50<\/span>)<\/span>;<\/span>\r\n    insert_minheap<\/span>(<\/span>heap,<\/span> 5<\/span>)<\/span>;<\/span>\r\n    print_heap<\/span>(<\/span>heap)<\/span>;<\/span>\r\n    \r\n    \/\/ \u5220\u9664heap->arr[1] (50)<\/span>\r\n    delete_element<\/span>(<\/span>heap,<\/span> 1<\/span>)<\/span>;<\/span>\r\n\r\n    print_heap<\/span>(<\/span>heap)<\/span>;<\/span>\r\n    free_minheap<\/span>(<\/span>heap)<\/span>;<\/span>\r\n    return<\/span> 0<\/span>;<\/span>\r\n}<\/span>\r\n<\/code><\/pre>\n
      \u8f93\u51fa\u7ed3\u679c<\/h3>\n
      \u6700\u5c0f\u5806\uff1a\r\n5<\/span> -><\/span> 50<\/span> -><\/span> 40<\/span> -><\/span> \r\n\u6700\u5c0f\u5806\uff1a\r\n5<\/span> -><\/span> 40<\/span> -><\/span> \r\n<\/code><\/pre>\n
      \n
      \u5b9e\u73b0\u7684\u65f6\u95f4\u590d\u6742\u5ea6<\/h2>\n
      \u6700\u5c0f\u5806\u7684\u5404\u4e2a\u64cd\u4f5c\u5177\u6709\u4e0d\u540c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u4e86\u89e3\u8fd9\u4e9b\u590d\u6742\u5ea6\u5bf9\u4e8e\u8bc4\u4f30\u7b97\u6cd5\u6548\u7387\u81f3\u5173\u91cd\u8981\uff1a<\/p>\n
        \n
      • \u521d\u59cb\u5316\u5806\uff08init_minheap\uff09<\/strong>\uff1aO(1) – \u4ec5\u5206\u914d\u5185\u5b58\u5e76\u8bbe\u7f6e\u521d\u59cb\u503c<\/li>\n
      • \u83b7\u53d6\u6700\u5c0f\u503c\uff08get_min\uff09<\/strong>\uff1aO(1) – \u76f4\u63a5\u8fd4\u56de\u6839\u8282\u70b9\u5143\u7d20<\/li>\n
      • \u63d2\u5165\u5143\u7d20\uff08insert_minheap\uff09<\/strong>\uff1aO(log n) – \u6700\u574f\u60c5\u51b5\u4e0b\u9700\u8981\u4ece\u53f6\u5b50\u8282\u70b9\u5230\u6839\u8282\u70b9\u8fdb\u884c\u4ea4\u6362<\/li>\n
      • \u5220\u9664\u6700\u5c0f\u503c\uff08delete_minimum\uff09<\/strong>\uff1aO(log n) – \u5220\u9664\u6839\u8282\u70b9\u540e\u9700\u8981\u91cd\u65b0\u8c03\u6574\u5806\u7ed3\u6784<\/li>\n
      • \u5220\u9664\u6307\u5b9a\u5143\u7d20\uff08delete_element\uff09<\/strong>\uff1aO(log n) – \u9700\u8981\u5148\u8c03\u6574\u5143\u7d20\u4f4d\u7f6e\uff0c\u518d\u5220\u9664\u6700\u5c0f\u503c<\/li>\n
      • \u5806\u5316\uff08heapify\uff09<\/strong>\uff1aO(log n) – \u4ece\u6307\u5b9a\u8282\u70b9\u5411\u4e0b\u8c03\u6574\u5806\u7ed3\u6784<\/li>\n<\/ul>\n
        \u6700\u5c0f\u5806\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f18\u52bf\u4e3b\u8981\u4f53\u73b0\u5728\u9891\u7e41\u83b7\u53d6\u6700\u5c0f\u503c\u548c\u52a8\u6001\u7ef4\u62a4\u6570\u636e\u96c6\u7684\u573a\u666f\u4e2d\u3002\u76f8\u6bd4\u7ebf\u6027\u641c\u7d22\u6700\u5c0f\u503c\u7684O(n)\u590d\u6742\u5ea6\uff0c\u6700\u5c0f\u5806\u7684O(1)\u83b7\u53d6\u6700\u5c0f\u503c\u548cO(log n)\u7684\u63d2\u5165\u5220\u9664\u64cd\u4f5c\u4f7f\u5176\u5728\u4f18\u5148\u961f\u5217\u3001\u56fe\u7b97\u6cd5\uff08\u5982Dijkstra\u7b97\u6cd5\uff09\u548c\u5806\u6392\u5e8f\u7b49\u5e94\u7528\u4e2d\u8868\u73b0\u51fa\u8272\u3002<\/p>\n
        \n
        \n\n\n\n\n\n\n\n\n\n
        \u51fd\u6570<\/strong><\/th>\n\u65f6\u95f4\u590d\u6742\u5ea6<\/strong><\/th>\n<\/tr>\n<\/thead>\n
        get_min()<\/code><\/td>\nO(1)<\/strong><\/td>\n<\/tr>\n
        insert_minheap()<\/code><\/td>\nO(logN)<\/strong><\/td>\n<\/tr>\n
        delete_minimum()<\/code><\/td>\n\u4e0e\u63d2\u5165\u76f8\u540c – O(logN)<\/strong><\/td>\n<\/tr>\n
        heapify()<\/code><\/td>\nO(logN)<\/strong><\/td>\n<\/tr>\n
        delete_element()<\/code><\/td>\nO(logN)<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
        \n
        \u4e0b\u8f7d\u4ee3\u7801<\/h2>\n
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