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The Exchange Argument with Time on Task\"><span class=\"ati-hero-title-line\"><span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:0\">W<\/span><span class=\"ati-letter\" style=\"--i:1\">h<\/span><span class=\"ati-letter\" style=\"--i:2\">y<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:4\">D<\/span><span class=\"ati-letter\" style=\"--i:5\">o<\/span><span class=\"ati-letter\" style=\"--i:6\">e<\/span><span class=\"ati-letter\" style=\"--i:7\">s<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:9\">G<\/span><span class=\"ati-letter\" style=\"--i:10\">r<\/span><span class=\"ati-letter\" style=\"--i:11\">e<\/span><span class=\"ati-letter\" style=\"--i:12\">e<\/span><span class=\"ati-letter\" style=\"--i:13\">d<\/span><span class=\"ati-letter\" style=\"--i:14\">y<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:16\">S<\/span><span class=\"ati-letter\" style=\"--i:17\">o<\/span><span class=\"ati-letter\" style=\"--i:18\">r<\/span><span class=\"ati-letter\" style=\"--i:19\">t<\/span><span class=\"ati-letter\" style=\"--i:20\">i<\/span><span class=\"ati-letter\" style=\"--i:21\">n<\/span><span class=\"ati-letter\" style=\"--i:22\">g<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:24\">A<\/span><span class=\"ati-letter\" style=\"--i:25\">l<\/span><span class=\"ati-letter\" style=\"--i:26\">w<\/span><span class=\"ati-letter\" style=\"--i:27\">a<\/span><span class=\"ati-letter\" style=\"--i:28\">y<\/span><span class=\"ati-letter\" style=\"--i:29\">s<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:31\">W<\/span><span class=\"ati-letter\" style=\"--i:32\">o<\/span><span class=\"ati-letter\" style=\"--i:33\">r<\/span><span class=\"ati-letter\" style=\"--i:34\">k<\/span><span class=\"ati-letter\" style=\"--i:35\">?<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:37\">T<\/span><span class=\"ati-letter\" style=\"--i:38\">h<\/span><span class=\"ati-letter\" style=\"--i:39\">e<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:41\">E<\/span><span class=\"ati-letter\" style=\"--i:42\">x<\/span><span class=\"ati-letter\" style=\"--i:43\">c<\/span><span class=\"ati-letter\" style=\"--i:44\">h<\/span><span class=\"ati-letter\" style=\"--i:45\">a<\/span><span class=\"ati-letter\" style=\"--i:46\">n<\/span><span class=\"ati-letter\" style=\"--i:47\">g<\/span><span class=\"ati-letter\" style=\"--i:48\">e<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:50\">A<\/span><span class=\"ati-letter\" style=\"--i:51\">r<\/span><span class=\"ati-letter\" style=\"--i:52\">g<\/span><span class=\"ati-letter\" style=\"--i:53\">u<\/span><span class=\"ati-letter\" style=\"--i:54\">m<\/span><span class=\"ati-letter\" style=\"--i:55\">e<\/span><span class=\"ati-letter\" style=\"--i:56\">n<\/span><span class=\"ati-letter\" style=\"--i:57\">t<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:59\">w<\/span><span class=\"ati-letter\" style=\"--i:60\">i<\/span><span class=\"ati-letter\" style=\"--i:61\">t<\/span><span class=\"ati-letter\" style=\"--i:62\">h<\/span><\/span> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:64\">T<\/span><span class=\"ati-letter\" style=\"--i:65\">i<\/span><span class=\"ati-letter\" style=\"--i:66\">m<\/span><span class=\"ati-letter\" style=\"--i:67\">e<\/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> <span class=\"ati-word\"><span class=\"ati-letter\" style=\"--i:72\">T<\/span><span class=\"ati-letter\" style=\"--i:73\">a<\/span><span class=\"ati-letter\" style=\"--i:74\">s<\/span><span class=\"ati-letter\" style=\"--i:75\">k<\/span><\/span><\/span><\/h1>\n<p>Use CCC 2013 Time on Task to understand shortest-first greedy selection and prove it 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 by Duration<br>Take Shortest First<br>Prove by Exchange<\/strong>\n<p>Turn a plausible greedy instinct into a reusable correctness proof.<\/p>\n<\/aside>\n<\/section>\n<section class=\"ati-hero ati-lang-zh\">\n<div>\n<p class=\"ati-label\">Python \u5b66\u4e60\u7b14\u8bb0<\/p>\n<h1 aria-label=\"\u8d2a\u5fc3\u6392\u5e8f\u4e3a\u4ec0\u4e48\u4e00\u5b9a\u5bf9\uff1f\u4ece Time on Task \u8bb2\u6e05\u4ea4\u6362\u8bba\u8bc1\">\u8d2a\u5fc3\u6392\u5e8f\u4e3a\u4ec0\u4e48\u4e00\u5b9a\u5bf9\uff1f\u4ece Time on Task \u8bb2\u6e05\u4ea4\u6362\u8bba\u8bc1<\/h1>\n<p>\u7528 CCC 2013 Time on Task \u8bb2\u6e05\u6700\u77ed\u4efb\u52a1\u4f18\u5148\u7684\u8d2a\u5fc3\u7b56\u7565\uff0c\u5e76\u7528\u4ea4\u6362\u8bba\u8bc1\u8bc1\u660e\u5b83\u4e00\u5b9a\u6b63\u786e\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>\u6309\u65f6\u957f\u6392\u5e8f<br>\u6700\u77ed\u4f18\u5148<br>\u4ea4\u6362\u8bba\u8bc1<\/strong>\n<p>\u628a\u76f4\u89c9\u4e0a\u7684\u8d2a\u5fc3\u7b56\u7565\uff0c\u53d8\u6210\u53ef\u590d\u7528\u7684\u6b63\u786e\u6027\u8bc1\u660e\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>You have 6 minutes and three chores that take 3, 6, and 3 minutes \u2014 how many can you finish? The instinct says \"do the quick ones first\": sort the list, then start from the front. That instinct is greediness. But contests do not grade on instinct: why does \"shortest first\" always deliver the maximum count? If it fails even once, you lose the whole problem. This note uses CCC 2013's Time on Task to walk through the standard proof behind this kind of greedy \u2014 the exchange argument. By the end you will recognize it as the exact same pattern that justified sort-and-pair in the <a href=\"\/zh_cn\/ccc-2016-j5-s2-tandem-bicycle-solution-analysis\/\">same-week Tandem Bicycle walkthrough<\/a>.<\/p>\n<h2>The Common Mistake<\/h2>\n<pre><code class=\"language-python\">total_time = int(input())\ncount = int(input())\nchores = [int(input()) for _ in range(count)]\n\ndone = 0\nfor chore in chores:          # in input order\n    if chore &lt;= total_time:\n        total_time -= chore\n        done += 1\nprint(done)<\/code><\/pre>\n<p>The flaw is letting the input decide the order. Run it on official sample 2 (T=6, chores 5, 4, 3, 2, 1 minutes): it does the 5-minute chore first, wastes the remaining minute, and finishes only 1 chore \u2014 while the answer is 3 (1+2+3). The same data gives different answers under different orders, so the order is itself part of the decision. Leaving it to the input format means abandoning half the problem.<\/p>\n<h2>The Core Idea<\/h2>\n<p>State the task precisely: choose a subset of chores whose total duration \u2264 T, with the <strong>largest possible count<\/strong>. Note we are maximizing the count, not minimizing the total time \u2014 those are different classic problems, and only the count is asked here.<\/p>\n<p>Now the key lemma: <strong>among all selections of exactly k chores, the k shortest have the minimum total duration.<\/strong> Proof by one replacement: take any selection S of k chores that is not \"the k shortest\". Then some shorter chore x is unselected while a longer chore y is selected. Swap y for x: the count is still k, and the total does not grow (x \u2264 y). Repeating finitely many times turns any selection into \"the k shortest\", never increasing the total. Lemma proved.<\/p>\n<p>By the lemma, the problem becomes a scan: sort ascending, accumulate prefix sums. Let S(k) be the sum of the k shortest; S(k) is non-decreasing, and the maximum finishable count is exactly \"the last k with S(k) \u2264 T\". And by the other side of the lemma: if the k shortest already exceed T, no k chores can fit (any k chores sum to at least S(k)). Both directions close \u2014 the greedy is not just \"an answer\", it <strong>equals the optimum<\/strong>.<\/p>\n<p>Walk sample 2 by hand: sorted [1,2,3,4,5], prefix sums 1, 3, 6, 10, 15. With T=6 the first three fit exactly, the fourth breaks the budget \u2014 answer 3, matching the official output. Sample 1 (T=6, [3,6,3]) sorts to [3,3,6], prefix sums 3, 6, 12, answer 2.<\/p>\n<h2>The Recommended Solution<\/h2>\n<pre><code class=\"language-python\">total_time = int(input())\ncount = int(input())\nchores = [int(input()) for _ in range(count)]\n\nchores.sort()\n\nused = 0\ndone = 0\nfor chore in chores:\n    if used + chore &lt;= total_time:\n        used += chore\n        done += 1\n    else:\n        break\n\nprint(done)<\/code><\/pre>\n<pre><code class=\"language-text\">6\n3\n3\n6\n3\n2<\/code><\/pre>\n<p>Three details worth keeping. First, <code>break<\/code> instead of <code>continue<\/code>: after sorting, everything later is longer \u2014 if the current chore does not fit, nothing after it will either. Second, accumulate into a separate <code>used<\/code> rather than rewriting <code>total_time<\/code> \u2014 the remaining budget stays inspectable while debugging. Third, C \u2264 100, each chore \u2264 100000, T \u2264 100000, so the sums fit easily in an int; but if the limits grow, big-integer accumulation is cheap insurance.<\/p>\n<h2>The Same Proof: From Pairing to Counting<\/h2>\n<p>Zoom out: this problem and the same-week Tandem Bicycle share one mold. Tandem Bicycle pairs N tandem riders to minimize or maximize the total speed; its proof swaps crossed pairs back into same order and shows the total never worsens. Time on Task swaps any k chores for the k shortest and shows the budget never worsens. Both say \"<strong>there exists a tidy solution that is no worse<\/strong>\": turn any solution into the tidy one step by step, then identify the best among tidy ones. Whenever you see sorting plus greedy, ask \"does one replacement step ever make it worse?\" \u2014 if you can answer, write the code. That question is the line between a slogan and a tool.<\/p>\n<h2>Side by Side<\/h2>\n<div class=\"ati-table-wrap\">\n<table>\n<thead>\n<tr>\n<th>Approach<\/th>\n<th>Result on sample 2<\/th>\n<th>Why<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Input order<\/td>\n<td>1 chore<\/td>\n<td>Random order; a long chore first blocks the budget<\/td>\n<\/tr>\n<tr>\n<td>Sorted, shortest first<\/td>\n<td>3 (optimal)<\/td>\n<td>The k shortest minimize total duration, maximizing the count<\/td>\n<\/tr>\n<tr>\n<td>Sorted, longest first<\/td>\n<td>1 chore<\/td>\n<td>Reversed direction \u2014 the replacement lemma no longer holds<\/td>\n<\/tr>\n<tr>\n<td>Each step: longest that still fits<\/td>\n<td>1 chore<\/td>\n<td>A different greedy rule with no proof behind it fails immediately<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Practice<\/h2>\n<ol>\n<li>Change T to 7 in sample 1: predict the answer with prefix sums, then verify by running. (Can you finish the two 3-minute chores? Does the 6-minute one fit after that? Work it out.)<\/li>\n<li>With chores [4, 4, 4, 4] and T=9, how many fit? Use the lemma to explain why shortest-first is still correct here.<\/li>\n<li>Challenge: if every chore requires an extra 1-minute rest (real cost = duration + 1), does \"sort and scan from the front\" still hold? Which single line would you change? (Hint: +1 per chore is like the budget paying an extra \"done\" minutes in advance\u2026)<\/li>\n<\/ol>\n<h2>One Line to Remember<\/h2>\n<p>Prove \"swapping cannot make it worse\" first, then write \"sort and pick from the front\" \u2014 greedy is a provable replacement, not a gamble.<\/p>\n<\/article>\n<\/div>\n<div class=\"ati-article-content ati-lang-zh\">\n<article class=\"ati-post-article\">\n<p>\u53ea\u6709 6 \u5206\u949f\uff0c\u5bb6\u52a1\u6e05\u5355\u4e0a\u5374\u6392\u7740 3 \u5206\u949f\u30016 \u5206\u949f\u30013 \u5206\u949f\u4e09\u4ef6\u4e8b\u2014\u2014\u6700\u591a\u80fd\u505a\u5b8c\u51e0\u4ef6\uff1f\u76f4\u89c9\u8bf4\"\u5148\u6311\u5feb\u7684\"\uff0c\u628a\u6e05\u5355\u6309\u8017\u65f6\u6392\u4e2a\u5e8f\uff0c\u4ece\u5934\u5f00\u59cb\u505a\u3002\u8fd9\u4e2a\u76f4\u89c9\u5c31\u662f\u8d2a\u5fc3\u3002\u4f46\u5728\u7ade\u8d5b\u91cc\u4e0d\u80fd\u9760\u76f4\u89c9\u4ea4\u5377\uff1a\u4e3a\u4ec0\u4e48\"\u5148\u6311\u6700\u77ed\u7684\"\u7ed9\u51fa\u7684\u4ef6\u6570\u4e00\u5b9a\u6700\u591a\uff1f\u5982\u679c\u67d0\u6b21\u5b83\u5931\u8d25\u4e86\uff0c\u4f60\u4f1a\u635f\u5931\u6574\u9053\u9898\u7684\u5206\u6570\u3002\u8fd9\u7bc7\u7528 CCC 2013 \u7684 Time on Task\uff0c\u628a\u652f\u6491\u8fd9\u7c7b\u8d2a\u5fc3\u7684\u4e00\u9053\u6807\u51c6\u8bc1\u660e\u2014\u2014\u4ea4\u6362\u8bba\u8bc1\u2014\u2014\u5b8c\u6574\u8d70\u4e00\u904d\u3002\u8bfb\u5b8c\u4f60\u4f1a\u8ba4\u51fa\uff1a\u4e0a\u5468 Tandem Bicycle \u91cc\"\u6392\u5e8f\u540e\u914d\u5bf9\"\u7684\u6b63\u786e\u6027\uff0c\u548c\u5b83\u662f\u540c\u4e00\u5957\u624b\u6cd5\u3002<\/p>\n<h2>\u5e38\u89c1\u9519\u8bef<\/h2>\n<pre><code class=\"language-python\">total_time = int(input())\ncount = int(input())\nchores = [int(input()) for _ in range(count)]\n\ndone = 0\nfor chore in chores:          # \u6309\u8f93\u5165\u987a\u5e8f\u505a\n    if chore &lt;= total_time:\n        total_time -= chore\n        done += 1\nprint(done)<\/code><\/pre>\n<p>\u9519\u5728\u628a\"\u987a\u5e8f\"\u4ea4\u7ed9\u4e86\u8f93\u5165\u3002\u8f93\u5165\u987a\u5e8f\u662f\u4efb\u610f\u7684\uff1a\u7528\u5b98\u65b9\u6837\u4f8b 2\uff08T=6\uff0c\u4e94\u4ef6\u5bb6\u52a1 5\u30014\u30013\u30012\u30011 \u5206\u949f\uff09\u8dd1\u8fd9\u6bb5\u4ee3\u7801\uff0c\u5b83\u4f1a\u5148\u505a 5 \u5206\u949f\u7684\uff0c\u5269 1 \u5206\u949f\u4ec0\u4e48\u4e5f\u88c5\u4e0d\u4e0b\uff0c\u53ea\u5b8c\u6210 1 \u4ef6\uff1b\u800c\u7b54\u6848\u662f 3 \u4ef6\uff081+2+3\uff09\u3002\u540c\u6837\u7684\u6570\u636e\uff0c\u987a\u5e8f\u4e0d\u540c\u3001\u7b54\u6848\u4e0d\u540c\uff0c\u8bf4\u660e<strong>\u987a\u5e8f\u672c\u8eab\u5c31\u662f\u51b3\u7b56\u7684\u4e00\u90e8\u5206<\/strong>\uff0c\u628a\u5b83\u7559\u7ed9\u8f93\u5165\u683c\u5f0f\u7b49\u4e8e\u653e\u5f03\u4e86\u4e00\u534a\u7684\u9898\u76ee\u3002<\/p>\n<h2>\u6838\u5fc3\u6982\u5ff5<\/h2>\n<p>\u5148\u628a\u95ee\u9898\u8bf4\u51c6\u786e\uff1a\u4ece C \u4ef6\u5bb6\u52a1\u4e2d\u9009\u4e00\u4e2a\u5b50\u96c6\uff0c\u4f7f\u603b\u65f6\u957f\u4e0d\u8d85\u8fc7 T\uff0c\u5e76\u4e14<strong>\u4ef6\u6570\u6700\u591a<\/strong>\u3002\u6ce8\u610f\u6211\u4eec\u4f18\u5316\u7684\u4e0d\u662f\"\u7528\u65f6\u6700\u5c11\"\uff0c\u800c\u662f\"\u4ef6\u6570\u6700\u591a\"\u2014\u2014\u8fd9\u4e24\u4ef6\u4e8b\u5bb9\u6613\u6df7\uff1a\u524d\u8005\u662f\u53e6\u4e00\u9053\u7ecf\u5178\u9898\uff08\u8c03\u5ea6\uff09\uff0c\u540e\u8005\u7684\u7b54\u6848\u624d\u662f\u672c\u9898\u3002<\/p>\n<p>\u73b0\u5728\u7ed9\u51fa\u5173\u952e\u5f15\u7406\uff1a<strong>\u5728\u6240\u6709\u6070\u597d\u542b k \u4ef6\u5bb6\u52a1\u7684\u9009\u62e9\u91cc\uff0c\u8017\u65f6\u6700\u77ed\u7684 k \u4ef6\uff0c\u603b\u65f6\u957f\u6700\u5c0f\u3002<\/strong> \u8bc1\u660e\u7528\"\u4e00\u6b21\u66ff\u6362\"\uff1a\u4efb\u53d6\u4e00\u4e2a\u542b k \u4ef6\u7684\u9009\u62e9 S\uff0c\u5982\u679c\u5b83\u4e0d\u662f\"\u6700\u77ed\u7684 k \u4ef6\"\uff0c\u90a3\u5fc5\u6709\u4e00\u4ef6\u8f83\u77ed\u7684 chores[x] \u6ca1\u88ab\u9009\u3001\u800c\u4e00\u4ef6\u8f83\u957f\u7684 chores[y] \u88ab\u9009\u3002\u628a y \u6362\u6210 x\uff1a\u4ef6\u6570\u4ecd\u662f k\uff0c\u603b\u65f6\u957f\u4e0d\u4f1a\u589e\u52a0\uff08x \u2264 y\uff09\u3002\u91cd\u590d\u8fd9\u4e2a\u66ff\u6362\u6709\u9650\u6b21\uff0c\u4efb\u4f55\u9009\u62e9\u90fd\u80fd\u53d8\u6210\"\u6700\u77ed\u7684 k \u4ef6\"\uff0c\u4e14\u603b\u65f6\u957f\u53ea\u51cf\u4e0d\u589e\u3002\u5f15\u7406\u6210\u7acb\u3002<\/p>\n<p>\u7531\u5f15\u7406\uff0c\u9898\u76ee\u7acb\u523b\u53d8\u6210\u4e00\u9053\"\u626b\u63cf\"\u9898\uff1a\u628a\u5bb6\u52a1\u6309\u8017\u65f6\u5347\u5e8f\u6392\u597d\uff0c\u7d2f\u52a0\u524d\u7f00\u548c\u3002\u8bbe\u6700\u77ed\u7684 k \u4ef6\u4e4b\u548c\u4e3a S(k)\uff0c\u5219 S(k) \u5355\u8c03\u9012\u589e\uff1b\u80fd\u5b8c\u6210\u7684\u6700\u5927\u4ef6\u6570\u5c31\u662f\"\u6700\u540e\u4e00\u4e2a\u6ee1\u8db3 S(k) \u2264 T \u7684 k\"\u3002\u800c\u4e14\u7531\u5f15\u7406\u7684\u53e6\u4e00\u9762\uff1a\u5982\u679c\u6700\u77ed\u7684 k \u4ef6\u90fd\u8d85\u8fc7 T\uff0c\u4efb\u4f55 k \u4ef6\u90fd\u4e0d\u53ef\u80fd\u585e\u8fdb T\uff08\u4efb\u610f k \u4ef6\u4e4b\u548c \u2265 S(k)\uff09\u3002\u4e24\u4e2a\u65b9\u5411\u5408\u62e2\uff0c\u8d2a\u5fc3\u4e0d\u4ec5\"\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7b54\u6848\"\uff0c\u800c\u662f<strong>\u6070\u597d\u7b49\u4e8e\u6700\u4f18\u89e3<\/strong>\u3002<\/p>\n<p>\u628a\u6837\u4f8b 2 \u624b\u7b97\u4e00\u904d\uff1a\u6392\u5e8f\u540e [1,2,3,4,5]\uff0c\u524d\u7f00\u548c 1\u30013\u30016\u300110\u300115\u3002T=6 \u65f6\uff0c\u524d\u4e09\u4e2a\u4e4b\u548c 6 \u6070\u597d\u653e\u4e0b\uff0c\u7b2c\u56db\u4e2a\u5c31\u8d85\u4e86\u2014\u2014\u7b54\u6848 3\uff0c\u4e0e\u5b98\u65b9\u8f93\u51fa\u4e00\u81f4\u3002\u6837\u4f8b 1\uff08T=6\uff0c[3,6,3]\uff09\u6392\u5e8f\u540e [3,3,6]\uff0c\u524d\u7f00\u548c 3\u30016\u300112\uff0c\u7b54\u6848 2\u3002<\/p>\n<h2>\u63a8\u8350\u5199\u6cd5<\/h2>\n<pre><code class=\"language-python\">total_time = int(input())\ncount = int(input())\nchores = [int(input()) for _ in range(count)]\n\nchores.sort()\n\nused = 0\ndone = 0\nfor chore in chores:\n    if used + chore &lt;= total_time:\n        used += chore\n        done += 1\n    else:\n        break\n\nprint(done)<\/code><\/pre>\n<pre><code class=\"language-text\">6\n3\n3\n6\n3\n2<\/code><\/pre>\n<p>\u4e09\u4e2a\u7ec6\u8282\u503c\u5f97\u8bb0\u4f4f\u3002\u7b2c\u4e00\uff0c<code>break<\/code> \u800c\u4e0d\u662f <code>continue<\/code>\uff1a\u6392\u5e8f\u540e\u6bd4\u5f53\u524d\u4ef6\u66f4\u957f\u7684\u90fd\u5728\u540e\u9762\uff0c\u5f53\u524d\u90fd\u88c5\u4e0d\u4e0b\uff0c\u540e\u9762\u66f4\u4e0d\u53ef\u80fd\uff0c\u76f4\u63a5\u505c\u3002\u7b2c\u4e8c\uff0c\u7528\u72ec\u7acb\u7684 <code>used<\/code> \u7d2f\u8ba1\u5df2\u8017\u65f6\u95f4\uff0c\u4e0d\u8981\u56de\u5199 <code>total_time<\/code>\u2014\u2014\u9884\u7b97\u8fd8\u5269\u591a\u5c11\u968f\u65f6\u53ef\u67e5\uff0c\u8c03\u8bd5\u65f6\u5c11\u4e00\u5c42\u5fc3\u7b97\u3002\u7b2c\u4e09\uff0cC \u2264 100\u3001\u6bcf\u4ef6 \u2264 100000\u3001T \u2264 100000\uff0c\u603b\u548c\u8fdc\u5728 int \u8303\u56f4\u5185\uff1b\u4f46\u5982\u679c\u628a\u89c4\u6a21\u6539\u5927\uff0c\u628a\u7d2f\u52a0\u53d8\u91cf\u517b\u6210\u5927\u6574\u6570\u4e60\u60ef\u662f\u5ec9\u4ef7\u7684\u4fdd\u9669\u3002<\/p>\n<h2>\u540c\u4e00\u5957\u8bc1\u660e\uff1a\u4ece\u914d\u5bf9\u5230\u8ba1\u6570<\/h2>\n<p>\u628a\u955c\u5934\u62c9\u8fdc\uff0c\u8fd9\u9053\u9898\u548c\u540c\u5468\u7684 Tandem Bicycle \u662f\u540c\u4e00\u4e2a\u6a21\u5b50\u3002Tandem Bicycle \u8981\u914d N \u5bf9\u53cc\u4eba\u8f66\u624b\u4f7f\u603b\u901f\u5ea6\u6700\u5c0f\u6216\u6700\u5927\uff0c\u8bc1\u660e\u662f\uff1a\u5bf9 a \u2264 b\u3001c \u2264 d\uff0c\u628a\u4ea4\u53c9\u914d\u5bf9\u6362\u56de\u540c\u5e8f\uff0c\u603b\u6570\u4e0d\u4f1a\u53d8\u5dee\uff1bTime on Task \u8981\u9009\u7684\"\u4ef6\u6570\u6700\u591a\"\uff0c\u8bc1\u660e\u662f\uff1a\u4efb\u610f k \u4ef6\u6362\u6210\u6700\u77ed\u7684 k \u4ef6\uff0c\u9884\u7b97\u4e0d\u4f1a\u53d8\u5dee\u3002\u4e24\u53e5\u90fd\u662f\"<strong>\u5b58\u5728\u4e00\u79cd\u4e0d\u66f4\u5dee\u7684\u6574\u9f50\u65b9\u6848<\/strong>\"\uff1a\u5148\u628a\u4efb\u610f\u89e3\u4e00\u6b65\u6b65\u6362\u6210\u6574\u9f50\u89e3\uff0c\u518d\u8bc1\u660e\u6574\u9f50\u89e3\u91cc\u6700\u597d\u7684\u662f\u4ec0\u4e48\u3002\u770b\u5230\u6392\u5e8f + \u8d2a\u5fc3\u65f6\uff0c\u5148\u5728\u8111\u5b50\u91cc\u95ee\u4e00\u53e5\"\u66ff\u6362\u4e00\u6b65\u4f1a\u4e0d\u4f1a\u66f4\u5dee\"\uff0c\u7b54\u5f97\u51fa\u6765\u518d\u5199\u4ee3\u7801\u2014\u2014\u8fd9\u662f\u628a\u8d2a\u5fc3\u4ece\u53e3\u8bc0\u53d8\u6210\u5de5\u5177\u7684\u5206\u6c34\u5cad\u3002<\/p>\n<h2>\u5bf9\u6bd4\u4e00\u4e0b<\/h2>\n<div class=\"ati-table-wrap\">\n<table>\n<thead>\n<tr>\n<th>\u5199\u6cd5<\/th>\n<th>\u6837\u4f8b 2 \u7ed3\u679c<\/th>\n<th>\u4e3a\u4ec0\u4e48<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u6309\u8f93\u5165\u987a\u5e8f\u505a<\/td>\n<td>1 \u4ef6<\/td>\n<td>\u987a\u5e8f\u968f\u673a\uff0c\u5148\u505a\u957f\u7684\u4f1a\u5835\u6b7b\u9884\u7b97<\/td>\n<\/tr>\n<tr>\n<td>\u6392\u5e8f\u540e\u4ece\u5c0f\u5230\u5927\u505a<\/td>\n<td>3 \u4ef6\uff08\u6700\u4f18\uff09<\/td>\n<td>\u6700\u77ed\u7684 k \u4ef6\u603b\u65f6\u957f\u6700\u5c0f\uff0c\u80fd\u88c5\u7684\u4ef6\u6570\u6700\u591a<\/td>\n<\/tr>\n<tr>\n<td>\u6392\u5e8f\u540e\u4ece\u5927\u5230\u5c0f\u505a<\/td>\n<td>1 \u4ef6<\/td>\n<td>\u65b9\u5411\u53cd\u4e86\uff0c\"\u66ff\u6362\u4e0d\u53d8\u5dee\"\u7684\u5f15\u7406\u4e0d\u6210\u7acb<\/td>\n<\/tr>\n<tr>\n<td>\u6bcf\u6b21\u9009\"\u5f53\u524d\u80fd\u653e\u4e0b\u7684\u6700\u957f\u4e00\u4ef6\"<\/td>\n<td>1 \u4ef6<\/td>\n<td>\u6362\u4e2a\u8d2a\u5fc3\u89c4\u5219\u6ca1\u6709\u8bc1\u660e\u652f\u6491\uff0c\u7acb\u523b\u5931\u6548<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>\u5c0f\u7ec3\u4e60<\/h2>\n<ol>\n<li>\u628a\u6837\u4f8b 1 \u7684 T \u6539\u6210 7\uff1a\u5148\u6309\u524d\u7f00\u548c\u624b\u7b97\u9884\u6d4b\u7b54\u6848\uff0c\u518d\u8fd0\u884c\u9a8c\u8bc1\u3002\uff08\u7b54\u6848\uff1a\u4ecd\u80fd\u505a\u5b8c 3 \u548c 3 \u4e24\u4ef6\uff0c\u7b2c\u4e09\u4ef6 6 \u653e\u4e0d\u4e0b\uff1f\u624b\u7b97\u4e00\u904d\u4f60\u5c31\u77e5\u9053\u4e86\u3002\uff09<\/li>\n<li>\u5bb6\u52a1\u65f6\u957f [4, 4, 4, 4]\u3001T=9\uff0c\u6700\u591a\u51e0\u4ef6\uff1f\u7528\u5f15\u7406\u89e3\u91ca\u4e3a\u4ec0\u4e48\"\u6700\u77ed\u4f18\u5148\"\u5728\u8fd9\u91cc\u4f9d\u7136\u662f\u5bf9\u7684\u3002<\/li>\n<li>\u6311\u6218\uff1a\u5982\u679c\u6bcf\u505a\u5b8c\u4e00\u4ef6\u5fc5\u987b\u4f11\u606f 1 \u5206\u949f\uff08\u6bcf\u4ef6\u5b9e\u9645\u6d88\u8017 = \u65f6\u957f + 1\uff09\uff0c\"\u6392\u5e8f\u540e\u4ece\u5934\u9009\"\u8fd8\u6210\u7acb\u5417\uff1f\u9700\u8981\u6539\u54ea\u4e00\u884c\u4ee3\u7801\uff1f\uff08\u63d0\u793a\uff1a\u6bcf\u4ef6 +1 \u76f8\u5f53\u4e8e\u9884\u7b97\u5148\u6263\u6389 done \u4ef6\u2026\u2026\uff09<\/li>\n<\/ol>\n<h2>\u4e00\u53e5\u8bdd\u8bb0\u4f4f<\/h2>\n<p>\u5148\u8bc1\u660e\"\u6362\u4e00\u6362\u4e0d\u4f1a\u66f4\u5dee\"\uff0c\u518d\u5199\"\u6392\u5e8f\u540e\u4ece\u5934\u9009\"\u2014\u2014\u8d2a\u5fc3 = \u53ef\u8bc1\u660e\u7684\u66ff\u6362\uff0c\u4e0d\u662f\u78b0\u8fd0\u6c14\u3002<\/p>\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 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