{"id":1923,"date":"2026-10-09T12:00:00","date_gmt":"2026-10-09T12:00:00","guid":{"rendered":"https:\/\/accelthinking.com\/ccc-2016-j5-s2-tandem-bicycle-solution-analysis\/"},"modified":"2026-10-10T04:01:18","modified_gmt":"2026-10-10T04:01:18","slug":"ccc-2016-j5-s2-tandem-bicycle-solution-analysis","status":"publish","type":"post","link":"https:\/\/accelthinking.com\/zh_cn\/ccc-2016-j5-s2-tandem-bicycle-solution-analysis\/","title":{"rendered":"CCC 2016 J5\/S2 Tandem Bicycle Solution: Sort First, Then Pairing Has Only One Answer"},"content":{"rendered":"<style>\nhtml,body,#page{background:#f8fafc!important}.site-header,.site-footer,#masthead,#colophon,.entry-header,.post-navigation,.comments-area{display:none!important}.entry-title{display:none!important}.site-content .ast-container{max-width:100%!important;padding:0!important}.entry-content{margin:0!important;line-height:0!important}.site-content,#content,#primary,#main,.ast-plain-container 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class=\"ati-letter\" style=\"--i:1\">C<\/span><span class=\"ati-letter\" style=\"--i:2\">C<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:4\">2<\/span><span class=\"ati-letter\" style=\"--i:5\">0<\/span><span class=\"ati-letter\" style=\"--i:6\">1<\/span><span class=\"ati-letter\" style=\"--i:7\">6<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:9\">J<\/span><span class=\"ati-letter\" style=\"--i:10\">5<\/span><span class=\"ati-letter\" style=\"--i:11\">\/<\/span><span class=\"ati-letter\" style=\"--i:12\">S<\/span><span class=\"ati-letter\" style=\"--i:13\">2<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:15\">T<\/span><span class=\"ati-letter\" style=\"--i:16\">a<\/span><span class=\"ati-letter\" style=\"--i:17\">n<\/span><span class=\"ati-letter\" style=\"--i:18\">d<\/span><span class=\"ati-letter\" style=\"--i:19\">e<\/span><span class=\"ati-letter\" style=\"--i:20\">m<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:22\">B<\/span><span class=\"ati-letter\" style=\"--i:23\">i<\/span><span class=\"ati-letter\" style=\"--i:24\">c<\/span><span class=\"ati-letter\" style=\"--i:25\">y<\/span><span class=\"ati-letter\" style=\"--i:26\">c<\/span><span class=\"ati-letter\" style=\"--i:27\">l<\/span><span class=\"ati-letter\" style=\"--i:28\">e<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:30\">S<\/span><span class=\"ati-letter\" style=\"--i:31\">o<\/span><span class=\"ati-letter\" style=\"--i:32\">l<\/span><span class=\"ati-letter\" style=\"--i:33\">u<\/span><span class=\"ati-letter\" style=\"--i:34\">t<\/span><span class=\"ati-letter\" style=\"--i:35\">i<\/span><span class=\"ati-letter\" style=\"--i:36\">o<\/span><span class=\"ati-letter\" style=\"--i:37\">n<\/span><span class=\"ati-letter\" style=\"--i:38\">:<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:40\">S<\/span><span class=\"ati-letter\" style=\"--i:41\">o<\/span><span class=\"ati-letter\" style=\"--i:42\">r<\/span><span class=\"ati-letter\" style=\"--i:43\">t<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:45\">F<\/span><span class=\"ati-letter\" style=\"--i:46\">i<\/span><span class=\"ati-letter\" style=\"--i:47\">r<\/span><span class=\"ati-letter\" style=\"--i:48\">s<\/span><span class=\"ati-letter\" style=\"--i:49\">t<\/span><span class=\"ati-letter\" style=\"--i:50\">,<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:52\">T<\/span><span class=\"ati-letter\" style=\"--i:53\">h<\/span><span class=\"ati-letter\" style=\"--i:54\">e<\/span><span class=\"ati-letter\" style=\"--i:55\">n<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:57\">P<\/span><span class=\"ati-letter\" style=\"--i:58\">a<\/span><span class=\"ati-letter\" style=\"--i:59\">i<\/span><span class=\"ati-letter\" style=\"--i:60\">r<\/span><span class=\"ati-letter\" style=\"--i:61\">i<\/span><span class=\"ati-letter\" style=\"--i:62\">n<\/span><span class=\"ati-letter\" style=\"--i:63\">g<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:65\">H<\/span><span class=\"ati-letter\" style=\"--i:66\">a<\/span><span class=\"ati-letter\" style=\"--i:67\">s<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:69\">O<\/span><span class=\"ati-letter\" style=\"--i:70\">n<\/span><span class=\"ati-letter\" style=\"--i:71\">l<\/span><span class=\"ati-letter\" style=\"--i:72\">y<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:74\">O<\/span><span class=\"ati-letter\" style=\"--i:75\">n<\/span><span class=\"ati-letter\" style=\"--i:76\">e<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:78\">A<\/span><span class=\"ati-letter\" style=\"--i:79\">n<\/span><span class=\"ati-letter\" style=\"--i:80\">s<\/span><span class=\"ati-letter\" style=\"--i:81\">w<\/span><span class=\"ati-letter\" style=\"--i:82\">e<\/span><span class=\"ati-letter\" style=\"--i:83\">r<\/span><\/span><\/span><\/h1>\n<p>Sort both teams, pair in the same order for the minimum or opposite order for the maximum, and prove why with an exchange argument.<\/p>\n<div class=\"ati-article-meta\"><span>\u4f5c\u8005\uff1aBerny<\/span><span>October 9, 2026<\/span><\/div>\n<\/div>\n<aside class=\"ati-side\"><strong>Sort Both Teams<br>Pair by Mode<br>Prove by Exchange<\/strong>\n<p>A factorial-looking pairing problem becomes one sort and one linear scan.<\/p>\n<\/aside>\n<\/section>\n<section class=\"ati-hero ati-lang-zh\">\n<div>\n<p class=\"ati-label\">\u7ade\u8d5b\u7f16\u7a0b\u6bcf\u5468\u6311\u6218<\/p>\n<h1 aria-label=\"CCC 2016 J5\/S2 Tandem Bicycle \u9898\u89e3\uff1a\u6392\u5e8f\u4e4b\u540e\uff0c\u914d\u5bf9\u5c31\u53ea\u5269\u4e00\u79cd\u7b54\u6848\">CCC 2016 J5\/S2 Tandem Bicycle \u9898\u89e3\uff1a\u6392\u5e8f\u4e4b\u540e\uff0c\u914d\u5bf9\u5c31\u53ea\u5269\u4e00\u79cd\u7b54\u6848<\/h1>\n<p>\u5148\u6392\u5e8f\uff1a\u540c\u5e8f\u914d\u5bf9\u5f97\u5230\u6700\u5c0f\u603b\u901f\u5ea6\uff0c\u9006\u5e8f\u914d\u5bf9\u5f97\u5230\u6700\u5927\u603b\u901f\u5ea6\uff0c\u518d\u7528\u4ea4\u6362\u8bba\u8bc1\u8bc1\u660e\u6b63\u786e\u6027\u3002<\/p>\n<div class=\"ati-article-meta\"><span>\u4f5c\u8005\uff1aBerny<\/span><span>2026 \u5e74 10 \u6708 9 \u65e5<\/span><\/div>\n<\/div>\n<aside class=\"ati-side\"><strong>\u4e24\u961f\u6392\u5e8f<br>\u6309\u6a21\u5f0f\u914d\u5bf9<br>\u4ea4\u6362\u8bba\u8bc1<\/strong>\n<p>\u770b\u4f3c\u9700\u8981\u679a\u4e3e\u6240\u6709\u914d\u5bf9\uff0c\u5b9e\u9645\u53ea\u9700\u6392\u5e8f\u4e00\u6b21\u3001\u7ebf\u6027\u626b\u63cf\u4e00\u6b21\u3002<\/p>\n<\/aside>\n<\/section>\n<section class=\"ati-article-shell\">\n<article class=\"ati-article-card\">\n<div class=\"ati-share-tools\" data-ati-share>\n<div class=\"ati-share-copy\">\n<p class=\"ati-share-kicker\">\u5206\u4eab\u8fd9\u7bc7\u6587\u7ae0<\/p>\n<p class=\"ati-share-note\">\u590d\u5236\u94fe\u63a5\u3001\u4f7f\u7528\u624b\u673a\u5206\u4eab\u3001\u7528\u5fae\u4fe1\u626b\u7801\uff0c\u6216\u901a\u8fc7\u90ae\u4ef6\u53d1\u9001\u3002<\/p>\n<\/div>\n<div class=\"ati-share-actions\">\n    <button type=\"button\" data-share-native>\u5206\u4eab<\/button><br>\n    <button type=\"button\" data-share-copy-link>\u590d\u5236\u94fe\u63a5<\/button><br>\n    <button type=\"button\" data-share-wechat>\u5fae\u4fe1\u4e8c\u7ef4\u7801<\/button><br>\n    <a data-share-email>\u90ae\u7bb1<\/a>\n  <\/div>\n<div class=\"ati-share-qr\" data-share-qr hidden>\n    <img loading=\"lazy\" data-share-qr-img alt=\"QR code for sharing this article\">\n<p>\u4f7f\u7528\u5fae\u4fe1\u626b\u7801\uff0c\u7136\u540e\u5206\u4eab\u6587\u7ae0\u94fe\u63a5\u3002<\/p>\n<\/div>\n<p class=\"ati-share-status\" data-share-status aria-live=\"polite\">\n<\/p><\/div>\n<div class=\"ati-article-content ati-lang-en\">\n<article class=\"ati-post-article\">\n<p>Two countries each send N cyclists to ride tandem bicycles, and every bike's speed is decided by \"the faster of its two riders\". The question: pair them so the total speed of all N bikes is as small as possible \u2014 or as large as possible. CCC 2016 J5\/S2 Tandem Bicycle looks like it requires comparing all N! pairings. What it really tests is one greedy line: <strong>sort first, then pair<\/strong>. Once sorted, \"same-order pairing minimizes, opposite-order pairing maximizes\" can be proved by a single exchange argument \u2014 one of the most common greedy shapes in contests.<\/p>\n<h2>\u672c\u9898\u5728 CCC \u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u8def\u7ebf\u56fe\u4e2d\u7684\u4f4d\u7f6e<\/h2>\n<ul>\n<li>Level: Junior J5 \u2261 Senior S2 (the same problem serves both levels)<\/li>\n<li>Pattern: Sorting + Greedy Pairing<\/li>\n<li>Prerequisite: sorting lists, loops, <code>max()<\/code>, Big-O basics (<a href=\"\/zh_cn\/python-syntax-basics-input-operators-conditions\/\">Python basics: input, operators, and conditions<\/a>, <a href=\"\/zh_cn\/python-list-append-vs-plus\/\">Python Lists: append() vs +<\/a>)<\/li>\n<li>What this teaches: prove a greedy rule with an \"one exchange tells the direction\" argument, reducing N! pairings to one scan after sorting<\/li>\n<li>Where it appears again: the greedy topic (planned), the same-week DSA-025 Time on Task greedy proof (python-notes), CPW-026 Time on Task (planned)<\/li>\n<\/ul>\n<h2>What to Study Next<\/h2>\n<ul>\n<li>Related CP Weekly problems: CCC 2013 J4 Time on Task (coming soon \u2014 greedy counting under a budget), and <a href=\"\/zh_cn\/time-on-task-greedy-sorting-exchange-argument\/\">\"Why Does Greedy Sorting Always Work? The Exchange Argument with Time on Task\"<\/a> (Python Notes, same week)<\/li>\n<li>Related Python \/ C++ foundations: <a href=\"\/zh_cn\/python-syntax-basics-input-operators-conditions\/\">Python Basics: Input, Operators, and Conditions<\/a>, <a href=\"\/zh_cn\/python-list-append-vs-plus\/\">Python Lists: append() vs +<\/a><\/li>\n<li>Related DSA roadmap article: Greedy and Binary Search Patterns (planned)<\/li>\n<\/ul>\n<h2>What the Problem Is Asking<\/h2>\n<p>The first line gives q: q=1 asks for the <strong>minimum<\/strong> total speed, q=2 for the <strong>maximum<\/strong>. The second line gives N (1 \u2264 N \u2264 100), the third the N speeds of Dmojistan, the fourth the N speeds of Pegland (each between 1 and 10\u2076). Each tandem bike pairs one rider from each country, and its speed is the larger of the two riders' speeds. Output one integer: the requested total speed.<\/p>\n<p>Official sample 1 (q=1): Dmoj [5 1 4], Peg [6 2 4] \u2192 pair 5-6, 1-2, 4-4, total 6+2+4 = <strong>12<\/strong>.<\/p>\n<p>Official sample 2 (q=2): same data, maximize \u2192 pair 5-2, 1-6, 4-4, total 5+6+4 = <strong>15<\/strong>.<\/p>\n<p>Official sample 3 (q=2, N=5): Dmoj [202 177 189 589 102], Peg [17 78 1 496 540] \u2192 <strong>2016<\/strong>.<\/p>\n<h2>Where Beginners Often Get Stuck<\/h2>\n<ul>\n<li><strong>Enumerating pairings for real<\/strong>: N! pairings sounds hopeless. After sorting, the answer is uniquely determined \u2014 there is nothing to \"choose\".<\/li>\n<li><strong>Adding both riders' speeds<\/strong>: the bike speed is decided by the faster rider \u2014 it is <code>max(a, b)<\/code>; computing a+b (which gives 22 on the sample) solves the wrong objective.<\/li>\n<li><strong>Forgetting to reverse for the maximum<\/strong>: q=2 needs one list ascending and the other descending; skipping the reverse still computes the minimum's shape.<\/li>\n<li><strong>Reversing both lists<\/strong>: reversing both preserves the original pairs and does nothing for the maximum \u2014 if you want speed, reverse exactly one.<\/li>\n<li><strong>Worrying about the proof<\/strong>: \"same-order minimizes\" feels like a guess. The exchange argument below shows it holds for all data, not by luck.<\/li>\n<\/ul>\n<h2>Core Algorithm Idea<\/h2>\n<p>Do the arithmetic of two bikes first. Take any two Dmoj riders a \u2264 b and any two Peg riders c \u2264 d. Only two pairings exist:<\/p>\n<pre><code class=\"language-text\">same-order: max(a, c) + max(b, d)\ncrossed:    max(a, d) + max(b, c)<\/code><\/pre>\n<p>As shown under \"Why the Algorithm Is Correct\", for every a \u2264 b and c \u2264 d, <strong>same-order \u2264 crossed<\/strong>. So every time a \"crossed\" pair is swapped back into same order, the total does not increase \u2014 pairing both ascending by index minimizes the total. The maximizer is the mirror image: one list ascending, the other descending.<\/p>\n<p>This also explains why <strong>summing first kills the greedy<\/strong>: if the bike speed were a+b, every pairing would give the same total, and greedy reasoning would have nothing to hold onto. Reading the objective \u2014 max or sum \u2014 is step one of this problem family.<\/p>\n<h2>State \/ Data Structure Design<\/h2>\n<ul>\n<li><code>q<\/code>: objective type, 1 = minimum total, 2 = maximum total.<\/li>\n<li><code>n<\/code>: riders per country, i.e., the number of tandem bikes.<\/li>\n<li><code>dmoj<\/code>, <code>peg<\/code>: the two speed lists, sorted (and possibly reversed), then paired by index.<\/li>\n<li><code>total<\/code>: the sum of <code>max(dmoj[i], peg[i])<\/code> over all pairs.<\/li>\n<\/ul>\n<p>No need to record \"who paired with whom\" \u2014 the pairing is uniquely decided by the sorted order.<\/p>\n<h2>Algorithm Steps<\/h2>\n<ol>\n<li>Read q, n, and the two speed lists of length n each.<\/li>\n<li>Sort both lists in ascending order.<\/li>\n<li>If q=2, reverse <code>peg<\/code> (exactly one list).<\/li>\n<li>Walk the indices, adding <code>max(dmoj[i], peg[i])<\/code> into <code>total<\/code>.<\/li>\n<li>print<code>total<\/code>.<\/li>\n<\/ol>\n<h2>Sample Check with the Official Data<\/h2>\n<p>Walk both objectives on the sample data (sort [5 1 4] into [1 4 5], [6 2 4] into [2 4 6]):<\/p>\n<div class=\"ati-table-wrap\">\n<table>\n<thead>\n<tr>\n<th>Index<\/th>\n<th>dmoj<\/th>\n<th>peg (same order)<\/th>\n<th>Bike<\/th>\n<th>peg (reversed)<\/th>\n<th>Bike<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<td>2<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>Total<\/td>\n<td><\/td>\n<td><\/td>\n<td><strong>12 (min)<\/strong><\/td>\n<td><\/td>\n<td><strong>15 (max)<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Same-order gives 12, matching sample 1; reversed gives 15, matching sample 2. Sample 3's 2016 comes from the same \"ascending + descending\" pairing. This table is the whole core of greedy pairing: sort once, scan once per objective.<\/p>\n<h2>Python \u89e3\u6cd5<\/h2>\n<pre><code class=\"language-python\">q = int(input())\nn = int(input())\ndmoj = list(map(int, input().split()))\npeg = list(map(int, input().split()))\n\ndmoj.sort()\npeg.sort()\n\nif q == 2:\n    peg.reverse()\n\ntotal = 0\nfor i in range(n):\n    total += max(dmoj[i], peg[i])\n\nprint(total)<\/code><\/pre>\n<p>This matches the curriculum notebook (p2006, sorting and greedy reasoning) line for line \u2014 sort, reverse when asked, accumulate. <code>total \u2264 100 \u00d7 10\u2076 = 10\u2078<\/code>, which Python integers handle easily; a 32-bit signed int also just barely fits, though building the <code>long long<\/code> habit is safer.<\/p>\n<h2>C++ \u89e3\u6cd5<\/h2>\n<pre><code class=\"language-cpp\">#include &lt;algorithm&gt;\n#include &lt;iostream&gt;\n#include &lt;vector&gt;\nusing namespace std;\n\nint main() {\n    int q;\n    cin &gt;&gt; q;\n    int n;\n    cin &gt;&gt; n;\n    vector&lt;int&gt; dmoj(n);\n    for (int i = 0; i &lt; n; i++) {\n        cin &gt;&gt; dmoj[i];\n    }\n    vector&lt;int&gt; peg(n);\n    for (int i = 0; i &lt; n; i++) {\n        cin &gt;&gt; peg[i];\n    }\n\n    sort(dmoj.begin(), dmoj.end());\n    sort(peg.begin(), peg.end());\n    if (q == 2) {\n        reverse(peg.begin(), peg.end());\n    }\n\n    long long total = 0;\n    for (int i = 0; i &lt; n; i++) {\n        total += max(dmoj[i], peg[i]);\n    }\n\n    cout &lt;&lt; total &lt;&lt; &#x27;\\n&#x27;;\n    return 0;\n}<\/code><\/pre>\n<p>Mirrors the curriculum pseudocode step by step: <code>sort<\/code> is O(N log N), the accumulation O(N), and the official limits finish in well under a millisecond. Sorting aux space: Python's <code>sort<\/code> uses O(N) worst case, C++ introsort O(log N) stack.<\/p>\n<h2>Why the Algorithm Is Correct<\/h2>\n<ul>\n<li><strong>Each bike's speed is indeed a max<\/strong>: the statement defines the bike speed as the larger of the two riders' speeds, matching <code>max(dmoj[i], peg[i])<\/code>.<\/li>\n<li><strong>Same-order pairing minimizes the total<\/strong>: take any two \"crossed\" pairs (a,d) and (b,c) with a \u2264 b and d \u2265 c (as they appear in the sorted lists). Swap them back to (a,c), (b,d). For every a \u2264 b and c \u2264 d, max(a,c) + max(b,d) \u2264 max(a,d) + max(b,c): check the four size cases one by one (for example, when a \u2264 c \u2264 b \u2264 d, the left side is c + d and the right side is d + b, and c \u2264 b makes the left \u2264 right). Any pairing can be sorted into same order by finitely many such \"descent swaps\", each never increasing the total, so the same-order pairing is minimal.<\/li>\n<li><strong>Reversed pairing maximizes the total<\/strong>: swapping the two sides of the same inequality gives max(a,d) + max(b,c) \u2265 max(a,c) + max(b,d) \u2014 the reversed pairing is the mirror image of the same argument.<\/li>\n<li><strong>No better pairing is missed<\/strong>: sorting fixes the relative order of both sequences; every index-based pairing corresponds to exactly one \"same-order\" or \"opposite-order\" shape, so nothing better is left out.<\/li>\n<\/ul>\n<p>Therefore the printed total is exactly the requested minimum or maximum total speed.<\/p>\n<h2>\u590d\u6742\u5ea6\u5206\u6790<\/h2>\n<ul>\n<li>Time O(N log N): the two sorts dominate; the pairing pass is O(N). At N=100 this runs in well under a millisecond.<\/li>\n<li>Space O(N): the two speed lists (see above for sort aux space).<\/li>\n<li>If N grew to 10\u2075, this would still be the standard solution \u2014 the proof and the sorting both scale unchanged.<\/li>\n<\/ul>\n<h2>\u5e38\u89c1\u9519\u8bef<\/h2>\n<ol>\n<li>Summing both riders' speeds \u2014 misreading the objective as a+b (the sample would give 22).<\/li>\n<li>Forgetting the reverse for q=2 \u2014 or reversing both lists (which reverses nothing).<\/li>\n<li>Sorting only one list \u2014 the unsorted side makes the pairing depend on input order.<\/li>\n<li>Memorizing \"same-order minimizes\" without the proof \u2014 under a different objective (like a sum) the greedy dies instantly; be ready to retell the exchange argument.<\/li>\n<li>Misreading the input \u2014 q, n, then two lines of speeds; line up with the samples row by row.<\/li>\n<\/ol>\n<h2>Review Questions<\/h2>\n<ol>\n<li>Complete the exchange argument for all four relative orders of a \u2264 b and c \u2264 d, and explain why same-order pairing is never worse than crossed pairing.<\/li>\n<li>If the bike speed were changed to the sum of both riders' speeds, would sort-and-pair still work? Why or why not?<\/li>\n<li>Why does reversing both lists fail to maximize the total? Explain with the pairs at indices 0 and N\u22121.<\/li>\n<li>This problem shares one greedy habit with Time on Task (finish as many tasks as possible within a budget). What is that sentence? (Hint: see DSA-025.)<\/li>\n<li>With N \u2264 10\u2075 and speeds \u2264 10\u2079, what are the time and space complexities? Is there a better asymptotic order?<\/li>\n<\/ol>\n<\/article>\n<\/div>\n<div class=\"ati-article-content ati-lang-zh\">\n<article class=\"ati-post-article\">\n<p>\u4e24\u4e2a\u56fd\u5bb6\u5404\u6d3e\u51fa N \u540d\u9a91\u624b\u9a91\u53cc\u4eba\u81ea\u884c\u8f66\uff0c\u6bcf\u8f86\u8f66\u7684\u901f\u5ea6\u7531\"\u8f83\u5feb\u7684\u90a3\u4e2a\u4eba\"\u51b3\u5b9a\u3002\u95ee\uff1a\u600e\u4e48\u914d\u5bf9\uff0c\u624d\u80fd\u8ba9 N \u8f86\u8f66\u7684\u603b\u901f\u5ea6\u6700\u5c0f\uff1f\u6216\u8005\u6700\u5927\uff1fCCC 2016 \u7684 J5\/S2 Tandem Bicycle \u770b\u8d77\u6765\u6709 N! \u79cd\u914d\u5bf9\u65b9\u6848\u8981\u6bd4\u8f83\uff0c\u771f\u6b63\u8003\u7684\u5374\u662f\u4e00\u53e5\u8d2a\u5fc3\u53e3\u8bc0\uff1a<strong>\u5148\u6392\u5e8f\uff0c\u518d\u914d\u5bf9<\/strong>\u3002\u6392\u5e8f\u4e4b\u540e\uff0c\"\u540c\u5e8f\u914d\u5bf9\u5f97\u6700\u5c0f\u3001\u9006\u5e8f\u914d\u5bf9\u5f97\u6700\u5927\"\u53ef\u4ee5\u88ab\u4e00\u6761\u4ea4\u6362\u8bba\u8bc1\u4e25\u683c\u8bc1\u660e\u2014\u2014\u8fd9\u662f\u7ade\u8d5b\u91cc\u6700\u5e38\u89c1\u7684\u8d2a\u5fc3\u5f62\u6001\u4e4b\u4e00\u3002<\/p>\n<h2>\u672c\u9898\u5728 CCC DSA \u5730\u56fe\u91cc\u7684\u4f4d\u7f6e<\/h2>\n<ul>\n<li>Level: Junior J5 \u2261 Senior S2\uff08\u540c\u4e00\u9053\u9898\uff0c\u4e24\u4e2a\u7ea7\u522b\u5171\u7528\uff09<\/li>\n<li>Pattern: Sorting + Greedy Pairing\uff08\u6392\u5e8f + \u8d2a\u5fc3\u914d\u5bf9\uff09<\/li>\n<li>Prerequisite: \u5217\u8868\u6392\u5e8f\u3001\u5faa\u73af\u3001<code>max()<\/code>\u3001Big-O \u57fa\u7840\uff08<a href=\"\/zh_cn\/python-syntax-basics-input-operators-conditions\/\">Python \u57fa\u7840\uff1a\u8f93\u5165\u3001\u8fd0\u7b97\u7b26\u4e0e\u6761\u4ef6<\/a>\u3001<a href=\"\/zh_cn\/python-list-append-vs-plus\/\">Python \u5217\u8868 append() \u548c + \u7684\u533a\u522b<\/a>\uff09<\/li>\n<li>What this teaches: \u7528\"\u4ea4\u6362\u4e00\u5bf9\u5c31\u77e5\u65b9\u5411\"\u7684\u8bba\u8bc1\u8bc1\u660e\u8d2a\u5fc3\u6b63\u786e\uff0c\u628a N! \u79cd\u914d\u5bf9\u5316\u7b80\u4e3a\u6392\u5e8f\u540e\u7684\u4e00\u6b21\u626b\u63cf<\/li>\n<li>Where it appears again: \u8d2a\u5fc3\u4e13\u9898 \uff08planned\uff09\u3001\u540c\u5468\u53d1\u5e03\u7684 DSA-025 Time on Task \u8d2a\u5fc3\u8bc1\u660e\uff08python-notes\uff09\u3001CPW-026 Time on Task\uff08planned\uff09<\/li>\n<\/ul>\n<h2>\u4e0b\u4e00\u6b65\u63a8\u8350<\/h2>\n<p>\u5982\u679c\u4f60\u5df2\u7ecf\u7406\u89e3\u8fd9\u9053\u9898\uff0c\u53ef\u4ee5\u7ee7\u7eed\u770b\uff1a<\/p>\n<ul>\n<li>\u76f8\u5173 CP Weekly \u771f\u9898\uff1aCCC 2013 J4 Time on Task\uff08coming soon\uff0c\u9884\u7b97\u5185\u6700\u591a\u5b8c\u6210\u51e0\u4e2a\u4efb\u52a1\u7684\u8d2a\u5fc3\u8ba1\u6570\uff09\u3001<a href=\"\/zh_cn\/time-on-task-greedy-sorting-exchange-argument\/\">\u300a\u8d2a\u5fc3\u6392\u5e8f\u4e3a\u4ec0\u4e48\u4e00\u5b9a\u5bf9\uff1f\u4ece Time on Task \u8bb2\u6e05\u4ea4\u6362\u8bba\u8bc1\u300b<\/a>\uff08Python Notes\uff0c\u540c\u5468\u53d1\u5e03\uff09<\/li>\n<li>\u76f8\u5173 Python \/ C++ \u57fa\u7840\uff1a<a href=\"\/zh_cn\/python-syntax-basics-input-operators-conditions\/\">Python \u57fa\u7840\uff1a\u8f93\u5165\u3001\u8fd0\u7b97\u7b26\u4e0e\u6761\u4ef6<\/a>\u3001<a href=\"\/zh_cn\/python-list-append-vs-plus\/\">Python \u5217\u8868 append() \u548c + \u7684\u533a\u522b<\/a><\/li>\n<li>\u76f8\u5173 DSA \u4e13\u9898\uff1aGreedy and Binary Search Patterns\uff08planned\uff09<\/li>\n<\/ul>\n<h2>\u9898\u76ee\u8981\u6211\u4eec\u505a\u4ec0\u4e48<\/h2>\n<p>\u7b2c\u4e00\u884c\u4e00\u4e2a\u6574\u6570 q\uff1aq=1 \u6c42\u603b\u901f\u5ea6<strong>\u6700\u5c0f\u503c<\/strong>\uff0cq=2 \u6c42<strong>\u6700\u5927\u503c<\/strong>\u3002\u7b2c\u4e8c\u884c N\uff081 \u2264 N \u2264 100\uff09\uff0c\u7b2c\u4e09\u884c Dmojistan \u7684 N \u4e2a\u901f\u5ea6\uff0c\u7b2c\u56db\u884c Pegland \u7684 N \u4e2a\u901f\u5ea6\uff08\u6bcf\u4eba\u901f\u5ea6 1 \u5230 10\u2076\uff09\u3002\u6bcf\u8f86\u53cc\u4eba\u81ea\u884c\u8f66\u7531\u4e24\u56fd\u5404\u4e00\u4eba\u7ec4\u6210\uff0c\u8f66\u901f = \u4e24\u4eba\u901f\u5ea6\u7684\u8f83\u5927\u503c\u3002\u8f93\u51fa\u4e00\u4e2a\u6574\u6570\uff1a\u6240\u6c42\u7684\u603b\u901f\u5ea6\u3002<\/p>\n<p>\u5b98\u65b9\u6837\u4f8b 1\uff08q=1\uff09\uff1aDmoj [5 1 4]\uff0cPeg [6 2 4] \u2192 \u6700\u4f18\u914d\u5bf9 5-6\u30011-2\u30014-4\uff0c\u603b\u901f\u5ea6 6+2+4 = <strong>12<\/strong>\u3002<\/p>\n<p>\u5b98\u65b9\u6837\u4f8b 2\uff08q=2\uff09\uff1a\u540c\u6837\u6570\u636e\u6c42\u6700\u5927 \u2192 \u914d\u5bf9 5-2\u30011-6\u30014-4\uff0c\u603b\u901f\u5ea6 5+6+4 = <strong>15<\/strong>\u3002<\/p>\n<p>\u5b98\u65b9\u6837\u4f8b 3\uff08q=2\uff0cN=5\uff09\uff1aDmoj [202 177 189 589 102]\uff0cPeg [17 78 1 496 540] \u2192 <strong>2016<\/strong>\u3002<\/p>\n<h2>\u521d\u5b66\u8005\u5bb9\u6613\u5361\u5728\u54ea\u91cc<\/h2>\n<ul>\n<li><strong>\u771f\u7684\u53bb\u679a\u4e3e\u914d\u5bf9<\/strong>\uff1aN! \u79cd\u914d\u5bf9\u4e00\u60f3\u5c31\u653e\u5f03\u3002\u5176\u5b9e\u6392\u5e8f\u4e4b\u540e\u7b54\u6848\u552f\u4e00\u786e\u5b9a\uff0c\u6839\u672c\u4e0d\u7528\"\u9009\"\u914d\u5bf9\u3002<\/li>\n<li><strong>\u628a\u4e24\u4eba\u901f\u5ea6\u76f8\u52a0<\/strong>\uff1a\u9898\u76ee\u8bf4\u8f66\u901f\u7531\u8f83\u5feb\u8005\u51b3\u5b9a\uff0c\u662f <code>max(a, b)<\/code>\uff1b\u5982\u679c\u6309 a+b \u8ba1\u7b97\uff08\u6837\u4f8b\u4f1a\u5f97 22\uff09\uff0c\u5c31\u89e3\u9519\u4e86\u76ee\u6807\u3002<\/li>\n<li><strong>\u6700\u5927\u503c\u65f6\u5fd8\u8bb0\u53cd\u8f6c<\/strong>\uff1aq=2 \u8981\"\u4e00\u4e2a\u5347\u5e8f\u3001\u4e00\u4e2a\u964d\u5e8f\"\uff1b\u5fd8\u8bb0\u53cd\u8f6c\u3001\u4e24\u4e2a\u90fd\u5347\u5e8f\uff0c\u7b97\u51fa\u6765\u7684\u8fd8\u662f\u6700\u5c0f\u503c\u7684\u601d\u8def\u3002<\/li>\n<li><strong>\u4e24\u4e2a\u5217\u8868\u90fd\u53cd\u8f6c<\/strong>\uff1a\u53cd\u8f6c\u4e24\u4e2a\u5217\u8868\u7b49\u4e8e\u4fdd\u6301\u539f\u6765\u7684\u914d\u5bf9\uff0c\u5bf9\u6700\u5927\u503c\u6beb\u65e0\u4f5c\u7528\u2014\u2014\u60f3\u63d0\u901f\u7684\u8bdd\u53ea\u80fd\u53cd\u8f6c\u4e00\u4e2a\u3002<\/li>\n<li><strong>\u62c5\u5fc3\u8bc1\u660e<\/strong>\uff1a\u89c9\u5f97\"\u540c\u5e8f\u6700\u5c0f\"\u662f\u731c\u7684\u3002\u4e0b\u9762\u7684\u4ea4\u6362\u8bba\u8bc1\u4f1a\u8bf4\u660e\u5b83\u5bf9\u6240\u6709\u6570\u636e\u6210\u7acb\uff0c\u4e0d\u662f\u78b0\u8fd0\u6c14\u3002<\/li>\n<\/ul>\n<h2>\u6838\u5fc3\u7b97\u6cd5\u6982\u5ff5<\/h2>\n<p>\u5148\u628a\u4e24\u8f86\u8f66\u7684\u8d26\u7b97\u6e05\u695a\u3002\u53d6 Dmoj \u4e2d\u4efb\u610f\u4e24\u4eba a \u2264 b\uff0cPeg \u4e2d\u4efb\u610f\u4e24\u4eba c \u2264 d\uff0c\u53ea\u6709\u4e24\u79cd\u914d\u6cd5\uff1a<\/p>\n<pre><code class=\"language-text\">\u540c\u5e8f\uff1amax(a, c) + max(b, d)\n\u4ea4\u53c9\uff1amax(a, d) + max(b, c)<\/code><\/pre>\n<p>\u53ef\u4ee5\u8bc1\u660e\uff08\u89c1\"\u6b63\u786e\u6027\u8bf4\u660e\"\uff09\uff1a\u5bf9\u4efb\u610f a \u2264 b\u3001c \u2264 d\uff0c<strong>\u540c\u5e8f \u2264 \u4ea4\u53c9<\/strong>\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u53ea\u8981\u628a\"\u8c01\u8be5\u548c\u8c01\u914d\"\u7684\u6b21\u5e8f\u7406\u987a\uff0c\u6bcf\u4ea4\u6362\u56de\u4e00\u5bf9\uff0c\u603b\u901f\u5ea6\u5c31\u4e0d\u4f1a\u53d8\u5927\u2014\u2014\u4e8e\u662f\"\u4e24\u4e2a\u90fd\u5347\u5e8f\u3001\u6309\u4e0b\u6807\u914d\u5bf9\"\u8ba9\u603b\u901f\u5ea6\u6700\u5c0f\uff1b\u800c\u603b\u901f\u5ea6\u6700\u5927\u7684\u914d\u6cd5\u6070\u597d\u662f\u5b83\u7684\u955c\u50cf\uff1a\u4e00\u4e2a\u5347\u5e8f\u3001\u53e6\u4e00\u4e2a\u964d\u5e8f\u3002<\/p>\n<p>\u8fd9\u4e5f\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48<strong>\u4e0d\u80fd\u5148\u6c42\u548c\u518d\u6392\u5e8f<\/strong>\uff1a\u5982\u679c\u8f66\u901f\u662f a+b\uff0c\u65e0\u8bba\u600e\u4e48\u914d\u5bf9\u603b\u548c\u90fd\u4e00\u6837\uff0c\u8d2a\u5fc3\u7acb\u523b\u5931\u6548\u2014\u2014\u770b\u6e05\u76ee\u6807\u662f max \u8fd8\u662f sum\uff0c\u662f\u8fd9\u7c7b\u9898\u7684\u7b2c\u4e00\u6b65\u3002<\/p>\n<h2>\u72b6\u6001\u5b9a\u4e49<\/h2>\n<ul>\n<li><code>q<\/code>\uff1a\u76ee\u6807\u7c7b\u578b\uff0c1 = \u6700\u5c0f\u603b\u901f\u5ea6\uff0c2 = \u6700\u5927\u603b\u901f\u5ea6\u3002<\/li>\n<li><code>n<\/code>\uff1a\u6bcf\u56fd\u7684\u9a91\u624b\u6570\uff0c\u5373\u53cc\u4eba\u81ea\u884c\u8f66\u6570\u3002<\/li>\n<li><code>dmoj<\/code>\u3001<code>peg<\/code>\uff1a\u4e24\u56fd\u901f\u5ea6\u5217\u8868\uff0c\u6392\u5e8f\uff08\u5fc5\u8981\u65f6\u53cd\u8f6c\uff09\u540e\u6309\u4e0b\u6807\u4e00\u4e00\u914d\u5bf9\u3002<\/li>\n<li><code>total<\/code>\uff1a\u6240\u6709\u914d\u5bf9 <code>max(dmoj[i], peg[i])<\/code> \u7684\u548c\u3002<\/li>\n<\/ul>\n<p>\u4e0d\u9700\u8981\u8bb0\u5f55\"\u8c01\u914d\u4e86\u8c01\"\u2014\u2014\u914d\u5bf9\u7531\u6392\u5e8f\u7ed3\u679c\u552f\u4e00\u51b3\u5b9a\u3002<\/p>\n<h2>\u7b97\u6cd5\u6b65\u9aa4<\/h2>\n<ol>\n<li>\u8bfb\u5165 q\u3001n \u548c\u4e24\u4e2a\u957f\u5ea6\u5404\u4e3a n \u7684\u901f\u5ea6\u5217\u8868\u3002<\/li>\n<li>\u4e24\u4e2a\u5217\u8868\u5404\u81ea\u5347\u5e8f\u6392\u5e8f\u3002<\/li>\n<li>\u82e5 q=2\uff0c\u628a <code>peg<\/code> \u53cd\u8f6c\uff08\u53ea\u53cd\u8f6c\u4e00\u4e2a\uff09\u3002<\/li>\n<li>\u904d\u5386\u4e0b\u6807 i\uff0c\u7d2f\u52a0 <code>max(dmoj[i], peg[i])<\/code> \u5230 <code>total<\/code>\u3002<\/li>\n<li>\u8f93\u51fa <code>total<\/code>\u3002<\/li>\n<\/ol>\n<h2>\u5b98\u65b9\u6837\u4f8b\u6838\u5bf9<\/h2>\n<p>\u7528\u6837\u4f8b\u6570\u636e\u628a\u4e24\u79cd\u76ee\u6807\u5404\u8d70\u4e00\u904d\uff08\u5148\u628a [5 1 4] \u6392\u6210 [1 4 5]\uff0c[6 2 4] \u6392\u6210 [2 4 6]\uff09\uff1a<\/p>\n<div class=\"ati-table-wrap\">\n<table>\n<thead>\n<tr>\n<th>\u4e0b\u6807<\/th>\n<th>dmoj<\/th>\n<th>peg\uff08\u540c\u5e8f\uff09<\/th>\n<th>\u8f66\u901f<\/th>\n<th>peg\uff08\u9006\u5e8f\uff09<\/th>\n<th>\u8f66\u901f<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>2<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>6<\/td>\n<td>2<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>\u5408\u8ba1<\/td>\n<td><\/td>\n<td><\/td>\n<td><strong>12\uff08\u6700\u5c0f\uff09<\/strong><\/td>\n<td><\/td>\n<td><strong>15\uff08\u6700\u5927\uff09<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>\u540c\u5e8f\u5408\u8ba1 12 \u4e0e\u6837\u4f8b 1 \u4e00\u81f4\uff1b\u9006\u5e8f\u5408\u8ba1 15 \u4e0e\u6837\u4f8b 2 \u4e00\u81f4\u3002\u6837\u4f8b 3 \u7684 2016 \u540c\u6837\u7531\"\u5347\u5e8f + \u964d\u5e8f\"\u914d\u5bf9\u5f97\u5230\u3002\u8fd9\u5f20\u8868\u5c31\u662f\u8d2a\u5fc3 pairing \u7684\u5168\u90e8\u6838\u5fc3\uff1a\u6392\u5e8f\u4e00\u6b21\uff0c\u4e24\u79cd\u7b54\u6848\u5404\u626b\u4e00\u904d\u3002<\/p>\n<h2>Python \u89e3\u6cd5<\/h2>\n<pre><code class=\"language-python\">q = int(input())\nn = int(input())\ndmoj = list(map(int, input().split()))\npeg = list(map(int, input().split()))\n\ndmoj.sort()\npeg.sort()\n\nif q == 2:\n    peg.reverse()\n\ntotal = 0\nfor i in range(n):\n    total += max(dmoj[i], peg[i])\n\nprint(total)<\/code><\/pre>\n<p>\u8981\u70b9\uff1a\u4ee3\u7801\u4e0e\u8bfe\u7a0b\u6559\u6848\uff08p2006 \u6392\u5e8f\u4e0e\u8d2a\u5fc3\u63a8\u7406\uff09\u7684\u53c2\u8003\u5b9e\u73b0\u4e00\u81f4\u2014\u2014\u6392\u5e8f\u3001\u6309\u9700\u53cd\u8f6c\u3001\u4e00\u6b21\u7d2f\u52a0\u3002<code>total \u2264 100 \u00d7 10\u2076 = 10\u2078<\/code>\uff0cPython \u6574\u6570\u65e0\u538b\u529b\uff1b\u5982\u679c\u79fb\u690d\u5230\u5176\u4ed6\u8bed\u8a00\u6ce8\u610f\u7528 32 \u4f4d\u6709\u7b26\u53f7\u6574\u6570\u4e5f\u521a\u597d\u591f\u7528\uff0c\u4f46\u517b\u6210 <code>long long<\/code> \u7684\u4e60\u60ef\u66f4\u7a33\u59a5\u3002<\/p>\n<h2>C++ \u89e3\u6cd5<\/h2>\n<pre><code class=\"language-cpp\">#include &lt;algorithm&gt;\n#include &lt;iostream&gt;\n#include &lt;vector&gt;\nusing namespace std;\n\nint main() {\n    int q;\n    cin &gt;&gt; q;\n    int n;\n    cin &gt;&gt; n;\n    vector&lt;int&gt; dmoj(n);\n    for (int i = 0; i &lt; n; i++) {\n        cin &gt;&gt; dmoj[i];\n    }\n    vector&lt;int&gt; peg(n);\n    for (int i = 0; i &lt; n; i++) {\n        cin &gt;&gt; peg[i];\n    }\n\n    sort(dmoj.begin(), dmoj.end());\n    sort(peg.begin(), peg.end());\n    if (q == 2) {\n        reverse(peg.begin(), peg.end());\n    }\n\n    long long total = 0;\n    for (int i = 0; i &lt; n; i++) {\n        total += max(dmoj[i], peg[i]);\n    }\n\n    cout &lt;&lt; total &lt;&lt; &#x27;\\n&#x27;;\n    return 0;\n}<\/code><\/pre>\n<p>\u8981\u70b9\uff1a\u4e0e\u6559\u6848\u4f2a\u4ee3\u7801\u9010\u6b65\u5bf9\u5e94\uff1b<code>sort<\/code> \u4e3a O(N log N)\u3001\u7d2f\u52a0\u4e3a O(N)\uff0c\u5b98\u65b9\u6570\u636e\u89c4\u6a21\u4e0b\u6beb\u79d2\u7ea7\u5b8c\u6210\u3002\u6392\u5e8f\u7684\u8f85\u52a9\u7a7a\u95f4\uff1aPython <code>sort<\/code> \u6700\u574f O(N)\uff0cC++ introsort \u6808\u7a7a\u95f4 O(log N)\u3002<\/p>\n<h2>\u6b63\u786e\u6027\u8bf4\u660e<\/h2>\n<ul>\n<li><strong>\u6bcf\u8f86\u8f66\u786e\u5b9e\u7531 max \u51b3\u5b9a<\/strong>\uff1a\u9898\u9762\u89c4\u5b9a\u8f66\u901f\u4e3a\u4e24\u9a91\u624b\u901f\u5ea6\u7684\u8f83\u5927\u503c\uff0c\u7b97\u6cd5\u4e2d\u7684 <code>max(dmoj[i], peg[i])<\/code> \u4e0e\u9898\u9762\u4e00\u81f4\u3002<\/li>\n<li><strong>\u540c\u5e8f\u914d\u5bf9\u4f7f\u603b\u901f\u5ea6\u6700\u5c0f<\/strong>\uff1a\u53d6\u4efb\u610f\u4e24\u5bf9\"\u4ea4\u53c9\"\u7684\u914d\u5bf9 (a,d) \u4e0e (b,c)\uff0c\u5176\u4e2d a \u2264 b\u3001d \u2265 c\uff08\u90fd\u5728\u5404\u81ea\u5347\u5e8f\u5217\u8868\u4e2d\uff09\u3002\u628a\u5b83\u4eec\u6362\u56de\u540c\u5e8f (a,c)\u3001(b,d)\u3002\u5bf9\u4efb\u610f a \u2264 b\u3001c \u2264 d \u6709 max(a,c) + max(b,d) \u2264 max(a,d) + max(b,c)\uff1a\u5206\u56db\u79cd\u5927\u5c0f\u60c5\u5f62\u9010\u4e00\u5c55\u5f00\u5373\u53ef\u9a8c\u8bc1\uff08\u4f8b\u5982 a \u2264 c \u2264 b \u2264 d \u65f6\uff0c\u5de6\u8fb9 = c + d\u3001\u53f3\u8fb9 = d + b\uff0c\u7531 c \u2264 b \u5f97\u5de6\u8fb9 \u2264 \u53f3\u8fb9\uff09\u3002\u4efb\u610f\u914d\u5bf9\u90fd\u53ef\u901a\u8fc7\u6709\u9650\u6b21\u8fd9\u6837\u7684\"\u9006\u5e8f\u4ea4\u6362\"\u6392\u6210\u540c\u5e8f\uff0c\u6bcf\u6b21\u4ea4\u6362\u603b\u901f\u5ea6\u4e0d\u589e\uff0c\u6545\u540c\u5e8f\u914d\u5bf9\u6700\u5c0f\u3002<\/li>\n<li><strong>\u9006\u5e8f\u914d\u5bf9\u4f7f\u603b\u901f\u5ea6\u6700\u5927<\/strong>\uff1a\u628a\u4e0a\u5f0f\u5de6\u53f3\u5bf9\u8c03\u5373\u5f97 max(a,d) + max(b,c) \u2265 max(a,c) + max(b,d)\uff0c\u9006\u5e8f\u914d\u5bf9\u662f\u540c\u4e00\u8bba\u8bc1\u7684\u955c\u50cf\u3002<\/li>\n<li><strong>\u8986\u76d6\u5168\u90e8\u65b9\u6848<\/strong>\uff1a\u6392\u5e8f\u56fa\u5b9a\u4e86\u4e24\u4e2a\u5e8f\u5217\u7684\u76f8\u5bf9\u6b21\u5e8f\uff0c\u4efb\u4e00\u4e0b\u6807\u914d\u5bf9\u65b9\u6848\u90fd\u5bf9\u5e94\u4e00\u79cd\"\u6392\u5e8f\u540e\u6574\u4f53\u540c\u5e8f\/\u9006\u5e8f\"\u7684\u5f62\u6001\uff0c\u6545\u6ca1\u6709\u9057\u6f0f\u66f4\u4f18\u89e3\u3002<\/li>\n<\/ul>\n<p>\u56e0\u6b64\u8f93\u51fa\u7684 total \u5c31\u662f\u9898\u76ee\u6240\u6c42\u7684\u6700\u5c0f\u6216\u6700\u5927\u603b\u901f\u5ea6\u3002<\/p>\n<h2>\u590d\u6742\u5ea6\u5206\u6790<\/h2>\n<ul>\n<li>\u65f6\u95f4 O(N log N)\uff1a\u74f6\u9888\u662f\u4e24\u4e2a\u6392\u5e8f\uff1b\u914d\u5bf9\u7d2f\u52a0 O(N)\u3002N=100 \u65f6\u4e0d\u8db3\u6beb\u79d2\u3002<\/li>\n<li>\u7a7a\u95f4 O(N)\uff1a\u4e24\u4e2a\u901f\u5ea6\u5217\u8868\uff08\u6392\u5e8f\u8f85\u52a9\u7a7a\u95f4\u89c1\u4e0a\uff09\u3002<\/li>\n<li>\u82e5\u628a N \u653e\u5927\u5230 10\u2075\uff0c\u672c\u7b97\u6cd5\u4f9d\u7136\u662f\u6807\u51c6\u89e3\u6cd5\u2014\u2014\u6392\u5e8f\u7684\u7a33\u5b9a\u6027\u4e0e\u8bc1\u660e\u90fd\u4e0e N \u65e0\u5173\u3002<\/li>\n<\/ul>\n<h2>\u5e38\u89c1\u9519\u8bef<\/h2>\n<ol>\n<li><strong>\u6309\u4e24\u4eba\u901f\u5ea6\u6c42\u548c<\/strong>\uff1a\u76ee\u6807\u51fd\u6570\u770b\u9519\uff0c\u628a <code>max<\/code> \u5199\u6210 <code>a+b<\/code>\uff0c\u6837\u4f8b\u4f1a\u7b97\u51fa 22\u3002<\/li>\n<li><strong>q=2 \u65f6\u5fd8\u8bb0\u53cd\u8f6c<\/strong>\uff0c\u6216<strong>\u4e24\u4e2a\u5217\u8868\u90fd\u53cd\u8f6c<\/strong>\uff08\u7b49\u4e8e\u6ca1\u53cd\u8f6c\uff09\u3002<\/li>\n<li><strong>\u53ea\u5bf9\u4e00\u56fd\u6392\u5e8f<\/strong>\uff1a\u53e6\u4e00\u56fd\u4fdd\u6301\u8f93\u5165\u5e8f\uff0c\u914d\u5bf9\u968f\u8f93\u5165\u53d8\u5316\u800c\u9519\u3002<\/li>\n<li><strong>\u628a\"\u540c\u5e8f\u6700\u5c0f\"\u5f53\u7ecf\u9a8c\u80cc\u8bf5<\/strong>\uff1a\u6362\u4e00\u9053\u76ee\u6807\u51fd\u6570\u4e0d\u540c\u7684\u9898\uff08\u5982\u6c42\u548c\uff09\u8d2a\u5fc3\u5c31\u5931\u6548\uff1b\u8981\u4f1a\u590d\u8ff0\u4ea4\u6362\u8bba\u8bc1\u3002<\/li>\n<li><strong>\u8bfb\u5165\u9519\u4f4d<\/strong>\uff1aq\u3001n\u3001\u4e24\u884c\u901f\u5ea6\u5171\u56db\u884c\uff0c\u683c\u5f0f\u4e0e\u6837\u4f8b\u9010\u884c\u5bf9\u5e94\u3002<\/li>\n<\/ol>\n<h2>\u590d\u4e60\u95ee\u9898<\/h2>\n<ol>\n<li>\u8865\u5168\u4ea4\u6362\u8bba\u8bc1\u7684\u56db\u79cd\u5927\u5c0f\u60c5\u5f62\uff08a \u2264 b\u3001c \u2264 d \u7684\u5168\u90e8\u76f8\u5bf9\u987a\u5e8f\uff09\uff0c\u8bf4\u660e\u4e3a\u4ec0\u4e48\u540c\u5e8f\u914d\u5bf9\u603b\u4e0d\u52a3\u4e8e\u4ea4\u53c9\u914d\u5bf9\u3002<\/li>\n<li>\u5982\u679c\u628a\u9898\u76ee\u6539\u6210\"\u8f66\u901f = \u4e24\u4eba\u901f\u5ea6\u4e4b\u548c\"\uff0c\u6392\u5e8f\u914d\u5bf9\u8fd8\u9002\u7528\u5417\uff1f\u4e3a\u4ec0\u4e48\uff1f<\/li>\n<li>\u4e3a\u4ec0\u4e48\"\u4e24\u4e2a\u5217\u8868\u90fd\u53cd\u8f6c\"\u5bf9\u6c42\u6700\u5927\u503c\u65e0\u6548\uff1f\u7528\u4e0b\u6807 0 \u548c N\u22121 \u7684\u914d\u5bf9\u8bf4\u660e\u3002<\/li>\n<li>\u672c\u9898\u4e0e Time on Task\uff08\u9884\u7b97\u5185\u5c3d\u53ef\u80fd\u591a\u5b8c\u6210\u4efb\u52a1\uff09\u5171\u4eab\u540c\u4e00\u4e2a\u8d2a\u5fc3\u4e60\u60ef\uff0c\u90a3\u53e5\u8bdd\u662f\u4ec0\u4e48\uff1f\uff08\u63d0\u793a\uff1a\u89c1 DSA-025\uff09<\/li>\n<li>\u82e5 N \u2264 10\u2075\u3001\u901f\u5ea6 \u2264 10\u2079\uff0c\u672c\u7b97\u6cd5\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u5404\u662f\u591a\u5c11\uff1f\u6709\u6ca1\u6709\u66f4\u4f18\u7684\u6e10\u8fdb\u9636\uff1f<\/li>\n<\/ol>\n<\/article>\n<\/div>\n<section class=\"ati-feedback-cta ati-lang-en\" data-ati-feedback>\n<div class=\"ati-feedback-copy\">\n<p class=\"ati-feedback-title\">\u6709\u95ee\u9898\u6216\u5efa\u8bae\uff1f<\/p>\n<p class=\"ati-feedback-note\">\u5982\u679c\u4f60\u5bf9\u672c\u6587\u6709\u7591\u95ee\uff0c\u6216\u5e0c\u671b\u63d0\u51fa\u6539\u8fdb\u5efa\u8bae\uff0c\u8bf7\u7ed9\u6211\u4eec\u53d1\u9001\u79c1\u5bc6\u7559\u8a00\u3002<\/p>\n<\/div>\n<p>  <a class=\"ati-feedback-button\" href=\"\/zh_cn\/contact\/\" data-ati-feedback-link>\u53d1\u9001\u53cd\u9988<\/a><br>\n<\/p><\/section>\n<section class=\"ati-feedback-cta ati-lang-zh\" data-ati-feedback>\n<div class=\"ati-feedback-copy\">\n<p class=\"ati-feedback-title\">\u6709\u95ee\u9898\u6216\u5efa\u8bae\uff1f<\/p>\n<p 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