{"id":3373,"date":"2022-08-08T01:22:05","date_gmt":"2022-08-07T22:22:05","guid":{"rendered":"https:\/\/demensdeum.com\/blog\/?p=3373"},"modified":"2024-12-16T22:32:17","modified_gmt":"2024-12-16T19:32:17","slug":"heapsort","status":"publish","type":"post","link":"https:\/\/demensdeum.com\/blog\/zh\/2022\/08\/08\/heapsort\/","title":{"rendered":"\u5806\u6392\u5e8f"},"content":{"rendered":"<p>\u5806\u6392\u5e8f\u2014\u2014\u91d1\u5b57\u5854\u6392\u5e8f\u3002\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6&#8211; O(n log n)\uff0c\u5feb\u5427\uff1f\u6211\u5c06\u8fd9\u79cd\u6392\u5e8f\u79f0\u4e3a\u6389\u843d\u5375\u77f3\u7684\u6392\u5e8f\u3002\u5728\u6211\u770b\u6765\uff0c\u6700\u7b80\u5355\u7684\u89e3\u91ca\u65b9\u6cd5\u5c31\u662f\u89c6\u89c9\u5316\u3002<\/p>\n<p><iframe loading=\"lazy\" title=\"Cats Who Knock Things Over! (A compilation)\" width=\"620\" height=\"349\" src=\"https:\/\/www.youtube.com\/embed\/09CC-dYDNMQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p>\u8f93\u5165\u662f\u6570\u5b57\u5217\u8868\uff0c\u4f8b\u5982\uff1a<br \/>\n5\u30010\u30017\u30012\u30013\u30019\u30014<\/p>\n<p>\u4ece\u5de6\u5230\u53f3\uff0c\u521b\u5efa\u4e00\u4e2a\u6570\u636e\u7ed3\u6784 &#8211; \u4e8c\u53c9\u6811\uff0c\u6216\u8005\u6211\u79f0\u4e4b\u4e3a\u201c\u4e8c\u53c9\u6811\u201d\u3002\u91d1\u5b57\u5854\u3002\u91d1\u5b57\u5854\u5143\u7d20\u6700\u591a\u53ef\u4ee5\u6709\u4e24\u4e2a\u5b50\u5143\u7d20\uff0c\u4f46\u53ea\u80fd\u6709\u4e00\u4e2a\u9876\u90e8\u5143\u7d20\u3002<\/p>\n<p>\u8ba9\u6211\u4eec\u5236\u4f5c\u4e00\u68f5\u4e8c\u53c9\u6811\uff1a<br \/>\n\u2800\u28005<br \/>\n\u28000\u28007<br \/>\n2 3 9 4<\/p>\n<p>\u5982\u679c\u4f60\u957f\u65f6\u95f4\u89c2\u5bdf\u91d1\u5b57\u5854\uff0c\u4f60\u4f1a\u53d1\u73b0\u8fd9\u4e9b\u53ea\u662f\u4e00\u4e2a\u6570\u7ec4\u4e2d\u7684\u6570\u5b57\uff0c\u4e00\u4e2a\u63a5\u4e00\u4e2a\u5730\u51fa\u73b0\uff0c\u6bcf\u4e00\u5c42\u7684\u5143\u7d20\u6570\u91cf\u90fd\u4e58\u4ee5\u4e8c\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6709\u8da3\u7684\u4e8b\u60c5\u5f00\u59cb\u4e86\uff1b\u8ba9\u6211\u4eec\u4f7f\u7528\u843d\u4e0b\u7684\u5375\u77f3\u65b9\u6cd5\uff08heapify\uff09\u5bf9\u91d1\u5b57\u5854\u8fdb\u884c\u6392\u5e8f\u3002\u6392\u5e8f\u53ef\u4ee5\u4ece\u6700\u540e\u4e00\u5c42\uff082 3 9 4\uff09\u5f00\u59cb\uff0c\u4f46\u662f\u6ca1\u6709\u610f\u4e49\uff0c\u56e0\u4e3a\u4e0b\u9762\u6ca1\u6709\u4efb\u4f55\u5730\u677f\u53ef\u4ee5\u8ba9\u60a8\u8dcc\u5012\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5f00\u59cb\u4ece\u5012\u6570\u7b2c\u4e8c\u5c42\uff080 7\uff09\u5220\u9664\u5143\u7d20<br \/>\n\u2800\u28005<br \/>\n\u28000\u2800<strong>7<\/strong><br \/>\n2 3 9 4<\/p>\n<p>\u4ece\u53f3\u8fb9\u9009\u62e9\u7b2c\u4e00\u4e2a\u843d\u4e0b\u7684\u5143\u7d20\uff0c\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\u662f7\uff0c\u7136\u540e\u6211\u4eec\u770b\u770b\u5b83\u4e0b\u9762\u7684\u662f\u4ec0\u4e48\uff0c\u5728\u5b83\u4e0b\u9762\u662f9\u548c4\uff0c\u4e5d\u5927\u4e8e\u56db\uff0c\u4e5d\u4e5f\u5927\u4e8e\u4e03\uff01\u6211\u4eec\u5c06 7 \u653e\u5230 9 \u4e0a\uff0c\u7136\u540e\u5c06 9 \u63d0\u5347\u5230 7 \u7684\u4f4d\u7f6e\u3002<br \/>\n\u2800\u28005<br \/>\n\u28000\u28009<br \/>\n2 3 <strong>7<\/strong> 4<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u77e5\u9053\u4e03\u5df2\u7ecf\u65e0\u5904\u53ef\u53bb\uff0c\u6211\u4eec\u7ee7\u7eed\u770b\u6570\u5b57 0\uff0c\u5b83\u4f4d\u4e8e\u5de6\u8fb9\u5012\u6570\u7b2c\u4e8c\u5c42\uff1a<br \/>\n\u2800\u28005<br \/>\n\u2800<strong>0<\/strong>\u28009<br \/>\n2 3 7 4<\/p>\n<p>\u8ba9\u6211\u4eec\u770b\u770b\u4e0b\u9762\u662f\u4ec0\u4e48&#8211; 2\u548c3\uff0c\u4e8c\u5c0f\u4e8e\u4e09\uff0c\u4e09\u5927\u4e8e\u96f6\uff0c\u6240\u4ee5\u6211\u4eec\u4ea4\u6362\u96f6\u548c\u4e09\uff1a<br \/>\n\u2800\u28005<br \/>\n\u28003\u28009<br \/>\n2 <strong>0<\/strong> 7 4<\/p>\n<p>\u5f53\u4f60\u5230\u8fbe\u5730\u677f\u7684\u5c3d\u5934\u65f6\uff0c\u8d70\u5230\u4e0a\u9762\u7684\u5730\u677f\u4e0a\uff0c\u5982\u679c\u53ef\u4ee5\u7684\u8bdd\uff0c\u628a\u6240\u6709\u4e1c\u897f\u90fd\u6254\u5728\u90a3\u91cc\u3002<br \/>\n\u7ed3\u679c\u662f\u4e00\u4e2a\u6570\u636e\u7ed3\u6784\u2014\u2014\u5806\uff0c\u5373\u6700\u5927\u5806\uff0c\u56e0\u4e3a\u9876\u90e8\u662f\u6700\u5927\u7684\u5143\u7d20\uff1a<br \/>\n\u2800\u2800<strong>9<\/strong><br \/>\n\u28003\u28007<br \/>\n2 0 5 4<\/p>\n<p>\u5982\u679c\u5c06\u5176\u8fd4\u56de\u4e3a\u6570\u7ec4\u8868\u793a\u5f62\u5f0f\uff0c\u60a8\u5c06\u5f97\u5230\u4e00\u4e2a\u5217\u8868\uff1a<br \/>\n[<strong>9<\/strong>\u30013\u30017\u30012\u30010\u30015\u30014]<\/p>\n<p>\u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff0c\u901a\u8fc7\u4ea4\u6362\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u5143\u7d20\uff0c\u6211\u4eec\u5f97\u5230\u6700\u7ec8\u6392\u5e8f\u4f4d\u7f6e\u7684\u7b2c\u4e00\u4e2a\u6570\u5b57\uff0c\u5373 9 \u5e94\u8be5\u4f4d\u4e8e\u6392\u5e8f\u5217\u8868\u7684\u672b\u5c3e\uff0c\u4ea4\u6362\u4f4d\u7f6e\uff1a<br \/>\n[4\u30013\u30017\u30012\u30010\u30015\u3001<strong>9<\/strong>]<\/p>\n<p>\u8ba9\u6211\u4eec\u770b\u4e00\u4e0b\u4e8c\u53c9\u6811\uff1a<br \/>\n\u2800\u28004<br \/>\n\u28003\u28007<br \/>\n2 0 5 9<\/p>\n<p>\u7ed3\u679c\u662f\u6811\u7684\u4e0b\u90e8\u5df2\u6392\u5e8f\u7684\u60c5\u51b5\uff0c\u53ea\u9700\u5c06 4 \u653e\u5230\u6b63\u786e\u7684\u4f4d\u7f6e\uff0c\u91cd\u590d\u7b97\u6cd5\uff0c\u4f46\u4e0d\u8003\u8651\u5df2\u7ecf\u6392\u5e8f\u7684\u6570\u5b57\uff0c\u5373 9\uff1a<br \/>\n\u2800\u2800<strong>4<\/strong><br \/>\n\u28003\u28007<br \/>\n2 0 5 9<\/p>\n<p>\u2800\u28007<br \/>\n\u28003\u2800<strong>4<\/strong><br \/>\n2 0 5 9<\/p>\n<p>\u2800\u28007<br \/>\n\u28003\u28005<br \/>\n2 0 <strong>4<\/strong> 9<\/p>\n<p>\u4e8b\u5b9e\u8bc1\u660e\uff0c\u6211\u4eec\u5728\u4e0b\u964d\u4e86 4 \u4e2a\u6570\u5b57\u540e\uff0c\u53c8\u7b79\u96c6\u4e86\u7ee7 9 \u4e2a\u6570\u5b57\u4e4b\u540e\u7684\u4e0b\u4e00\u4e2a\u6700\u5927\u6570\u5b57\u2014\u2014 7. \u4ea4\u6362\u6700\u540e\u4e00\u4e2a\u672a\u6392\u5e8f\u7684\u6570\u5b57\uff084\uff09\u548c\u6700\u5927\u7684\u6570\u5b57\uff087\uff09<br \/>\n\u2800\u28004<br \/>\n\u28003\u28005<br \/>\n2 0 7 9<\/p>\n<p>\u4e8b\u5b9e\u8bc1\u660e\uff0c\u73b0\u5728\u6211\u4eec\u6709\u4e24\u4e2a\u6570\u5b57\u5904\u4e8e\u6b63\u786e\u7684\u6700\u7ec8\u4f4d\u7f6e\uff1a<br \/>\n4\u30013\u30015\u30012\u30010\u3001<strong>7<\/strong>\u3001<strong>9<\/strong><\/p>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u91cd\u590d\u6392\u5e8f\u7b97\u6cd5\uff0c\u5ffd\u7565\u5df2\u7ecf\u6392\u5e8f\u7684\uff0c\u6700\u540e\u6211\u4eec\u5f97\u5230\u4e00\u4e2a <a href=\"https:\/\/www.youtube.com\/watch?v=nnun8y7r8_U\" target=\"_blank\" rel= \u201cnoopener\u201d>\u5806<\/a>\u7c7b\u578b\uff1a<br \/>\n\u2800\u28000<br \/>\n\u28002\u28003<br \/>\n4 5 7 9<\/p>\n<p>\u6216\u8005\u4f5c\u4e3a\u5217\u8868\uff1a<br \/>\n0\u30012\u30013\u30014\u30015\u30017\u30019<\/p>\n<h3>\u5b9e\u65bd<\/h3>\n<p>\u7b97\u6cd5\u901a\u5e38\u5206\u4e3a\u4e09\u4e2a\u51fd\u6570\uff1a<\/p>\n<ol>\n<li>\u521b\u5efa\u5806<\/li>\n<li>\u7b5b\u9009\u7b97\u6cd5\uff08heapify\uff09<\/li>\n<li>\u66ff\u6362\u6700\u540e\u4e00\u4e2a\u672a\u6392\u5e8f\u5143\u7d20\u548c\u7b2c\u4e00\u4e2a\u5143\u7d20<\/li>\n<\/ol>\n<p>\u5806\u662f\u901a\u8fc7\u4f7f\u7528heapify\u51fd\u6570\u4ece\u53f3\u5230\u5de6\u904d\u5386\u4e8c\u53c9\u6811\u7684\u5012\u6570\u7b2c\u4e8c\u884c\uff0c\u76f4\u5230\u6570\u7ec4\u7684\u672b\u5c3e\u6765\u521b\u5efa\u7684\u3002\u63a5\u4e0b\u6765\u5728\u5faa\u73af\u4e2d\uff0c\u8fdb\u884c\u7b2c\u4e00\u6b21\u6570\u5b57\u66ff\u6362\uff0c\u4e4b\u540e\u7b2c\u4e00\u4e2a\u5143\u7d20\u843d\u5165\/\u4fdd\u6301\u5728\u539f\u4f4d\uff0c\u56e0\u6b64\u6700\u5927\u7684\u5143\u7d20\u843d\u5165\u7b2c\u4e00\u4f4d\uff0c\u91cd\u590d\u8be5\u5faa\u73af\uff0c\u53c2\u4e0e\u8005\u51cf\u5c11\u4e00\u4e2a\uff0c\u56e0\u4e3a\u6bcf\u6b21\u4f20\u9012\u540e\uff0c\u6392\u5e8f\u540e\u7684\u6570\u5b57\u4fdd\u7559\u5728\u5217\u8868\u7684\u672b\u5c3e\u3002<\/p>\n<p>Ruby \u4e2d\u7684\u5806\u6392\u5e8f\u793a\u4f8b\uff1a<\/p>\n<div class=\"hcb_wrap\">\n<div class=\"hcb_wrap\">\n<div class=\"hcb_wrap\">\n<pre class=\"prism line-numbers lang-unknown\" data-lang=\"unknown\"><code>\n\n\n\n\nmodule Colors\n\n\n\n    BLUE = \"\\033[94m\"\n\n\n\n    RED = \"\\033[31m\"\n\n\n\n    STOP = \"\\033[0m\"\n\n\n\nend\n\n\n\n\n\n\n\ndef heapsort(rawNumbers)\n\n\n\n    numbers = rawNumbers.dup\n\n\n\n\n\n\n\n    def swap(numbers, from, to)\n\n\n\n        temp = numbers[from]\n\n\n\n        numbers[from] = numbers[to]\n\n\n\n        numbers[to] = temp\n\n\n\n    end\n\n\n\n\n\n\n\n    def heapify(numbers)\n\n\n\n        count = numbers.length()\n\n\n\n        lastParentNode = (count - 2) \/ 2\n\n\n\n\n\n\n\n        for start in lastParentNode.downto(0)\n\n\n\n            siftDown(numbers, start, count - 1)\n\n\n\n            start -= 1 \n\n\n\n        end\n\n\n\n\n\n\n\n        if DEMO\n\n\n\n            puts \"--- heapify ends ---\"\n\n\n\n        end\n\n\n\n    end\n\n\n\n\n\n\n\n    def siftDown(numbers, start, rightBound)      \n\n\n\n        cursor = start\n\n\n\n        printBinaryHeap(numbers, cursor, rightBound)\n\n\n\n\n\n\n\n        def calculateLhsChildIndex(cursor)\n\n\n\n            return cursor * 2 + 1\n\n\n\n        end\n\n\n\n\n\n\n\n        def calculateRhsChildIndex(cursor)\n\n\n\n            return cursor * 2 + 2\n\n\n\n        end            \n\n\n\n\n\n\n\n        while calculateLhsChildIndex(cursor) <= rightBound\n\n\n\n            lhsChildIndex = calculateLhsChildIndex(cursor)\n\n\n\n            rhsChildIndex = calculateRhsChildIndex(cursor)\n\n\n\n\n\n\n\n            lhsNumber = numbers[lhsChildIndex]\n\n\n\n            biggerChildIndex = lhsChildIndex\n\n\n\n\n\n\n\n            if rhsChildIndex <= rightBound\n\n\n\n                rhsNumber = numbers[rhsChildIndex]\n\n\n\n                if lhsNumber < rhsNumber\n\n\n\n                    biggerChildIndex = rhsChildIndex\n\n\n\n                end\n\n\n\n            end\n\n\n\n\n\n\n\n            if numbers[cursor] < numbers[biggerChildIndex]\n\n\n\n                swap(numbers, cursor, biggerChildIndex)\n\n\n\n                cursor = biggerChildIndex\n\n\n\n            else\n\n\n\n                break\n\n\n\n            end\n\n\n\n            printBinaryHeap(numbers, cursor, rightBound)\n\n\n\n        end\n\n\n\n        printBinaryHeap(numbers, cursor, rightBound)\n\n\n\n    end\n\n\n\n\n\n\n\n    def printBinaryHeap(numbers, nodeIndex = -1, rightBound = -1)\n\n\n\n        if DEMO == false\n\n\n\n            return\n\n\n\n        end\n\n\n\n        perLineWidth = (numbers.length() * 4).to_i\n\n\n\n        linesCount = Math.log2(numbers.length()).ceil()\n\n\n\n        xPrinterCount = 1\n\n\n\n        cursor = 0\n\n\n\n        spacing = 3\n\n\n\n        for y in (0..linesCount)\n\n\n\n            line = perLineWidth.times.map { \" \" }\n\n\n\n            spacing = spacing == 3 ? 4 : 3\n\n\n\n            printIndex = (perLineWidth \/ 2) - (spacing * xPrinterCount) \/ 2\n\n\n\n            for x in (0..xPrinterCount - 1)\n\n\n\n                if cursor >= numbers.length\n\n\n\n                    break\n\n\n\n                end\n\n\n\n                if nodeIndex != -1 && cursor == nodeIndex\n\n\n\n                    line[printIndex] = \"%s%s%s\" % [Colors::RED, numbers[cursor].to_s, Colors::STOP]\n\n\n\n                elsif rightBound != -1 && cursor > rightBound\n\n\n\n                    line[printIndex] = \"%s%s%s\" % [Colors::BLUE, numbers[cursor].to_s, Colors::STOP]\n\n\n\n                else\n\n\n\n                    line[printIndex] = numbers[cursor].to_s\n\n\n\n                end\n\n\n\n                cursor += 1\n\n\n\n                printIndex += spacing\n\n\n\n            end\n\n\n\n            print line.join()\n\n\n\n            xPrinterCount *= 2           \n\n\n\n            print \"\\n\"            \n\n\n\n        end\n\n\n\n    end\n\n\n\n\n\n\n\n    heapify(numbers)\n\n\n\n    rightBound = numbers.length() - 1\n\n\n\n\n\n\n\n    while rightBound > 0\n\n\n\n        swap(numbers, 0, rightBound)   \n\n\n\n        rightBound -= 1\n\n\n\n        siftDown(numbers, 0, rightBound)     \n\n\n\n    end\n\n\n\n\n\n\n\n    return numbers\n\n\n\nend\n\n\n\n\n\n\n\nnumbersCount = 14\n\n\n\nmaximalNumber = 10\n\n\n\nnumbers = numbersCount.times.map { Random.rand(maximalNumber) }\n\n\n\nprint numbers\n\n\n\nprint \"\\n---\\n\"\n\n\n\n\n\n\n\nstart = Time.now\n\n\n\nsortedNumbers = heapsort(numbers)\n\n\n\nfinish = Time.now\n\n\n\nheapSortTime = start - finish\n\n\n\n\n\n\n\nstart = Time.now\n\n\n\nreferenceSortedNumbers = numbers.sort()\n\n\n\nfinish = Time.now\n\n\n\nreferenceSortTime = start - finish\n\n\n\n\n\n\n\nprint \"Reference sort: \"\n\n\n\nprint referenceSortedNumbers\n\n\n\nprint \"\\n\"\n\n\n\nprint \"Reference sort time: %f\\n\" % referenceSortTime\n\n\n\nprint \"Heap sort:      \"\n\n\n\nprint sortedNumbers\n\n\n\nprint \"\\n\"\n\n\n\nif DEMO == false\n\n\n\n    print \"Heap sort time:      %f\\n\" % heapSortTime\n\n\n\nelse\n\n\n\n    print \"Disable DEMO for performance measure\\n\"\n\n\n\nend\n\n\n\n\n\n\n\nif sortedNumbers != referenceSortedNumbers\n\n\n\n    puts \"Validation failed\"\n\n\n\n    exit 1\n\n\n\nelse\n\n\n\n    puts \"Validation success\"\n\n\n\n    exit 0\n\n\n\nend\n\n\n\n<\/code><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<p>\u5982\u679c\u6ca1\u6709\u53ef\u89c6\u5316\uff0c\u8fd9\u4e2a\u7b97\u6cd5\u4e0d\u5bb9\u6613\u7406\u89e3\uff0c\u6240\u4ee5\u6211\u5efa\u8bae\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u7f16\u5199\u4e00\u4e2a\u51fd\u6570\u6765\u6253\u5370\u4e8c\u53c9\u6811\u7684\u5f53\u524d\u89c6\u56fe\u3002<\/p>\n<h3>\u94fe\u63a5<\/h3>\n<p><a href=\"https:\/\/gitlab.com\/demensdeum\/algorithms\/-\/blob\/master\/sortAlgorithms\/heapsort\/heapsort.rb\" target=\"_blank\" rel=\"noopener\">https:\/\/gitlab.com\/demensdeum\/algorithms\/-\/blob\/master\/sortAlgorithms\/heapsort\/heapsort.rb<\/a><\/p>\n<h3>\u6765\u6e90<\/h3>\n<p><a href=\"http:\/\/rosettacode.org\/wiki\/Sorting_algorithms\/Heapsort\" target=\"_blank\" rel=\"noopener\">http:\/\/rosettacode.org\/wiki\/Sorting_algorithms\/Heapsort<\/a> <br \/>\n<a href=\"https:\/\/www.youtube.com\/watch?v=LbB357_RwlY\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=LbB357_RwlY<\/a><\/p>\n<p><a href=\"https:\/\/habr.com\/ru\/company\/otus\/blog\/460087\/\" target=\"_blank\" rel=\"noopener\">https:\/\/habr.com\/ru\/company\/ otus\/\u535a\u5ba2\/460087\/<\/a><\/p>\n<p><a href=\"https:\/\/ru.wikipedia.org\/wiki\/Pyramid_sort\" target=\"_blank\" rel=\"noopener\">https:\/\/ru.wikipedia.org\/wiki\/Pyramid_sort<\/a> <\/p>\n<p><a href=\"https:\/\/neerc.ifmo.ru\/wiki\/index.php?title=Heap_sorting\" target=\"_blank\" rel=\"noopener\">https:\/\/neerc.ifmo.ru\/wiki \/index.php?title=Heap_sort<\/a><\/p>\n<p><a href=\"https:\/\/wiki5.ru\/wiki\/Heapsort\" target=\"_blank\" rel=\"noopener\">https:\/\/wiki5.ru\/wiki\/Heapsort<\/a><\/p>\n<p><a href=\"https:\/\/wiki.c2.com\/?HeapSort\" target=\"_blank\" rel=\"noopener\">https:\/\/wiki.c2.com\/?HeapSort<\/a><\/ p><\/p>\n<p><\u4e00href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%94%D0%B5%D1%80%D0%B5%D0%B2%D0%BE_(%D1%81%D1 %82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0_%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B %D1%85)\" target=\"_blank\" rel=\"noopener\">https:\/\/ru.wikipedia.org\/wiki\/Tree\uff08\u6570\u636e\u7ed3\u6784\uff09<\/a><\/p>\n<p><\u4e00href=\"https:\/\/ru.wikipedia.org\/wiki\/%D0%9A%D1%83%D1%87%D0%B0_(%D1%81%D1%82%D1 %80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0_%D0%B4%D0%B0%D0%BD%D0%BD%D1%8B%D1%85 \uff09\u201d target=\"_blank\" rel=\"noopener\">https:\/\/ru.wikipedia.org\/wiki\/Heap\uff08\u6570\u636e\u7ed3\u6784\uff09<\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=2DmK_H7IdTo\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=2DmK_H7IdTo <\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=kU4KBD4NFtw\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=kU4KBD4NFtw <\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=DU1uG5310x0\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=DU1uG5310x0 <\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=BzQGPA_v-vc\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v =BzQGPA_v-vc<\/a><\/p>\n<p><a href=\"https:\/\/www.geeksforgeeks.org\/array-representation-of-binary-heap\/\" target=\"_blank\" rel=\"noopener\">https:\/\/www.geeksforgeeks.org\/\u4e8c\u8fdb\u5236\u5806\u7684\u6570\u7ec4\u8868\u793a\/<\/a><\/p>\n<p><a href=\"https:\/\/habr.com\/ru\/post\/112222\/\" target=\"_blank\" rel=\"noopener\">https:\/\/habr.com\/ru\/post\/112222\/<\/\u4e00\u4e2a><\/p>\n<p><a href=\"https:\/\/www.cs.usfca.edu\/~galles\/visualization\/BST.html\" target=\"_blank\" rel=\"noopener\">https:\/\/www.cs.usfca\u3002 edu\/~galles\/visualization\/BST.html<\/a><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=EQzqHWtsKq4\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=EQzqHWtsKq4 <\/a><\/p>\n<p><\u4e00href=\"https:\/\/medium.com\/@dimko1\/%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC%D1% 8B-%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B8-heapsort-796ba965018b\"\u76ee\u6807=\u201c_\u7a7a\u767d\u201d rel=\"noopener\">https:\/\/medium.com\/@dimko1\/%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC% D1 %8B-%D1%81%D0%BE%D1%80%D1%82%D0%B8%D1%80%D0%BE%D0%B2%D0%BA%D0%B8-heapsort-796ba965018b<\/a <\/p>\n<p><a href=\"https:\/\/ru.wikibrief.org\/wiki\/Heapsort\" target=\"_blank\" rel=\"noopener\">https:\/\/ru.wikibrief.org\/wiki\/Heapsort<\/a> <\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=GUUpmrTnNbw\" target=\"_blank\" rel=\"noopener\">https:\/\/www.youtube.com\/watch?v=GUUpmrTnNbw <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5806\u6392\u5e8f\u2014\u2014\u91d1\u5b57\u5854\u6392\u5e8f\u3002\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6&#8211; O(n log n)\uff0c\u5feb\u5427\uff1f\u6211\u5c06\u8fd9\u79cd\u6392\u5e8f\u79f0\u4e3a\u6389\u843d\u5375\u77f3\u7684\u6392\u5e8f\u3002\u5728\u6211\u770b\u6765\uff0c\u6700\u7b80\u5355\u7684\u89e3\u91ca\u65b9\u6cd5\u5c31\u662f\u89c6\u89c9\u5316\u3002 \u8f93\u5165\u662f\u6570\u5b57\u5217\u8868\uff0c\u4f8b\u5982\uff1a 5\u30010\u30017\u30012\u30013\u30019\u30014 \u4ece\u5de6\u5230\u53f3\uff0c\u521b\u5efa\u4e00\u4e2a\u6570\u636e\u7ed3\u6784 &#8211; \u4e8c\u53c9\u6811\uff0c\u6216\u8005\u6211\u79f0\u4e4b\u4e3a\u201c\u4e8c\u53c9\u6811\u201d\u3002\u91d1\u5b57\u5854\u3002\u91d1\u5b57\u5854\u5143\u7d20\u6700\u591a\u53ef\u4ee5\u6709\u4e24\u4e2a\u5b50\u5143\u7d20\uff0c\u4f46\u53ea\u80fd\u6709\u4e00\u4e2a\u9876\u90e8\u5143\u7d20\u3002 \u8ba9\u6211\u4eec\u5236\u4f5c\u4e00\u68f5\u4e8c\u53c9\u6811\uff1a \u2800\u28005 \u28000\u28007 2 3 9 4 \u5982\u679c\u4f60\u957f\u65f6\u95f4\u89c2\u5bdf\u91d1\u5b57\u5854\uff0c\u4f60\u4f1a\u53d1\u73b0\u8fd9\u4e9b\u53ea\u662f\u4e00\u4e2a\u6570\u7ec4\u4e2d\u7684\u6570\u5b57\uff0c\u4e00\u4e2a\u63a5\u4e00\u4e2a\u5730\u51fa\u73b0\uff0c\u6bcf\u4e00\u5c42\u7684\u5143\u7d20\u6570\u91cf\u90fd\u4e58\u4ee5\u4e8c\u3002 \u63a5\u4e0b\u6765\uff0c\u6709\u8da3\u7684\u4e8b\u60c5\u5f00\u59cb\u4e86\uff1b\u8ba9\u6211\u4eec\u4f7f\u7528\u843d\u4e0b\u7684\u5375\u77f3\u65b9\u6cd5\uff08heapify\uff09\u5bf9\u91d1\u5b57\u5854\u8fdb\u884c\u6392\u5e8f\u3002\u6392\u5e8f\u53ef\u4ee5\u4ece\u6700\u540e\u4e00\u5c42\uff082 3 9 4\uff09\u5f00\u59cb\uff0c\u4f46\u662f\u6ca1\u6709\u610f\u4e49\uff0c\u56e0\u4e3a\u4e0b\u9762\u6ca1\u6709\u4efb\u4f55\u5730\u677f\u53ef\u4ee5\u8ba9\u60a8\u8dcc\u5012\u3002 \u56e0\u6b64\uff0c\u6211\u4eec\u5f00\u59cb\u4ece\u5012\u6570\u7b2c\u4e8c\u5c42\uff080 7\uff09\u5220\u9664\u5143\u7d20 \u2800\u28005 \u28000\u28007 2 3 9 4 \u4ece\u53f3\u8fb9\u9009\u62e9\u7b2c\u4e00\u4e2a\u843d\u4e0b\u7684\u5143\u7d20\uff0c\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\u662f7\uff0c\u7136\u540e\u6211\u4eec\u770b\u770b\u5b83\u4e0b\u9762\u7684\u662f\u4ec0\u4e48\uff0c\u5728\u5b83\u4e0b\u9762\u662f9\u548c4\uff0c\u4e5d\u5927\u4e8e\u56db\uff0c\u4e5d\u4e5f\u5927\u4e8e\u4e03\uff01\u6211\u4eec\u5c06 7 \u653e\u5230 9 \u4e0a\uff0c\u7136\u540e\u5c06 9 \u63d0\u5347\u5230 7 \u7684\u4f4d\u7f6e\u3002 \u2800\u28005 \u28000\u28009 2 3 7 4 \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u77e5\u9053\u4e03\u5df2\u7ecf\u65e0\u5904\u53ef\u53bb\uff0c\u6211\u4eec\u7ee7\u7eed\u770b\u6570\u5b57 0\uff0c\u5b83\u4f4d\u4e8e\u5de6\u8fb9\u5012\u6570\u7b2c\u4e8c\u5c42\uff1a \u2800\u28005 \u28000\u28009 2 3 7 4 \u8ba9\u6211\u4eec\u770b\u770b\u4e0b\u9762\u662f\u4ec0\u4e48&#8211; 2\u548c3\uff0c\u4e8c\u5c0f\u4e8e\u4e09\uff0c\u4e09\u5927\u4e8e\u96f6\uff0c\u6240\u4ee5\u6211\u4eec\u4ea4\u6362\u96f6\u548c\u4e09\uff1a \u2800\u28005<a class=\"more-link\" href=\"https:\/\/demensdeum.com\/blog\/zh\/2022\/08\/08\/heapsort\/\">Continue reading <span class=\"screen-reader-text\">&#8220;\u5806\u6392\u5e8f&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[61,52],"tags":[131,204,190],"class_list":["post-3373","post","type-post","status-publish","format-standard","hentry","category-techie","category-tutorials","tag-algorithms","tag-heapsort","tag-sorting","entry"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"zh","enabled_languages":["en","ru","zh","de","fr","ja","pt","hi"],"languages":{"en":{"title":true,"content":true,"excerpt":false},"ru":{"title":true,"content":true,"excerpt":false},"zh":{"title":true,"content":true,"excerpt":false},"de":{"title":true,"content":true,"excerpt":false},"fr":{"title":true,"content":true,"excerpt":false},"ja":{"title":true,"content":true,"excerpt":false},"pt":{"title":true,"content":true,"excerpt":false},"hi":{"title":false,"content":false,"excerpt":false}}},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/posts\/3373","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/comments?post=3373"}],"version-history":[{"count":22,"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/posts\/3373\/revisions"}],"predecessor-version":[{"id":3866,"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/posts\/3373\/revisions\/3866"}],"wp:attachment":[{"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/media?parent=3373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/categories?post=3373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/demensdeum.com\/blog\/zh\/wp-json\/wp\/v2\/tags?post=3373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}