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        "system": "You create Codeforces learning content for Nudge. Your job is to understand the best approach for the problem and teach it clearly in your own words, using existing solutions to inform your reasoning.\n\nStart with a brief, targeted web search for existing solutions so relevant editorials are in context before substantial independent problem-solving. Use any supplied tutorial links first; otherwise search by contest ID and problem index. Prefer the official tutorial/editorial, and read relevant explanations rather than relying on search snippets. Look at accessible alternatives when useful, especially if the official explanation is missing, unclear, or unnecessarily complicated. Accepted submissions can also help clarify an approach. Respect supplied source lookup statuses and avoid repeatedly retrying blocked sources. If no usable source is accessible, proceed from the supplied statement.\n\nTreat existing solutions as a starting point, not a constraint. If an approach is clear and suitable, build on it without unnecessary re-derivation. If an explanation has gaps, seems incorrect, or uses a harder method than necessary, reason through it and derive a better or simpler approach when worthwhile. Choose a correct approach that is easy to teach and fits the constraints. Verify it against the supplied statement and edge cases before writing the hints, editorial, and C++ solution.\n\nThe editorial must be self-contained: explain the key insight, algorithm, why it works, complexity, and implementation details a learner needs, filling in steps the source skips. Keep research and verification concise; spend the output on teaching the solution, not narrating the research process. Follow the user prompt and output schema exactly.",
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                "description": "If status is 'unsolvable', provide a detailed failure message to show users. Name the concrete statement/resource blocker and any relevant source lookup/access status, such as missing official tutorial, 403/Cloudflare challenge, 404, or unavailable accepted submissions. Otherwise null."
              },
              "hints": {
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          "text": "Generate Codeforces learning content: five progressive hints, an original editorial, and AC-quality C++.\n\nFollow the editorial-first research workflow in the system instructions. Use the supplied statement to verify that the source solves this exact problem.\n\nWrite clean Markdown with LaTeX as needed. Use quick and clever humor when appropriate. Tell it like it is (don't sugar-coat responses), and use very casual language. You are fully allowed to swear, just don't overdo it like a sailor (be natural). Deconstruct any false assumptions.\n\nGenerate content for Codeforces problem 2254A: \"Riptide\" (rated 800).\n\nKnown problem metadata:\n- Contest ID: 2254\n- Index: A\n- Name: Riptide\n- Rating: 800 (Codeforces difficulty rating)\n- Tags: implementation, sortings\n- Problem URL: https://codeforces.com/contest/2254/problem/A\n\nUse the rating and tags as weak signals only. The supplied statement is the source of truth.\n\nProblem Statement:\n<problem-statement>\n<div class=\"header\"><div class=\"title\">A. Riptide</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file input-standard\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file output-standard\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Alice, Bob, and Charlie are playing a game with tokens. They start with $$$a$$$, $$$b$$$, and $$$c$$$ tokens, respectively.</p><p>The game is played in rounds. Before the beginning of each round, they check the number of tokens everyone has:</p><ul> <li> If any two players have the exact same number of tokens, the game immediately ends. </li><li> Otherwise, the round begins, all three players have a strictly different number of tokens. The player with the strictly most tokens gives exactly $$$1$$$ token to the player with the strictly fewest tokens. </li></ul><p>Given the starting tokens $$$a$$$, $$$b$$$, and $$$c$$$, determine exactly how many rounds the game will last before it ends.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer $$$t$$$ ($$$1 \\le t \\le 10^3$$$) — the number of test cases.</p><p>Each test case consists of a single line containing three integers $$$a$$$, $$$b$$$, and $$$c$$$ ($$$1 \\le a, b, c \\le 10$$$).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each test case, output a single integer — the number of rounds the game will last before it ends.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Example</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre><div class=\"test-example-line test-example-line-even test-example-line-0\">6</div><div class=\"test-example-line test-example-line-odd test-example-line-1\">1 2 3</div><div class=\"test-example-line test-example-line-even test-example-line-2\">4 6 1</div><div class=\"test-example-line test-example-line-odd test-example-line-3\">3 3 7</div><div class=\"test-example-line test-example-line-even test-example-line-4\">1 7 10</div><div class=\"test-example-line test-example-line-odd test-example-line-5\">6 1 9</div><div class=\"test-example-line test-example-line-even test-example-line-6\">1 1 1</div></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre><div class=\"test-example-line test-example-line-odd test-example-line-1\">1</div><div class=\"test-example-line test-example-line-even test-example-line-2\">2</div><div class=\"test-example-line test-example-line-odd test-example-line-3\">0</div><div class=\"test-example-line test-example-line-even test-example-line-4\">3</div><div class=\"test-example-line test-example-line-odd test-example-line-5\">3</div><div class=\"test-example-line test-example-line-even test-example-line-6\">0</div></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first test case: </p><ul> <li> No two players have the same number of tokens. </li><li> Charlie has the most tokens ($$$3$$$ tokens), and Alice has the fewest tokens ($$$1$$$ token). Therefore, Charlie gives Alice a token. </li><li> Now, Alice has $$$2$$$ tokens, Bob has $$$2$$$ tokens, and Charlie has $$$2$$$ tokens. Since there are two players (or more) with the same number of tokens, the game ends. </li></ul><p>The game ended after $$$1$$$ round, so the answer is $$$1$$$.</p><p>In the second test case, the game is played as follows: </p><ul> <li> Bob gives Charlie a token, now Alice has $$$4$$$ tokens, Bob has $$$5$$$ tokens, and Charlie has $$$2$$$ tokens. </li><li> Bob gives Charlie a token, now Alice has $$$4$$$ tokens, Bob has $$$4$$$ tokens, and Charlie has $$$3$$$ tokens. Since two players have the same number of tokens, the game ends. </li></ul><p>The game lasted $$$2$$$ rounds.</p><p>In the third test case, two players already have the same number of tokens. So the answer is $$$0$$$ since no rounds were played.</p></div>\n</problem-statement>\n\n\nSource lookup status:\n<source-lookup-status>\n- Tutorial (en): https://codeforces.com/blog/entry/155666 loaded (200 OK; title: \"Codeforces Round 1114 (Div. 3) — Editorial - Codeforces\"; does not mention 2254A)\n</source-lookup-status>\n\nGenerate:\n1. Five progressive hints, from a gentle nudge to the key insight.\n2. A self-contained editorial that teaches the solution clearly, including the key insight, algorithm, correctness argument, complexity, and necessary implementation details. Explain non-obvious steps without padding or a discovery-process transcript.\n3. A complete C++26 solution that gets AC on Codeforces.\n\nFormatting & Style Rules:\n- Hints and editorial: valid Markdown with LaTeX as needed (e.g., $dp[i]$, $$\\sum_{i=1}^{n} a_i$$).\n- Hints and editorial must read like Nudge's own explanation. No research notes, source notes, citations, Markdown links, URLs, or references to editorials/submissions/posts.\n- Solution: raw C++ only, no Markdown fences.\n- Keep C++ short, clean, standard, and single-file. Comments are fine when they clarify the idea.\n\nOutput strictness:\n- Return JSON matching the provided schema exactly.\n- Never include NUL (U+0000) characters in any field. Use literal $ or $$ for math delimiters, never control characters.\n- If the problem is solvable, return `status: \"success\"`, `reason: null`, and fill in `hints`, `editorial`, and `solution`.\n- Return `status: \"unsolvable\"`, a short `reason`, and set `hints`, `editorial`, and `solution` to null only when the supplied statement is fundamentally incomplete, contradictory, or dependent on an inaccessible resource needed to define the task. Missing research, high rating, uncertainty, or \"can't guarantee AC\" is not a reason to return unsolvable.\n- If you return `status: \"unsolvable\"`, the `reason` is shown directly to users. Be concrete: say what exact statement/resource blocker stopped you, and include relevant source lookup status if it mattered (for example: official tutorial missing, Codeforces returned 403/Cloudflare challenge, tutorial page 404, accepted submissions unavailable).\n- Each hint must be an object with `order` (1 through 5) and `content` (the Markdown hint text), not a plain string. The `content` must contain just the hint text, with no \"Hint 1:\" or subtitles. The UI adds those automatically.\n- Do not start the editorial with an \"# Editorial\" heading. The UI already adds that section. Feel free to add other headers as needed though.\n- Use styling in the editorial if needed! Just that first header is no good but any subheaders or bolding or whatever is good!\n\nFor the C++ solution, you MUST use this template and work around it:\n\n```cpp\n#include <bits/stdc++.h>\nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n    ios::sync_with_stdio(false);\n    cin.tie(nullptr);\n}\n\nint main() {\n    setIO();\n}\n```",
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            "output": "Title: Riptide\nURL: https://codeforces.com/contest/2254/problem/A\nPublished: N/A\nAuthor: N/A\nHighlights:\nCodeforces\n\nEnter| Register\n\nCodeforces Round 1111 (Div. 2)\n\nBy makrav, 3 days ago, translation,\n\nHello Codeforces,\n\nI'm so excited to invite you to participate in Codeforces Round 1111 (Div. 2), which will be held on Saturday, July 18, 2026 at 14:35UTC!\n\nYou will be given 6 problems to solve, one of which will be divided into subtasks. The problems were authored by me, makrav, and PvPro.\n\nThe contest was prepared by two IOI 2026 participants from Russia, so you can be sure that the problems are of the highest possible quality.\n\nI would like to thank these people for making the contest possible:\n\n- PvPro for coming up with an enormous number of problems for this round (and having most of them rejected by me).\n- nifeshe for outstanding coordination and helping with problem preparation.\n- Um_nik for preliminary reviewing the round.\n- Intellegent, dinohaur, DizzyGroovy for being the first, second and third best testers respectively.\n- allvik66,__baozii__,_istil, Wansur, TeaTime, Noobish_Monk for VIP testing.\n- The rest of our testers: Mark_Pr, Proof_by_QED, omsincoconut, shorya1835, Argentum47, simplelife, naneosmic, nik_exists.\n- MikeMirzayanov and KAN for the Codeforces and Polygon platforms.\n- And You for participating!\n\nThe score distribution is as follows: 500 — 750 — 1250 — (1500 + 1250) — 3000 — 3500\n\nFull text and comments »\n\nSpectral::Cup 2026 Round 3 (Codeforces Round 1110, Div. 1 + Div. 2)\n\nBy__baozii__, history, 8 days ago,\n\nHello Codeforces!\n\nI am glad to invite you to participate in Spectral::Cup 2026 Round 3 (Codeforces Round 1110, Div. 1 + Div. 2), which will start on Thursday, July 16, 2026 at 14:45UTC. You will be given 2 hours and 30 minutes to solve 8 problems, where one problem will be split into subtasks. Also, there is at least one interactive problem, so you are recommended to read the guide to interactive problems if you have not encountered them before.\n\nNote that hacks will be disabled for problems A to D.\n\nAll problems are authored and prepared by myself.\n\nNote the rule restricting the use of AI. If you are caught breaking this rule, you will be thrown into SSerxhs's basement. For your own well-being, I suggest adhering to the rules.\n\nI would like to thank the following people for helping make this round possible!\n\n- SSerxhs for his/her satisfactory coordination.\n- Alexdat2000 for translating the statements to Russian.\n- nifeshe for \"I will solve this problem today\" — nifeshe.\n- StarSilk, EvenImage, tiger2005 for nutella testing.\n- zeemanz, 0.1w33hw3, nifeshe,_istil, SATSKY_2025target_LGM for red testing.\n- Seele_H, Proof_by_QED, GUAIKATTO, CReatiQ for orange testing.\n- -WIDA-, Liang_SYEA, Argentum47, wakanda-forever for purple testing.\n- fr200110217102, simplelife, XiaoXia, acmtoohard, big-mktx for blue testing.\n- yuki_Ishijo for cyan testing.\n- Whalica for green testing.\n- MikeMirzayanov and KAN for the incredible Codeforces and Polygon platforms.\n\nScore distribution:\n\n500−1000−1250−(1500−1000)−2500−3000−3500−5000\n\n### update:\n\nTutorial has been published: tutorial\n\nNow a few words from our sponsor.\n\n🏁The final round of Spectral::Cup 2026 is coming!\n\nThis round is special to us. Not only will it conclude our three-round Spectral::Cup tournament, but it will also take place during our company’s birthday month — Spectral::Technologies turned 7 this July 🎉\n\nRound 3 is the final part of our birthday celebration. The rest is in this video 😄\n\nFull text and comments »\n\nAnnouncement of Spectral::Cup 2026 Round 3 (Codeforces Round 1110, Div. 1 + Div. 2)\n\nCodeforces Round 1109 (Div. 3)\n\nBy itz_pabloo, history, 7 days ago, translation,\n\n### Hello, Codeforces!\n\nCodeforces Round 1109 (Div. 3) will start at Tuesday, July 14, 2026 at 14:35UTC. You will be offered 7 problems with expected difficulties to compose an interesting competition for participants with ratings up to 1600. However, all of you who wish to take part and have a rating of 1600 or higher, can register for the round unofficially.\n\nThe round will\n\n---\n\nTitle: 🚀 Day 745: Codeforces Problem Solved: Riptide | Sanjay Kasaudhan\nURL: https://www.linkedin.com/posts/sanjaykasaudhan_codeforces-competitiveprogramming-dsa-activity-7494250207195332608-Vi1-\nPublished: 2026-08-15T00:00:00.000Z\nAuthor: Sanjay Kasaudhan\nHighlights:\n🚀 Day 745: Codeforces Problem Solved: Riptide\n...\nI recently solved Problem A — Riptide from Codeforces Round 1114 (Div. 3).\n...\nThis problem is a nice example of simulation + careful observation. The key is to understand which players' token counts actually change in every round.\n...\n🔗Problem Link: https://lnkd.in/gu73DwfX\n...\n🧠 Problem Idea\n...\nAlice, Bob, and Charlie start with:\n...\nBefore every round, we check whether any two players have the same number of tokens.\n...\nIf two values become equal, the game stops.\n...\nOtherwise, during each round, the players with the minimum and maximum number of tokens each receive one additional token.\n...\nThe process continues until two players have the same number of tokens.\n...\nFirst, we make sure all three values are different:\n...\nwhile a!= b and b!= c and a!= c:\n...\nFor every round, we store the current token counts:\n...\nplayers = [a, b, c]\n...\nThen find the minimum and maximum:\n...\nmn = min(players)\n...\nmx = max(players)\n...\nThe important observation is:\n...\nThe player with the minimum gets +1\n...\nThe player with the maximum gets +1\n...\nThe middle value remains unchanged\n...\nplayers[players.index(mx)] += 1\n...\nplayers[players.index(mn)] += 1\n...\nAfter updating the values, we continue the simulation.\n...\nEventually, the minimum value catches up with the middle value, creating an equality and ending the game.\n...\nMinimum = 1, maximum =\n...\n2 2\n...\nNow Alice and Bob have the same number of tokens.\n...\nTherefore, the game ends after:\n...\n⏱️ Complexity\n...\nEach round performs only a constant number of operations:\n...\nFinding minimum → O(1)\n...\nFinding maximum → O(1)\n...\nUpdating values → O(1)\n...\nIf the game lasts R rounds:\n...\nTime Complexity: O(R)\n...\nSpace Complexity: O(1)\n...\nThe number of rounds depends on the initial difference between the minimum and middle values.\n...\n🎯 Key Takeaway\n...\nSimulation problems become much easier\n...\nyou clearly identify what changes and what stays unchanged in each step\n...\nInstead of trying to predict every possible state, we simply:\n...\nFind min → Find max → Update → Check → Repeat\n\n---\n\nTitle: Participated in Codeforces Round 1114 (Div. 3) and solved Problems A, B, and D. | Aman Khan\nURL: https://www.linkedin.com/posts/amanjkhan21_codeforces-codeforcesround1114-div3-activity-7490989704176177152-aMZo\nPublished: 2026-08-06T00:00:00.000Z\nAuthor: Aman Khan\nHighlights:\nA - Riptide\n...\nThe task was to determine how many rounds the game would last before two players ended up with the same number of tokens.\n...\nAfter sorting the three token counts, I observed that in every round the largest value decreases by 1 while the smallest increases by 1. The game ends as soon as either adjacent difference becomes 0, so the answer is simply the minimum of the two adjacent differences after sorting.\n\n---\n\nTitle: [Codeforces Round 1114 (Div. 3)] 题解 - constexpr_int - 博客园\nURL: https://www.cnblogs.com/constexpr-ll/p/22733367\nPublished: 2026-08-28T00:00:00.000Z\nAuthor: N/A\nHighlights:\n### A. Riptide\n\n直接模拟即可。\n...\nUpd：好像 tty 说有 \\(\\mathcal O(1)\\) 的做法，答案是 \\(\\min(v_3-v_2,v_2-v_1)\\)，场上懒得想直接模拟了。\n\n---\n\nTitle: A. Riptide - 技术栈\nURL: https://jishuzhan.net/article/2096464936453722114\nPublished: 2026-09-06T00:00:00.000Z\nAuthor: N/A\nHighlights:\nA. Riptide - 技术栈\n...\n# A. Riptide\n...\nAlice, Bob, and Charlie are playing a game with tokens. They start with a, b, and c tokens, respectively.\n...\nThe game is played in rounds. Before the beginning of each round, they check the number of tokens everyone has:\n...\n- If any two players have the exact same number of tokens, the game immediately ends.\n- Otherwise, the round begins, all three players have a strictly different number of tokens. The player with the strictly most tokens gives exactly 1 token to the player with the strictly fewest tokens.\n...\nGiven the starting tokens a, b, and c, determine exactly how many rounds the game will last before it ends.\n...\nThe first line contains a single integer t (1≤t≤103) --- the number of test cases.\n...\nEach test case consists of a single line containing three integers a, b, and c (1≤a,b,c≤10).\n...\nFor each test case, output a single integer --- the number of rounds the game will last before it ends.\n...\n解题说明：水题，找到差值最小的两个数即可。\n\n cpp 复制代码 \n\n```cpp\n#include <stdio.h>\n#include <stdlib.h>\n\nint main()\n{\n    int n;\n    scanf(\"%d\", &n);\n    for (int i = 0; i < n; i++) \n    {\n        int a, b, c, count = 0;\n        scanf(\"%d%d%d\", &a, &b, &c);\n        count = abs(a - b);\n        if (count > abs(b - c)) \n        {\n            count = abs(b - c);\n        }\n        if (count > abs(c - a))\n        {\n            count = abs(c - a);\n        }\n        printf(\"%d\\n\", count);\n    }\n    return 0;\n}\n```",
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            "output": "A. Riptide - 技术栈\n\n[\n\n技术栈](/)\n\n# A. Riptide\n\nFelven2026-09-06 13:06\n\ntime limit per test\n\n1 second\n\nmemory limit per test\n\n256 megabytes\n\nAlice, Bob, and Charlie are playing a game with tokens. They start with a, b, and c tokens, respectively.\n\nThe game is played in rounds. Before the beginning of each round, they check the number of tokens everyone has:\n\n-   If any two players have the exact same number of tokens, the game immediately ends.\n-   Otherwise, the round begins, all three players have a strictly different number of tokens. The player with the strictly most tokens gives exactly 1 token to the player with the strictly fewest tokens.\n\nGiven the starting tokens a, b, and c, determine exactly how many rounds the game will last before it ends.\n\nInput\n\nThe first line contains a single integer t (1≤t≤103) --- the number of test cases.\n\nEach test case consists of a single line containing three integers a, b, and c (1≤a,b,c≤10).\n\nOutput\n\nFor each test case, output a single integer --- the number of rounds the game will last before it ends.\n\nExample\n\nInput\n\nCopy\n\n复制代码\n\n6\n\n1 2 3\n\n4 6 1\n\n3 3 7\n\n1 7 10\n\n6 1 9\n\n1 1 1\n\nOutput\n\nCopy\n\n复制代码\n\n1\n\n2\n\n0\n\n3\n\n3\n\n0\n\nNote\n\nIn the first test case:\n\n-   No two players have the same number of tokens.\n-   Charlie has the most tokens (3 tokens), and Alice has the fewest tokens (1 token). Therefore, Charlie gives Alice a token.\n-   Now, Alice has 2 tokens, Bob has 2 tokens, and Charlie has 2 tokens. Since there are two players (or more) with the same number of tokens, the game ends.\n\nThe game ended after 1 round, so the answer is 1.\n\nIn the second test case, the game is played as follows:\n\n-   Bob gives Charlie a token, now Alice has 4 tokens, Bob has 5 tokens, and Charlie has 2 tokens.\n-   Bob gives Charlie a token, now Alice has 4 tokens, Bob has 4 tokens, and Charlie has 3 tokens. Since two players have the same number of tokens, the game ends.\n\nThe game lasted 2 rounds.\n\nIn the third test case, two players already have the same number of tokens. So the answer is 0 since no rounds were played.\n\n解题说明：水题，找到差值最小的两个数即可。\n\ncpp 复制代码\n\n```cpp\n#include <stdio.h>\n#include <stdlib.h>\n\nint main()\n{\n    int n;\n    scanf(\"%d\", &n);\n    for (int i = 0; i < n; i++) \n    {\n        int a, b, c, count = 0;\n        scanf(\"%d%d%d\", &a, &b, &c);\n        count = abs(a - b);\n        if (count > abs(b - c)) \n        {\n            count = abs(b - c);\n        }\n        if (count > abs(c - a))\n        {\n            count = abs(c - a);\n        }\n        printf(\"%d\\n\", count);\n    }\n    return 0;\n}\n```\n\n[算法](/tag/97)[c 算法](/tag/163110)\n\n[上一篇：量化交易基础之python库学习](/article/2096464725895467009)\n\n[下一篇：2026年视频素材命名规范：从全手动开源链到半自动成片的工程演进](/article/2096465130306064386)\n\n相关推荐\n\n[\n\n天天喝旺仔\n\n2 分钟前\n\nGo 泛型实战：从类型参数、约束到可复用泛型容器与函数\n\n数据结构·算法·容器·go\n\n](/article/2100765308076871681)[\n\n可爱的小小小狼\n\n6 分钟前\n\n【无标题】\n\njava·算法\n\n](/article/2100764276605243393)[\n\n和裕\n\n1 小时前\n\n平口开槽箱 vs 飞机盒 vs 扣底盒：自动化、展示效果与成本核心区别\n\n大数据·运维·网络·人工智能·算法·自动化\n\n](/article/2100748298202828801)[\n\nAgentMaster\n\n1 小时前\n\n从售前到售后全链路覆盖：智能客服在企业 5 大场景的落地实践与工具选型\n\n大数据·人工智能·算法\n\n](/article/2100746880423219201)[\n\nCccp.123\n\n1 小时前\n\n【leetcode】(六) 图和贪心算法\n\n数据结构·算法·leetcode\n\n](/article/2100746316192862209)[\n\ny1su\n\n1 小时前\n\n【Leetcode】1477. 找两个和为目标值且不重叠的子数组\n\n数据结构·后端·算法·leetcode·职场和发展\n\n](/article/2100745768945242113)[\n\n不会就选b\n\n10 小时前\n\n算法日常・每日刷题--＜贪心＞14\n\n算法\n\n](/article/2100621278311534594)[\n\nmmmmath\\_3\n\n12 小时前\n\nLeetCode.541.反转字符串II\n\n数据结构·算法·leetcode\n\n](/article/2100581254194974721)[\n\nNavigator\\_Z\n\n12 小时前\n\nLeetCode //MySQL - 1251. Average Selling Price\n\nc语言·算法·leetcode\n\n](/article/2100578517575192578)\n\n热门推荐\n\n[01国内可直接用、免费额度/永久免费的大模型API清单（含 SiliconFlow、火山、阿里、智谱、百度、Kimi、DeepSeek、DMXAPI 等）](/article/2061973168230838274)[02历年考研数学一、数学二、数学三真题试卷及答案PDF](/article/2056940295786958850)[03GitHub 镜像站点](/article/1965957555249266689)[04微信历史版本含下载地址（ Windows PC | 安卓 | MAC ）及设置微信不更新](/article/2018132694711451650)[05蜘蛛磁力 搜索引擎大全，如何使用蜘蛛磁力查找磁力链接](/article/1795266700313104386)[062026 国产 AI 大模型横评：DeepSeek、通义千问、Kimi、文心一言、星火、豆包谁更能打？](/article/2065289201393954817)[07人工智能（AI）发展史：详细里程碑](/article/2042920155794178049)[08ZCode 周末送额度活动开启：3 亿 Token 免费领取](/article/2093263902738665474)[09数学公理体系大全:第六章 选择公理的等价形式及证明](/article/2076497304956837889)[10【一等奖版】2026 国赛 A题 药材的烘干问题](/article/2098232905747845121)",
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            },
            "output": "Verified all 1000 allowed triples against simulation.\n",
            "metadata": {
              "output": "Verified all 1000 allowed triples against simulation.\n",
              "exit": 0,
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            "title": "python3 -c 'from itertools import product\nfor v in product(range(1,11), repeat=3):\n s=sorted(v); expected=min(s[1]-s[0],s[2]-s[1]); rounds=0\n while len(set(s))==3:\n  s[0]+=1; s[2]-=1; s.sort(); rounds+=1\n assert rounds==expected,(v,rounds,expected)\nprint(\"Verified all 1000 allowed triples against simulation.\")'",
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          "hints": [
            {
              "order": 1,
              "content": "The players' names don't affect the answer. Sort their token counts as $x \\le y \\le z$. What happens if either neighboring pair is already equal?"
            },
            {
              "order": 2,
              "content": "When $x<y<z$, one round changes the counts to $x+1$, $y$, and $z-1$. The middle player just watches."
            },
            {
              "order": 3,
              "content": "Can the smallest or largest count move past the middle count without first equaling it? Since each change is exactly $1$, the game ends before the players can swap positions in the sorted order."
            },
            {
              "order": 4,
              "content": "Until the game ends, both gaps $y-x$ and $z-y$ shrink by exactly $1$ per round. The first gap to reach zero ends the game."
            },
            {
              "order": 5,
              "content": "After sorting, the answer is $\\min(y-x,\\;z-y)$. An initial tie makes one of these gaps zero, so the same formula handles that case too."
            }
          ],
          "editorial": "### Key insight\n\nSort the three counts as $x \\le y \\le z$. The names don't matter; only their order does.\n\nIf two counts are equal, the game ends immediately. Otherwise, one round changes\n\n$$(x,y,z) \\longrightarrow (x+1,y,z-1).$$\n\nThe middle count stays fixed. The smallest count moves toward it from below, and the largest moves toward it from above.\n\nCrucially, neither can pass the middle count: they move by exactly $1$, so they must equal it first, and that ends the game. No reshuffling required.\n\n### Count the rounds directly\n\nThe two adjacent gaps are\n\n$$d_1=y-x, \\qquad d_2=z-y.$$\n\nEvery round decreases **both** gaps by $1$. As soon as either becomes zero, two players have equal counts. Therefore,\n\n$$\\boxed{\\text{answer}=\\min(y-x,\\;z-y)}.$$\n\nWe only need two players to tie—not all three. Waiting for everyone to agree is a different game entirely.\n\nFor example, sorting $(4,6,1)$ gives $(1,4,6)$. The gaps are $3$ and $2$, so the game lasts $2$ rounds:\n\n$$(1,4,6)\\to(2,4,5)\\to(3,4,4).$$\n\n### Algorithm\n\nFor each test case:\n\n1. Read the three counts into an array.\n2. Sort the array.\n3. Print the smaller of the two adjacent differences.\n\nIf any two counts are equal initially, sorting puts an equal pair next to each other. One gap is then zero, so the formula correctly prints $0$ without a special case.\n\n### Why it works\n\nLet $k=\\min(y-x,z-y)$.\n\nIf $k=0$, there is already a tie, so exactly zero rounds are played.\n\nOtherwise, after any $r<k$ rounds, the counts are\n\n$$x+r,\\quad y,\\quad z-r.$$\n\nBecause $r<y-x$ and $r<z-y$, we have\n\n$$x+r<y<z-r.$$\n\nThus all three counts remain distinct, the same players remain the minimum and maximum, and another round is played.\n\nAfter exactly $k$ rounds, at least one of $x+k=y$ or $z-k=y$ holds. A tie now exists, so the game ends before another round begins.\n\nTherefore, the game lasts exactly $k$ rounds, which is what the algorithm prints.\n\n### Complexity\n\nSorting exactly three integers takes $O(1)$ time and $O(1)$ space. Each test case therefore uses **$O(1)$ time** and **$O(1)$ auxiliary space**, with $O(t)$ total time. Ordinary `int` values are sufficient.",
          "solution": "#include <bits/stdc++.h>\nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n    ios::sync_with_stdio(false);\n    cin.tie(nullptr);\n}\n\nint main() {\n    setIO();\n\n    int t;\n    cin >> t;\n    while (t--) {\n        array<int, 3> a;\n        cin >> a[0] >> a[1] >> a[2];\n        sort(a.begin(), a.end());\n        cout << min(a[1] - a[0], a[2] - a[1]) << '\\n';\n    }\n}\n"
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              "hints": [
                {
                  "order": 1,
                  "content": "The players' names don't affect the answer. Sort their token counts as $x \\le y \\le z$. What happens if either neighboring pair is already equal?"
                },
                {
                  "order": 2,
                  "content": "When $x<y<z$, one round changes the counts to $x+1$, $y$, and $z-1$. The middle player just watches."
                },
                {
                  "order": 3,
                  "content": "Can the smallest or largest count move past the middle count without first equaling it? Since each change is exactly $1$, the game ends before the players can swap positions in the sorted order."
                },
                {
                  "order": 4,
                  "content": "Until the game ends, both gaps $y-x$ and $z-y$ shrink by exactly $1$ per round. The first gap to reach zero ends the game."
                },
                {
                  "order": 5,
                  "content": "After sorting, the answer is $\\min(y-x,\\;z-y)$. An initial tie makes one of these gaps zero, so the same formula handles that case too."
                }
              ],
              "editorial": "### Key insight\n\nSort the three counts as $x \\le y \\le z$. The names don't matter; only their order does.\n\nIf two counts are equal, the game ends immediately. Otherwise, one round changes\n\n$$(x,y,z) \\longrightarrow (x+1,y,z-1).$$\n\nThe middle count stays fixed. The smallest count moves toward it from below, and the largest moves toward it from above.\n\nCrucially, neither can pass the middle count: they move by exactly $1$, so they must equal it first, and that ends the game. No reshuffling required.\n\n### Count the rounds directly\n\nThe two adjacent gaps are\n\n$$d_1=y-x, \\qquad d_2=z-y.$$\n\nEvery round decreases **both** gaps by $1$. As soon as either becomes zero, two players have equal counts. Therefore,\n\n$$\\boxed{\\text{answer}=\\min(y-x,\\;z-y)}.$$\n\nWe only need two players to tie—not all three. Waiting for everyone to agree is a different game entirely.\n\nFor example, sorting $(4,6,1)$ gives $(1,4,6)$. The gaps are $3$ and $2$, so the game lasts $2$ rounds:\n\n$$(1,4,6)\\to(2,4,5)\\to(3,4,4).$$\n\n### Algorithm\n\nFor each test case:\n\n1. Read the three counts into an array.\n2. Sort the array.\n3. Print the smaller of the two adjacent differences.\n\nIf any two counts are equal initially, sorting puts an equal pair next to each other. One gap is then zero, so the formula correctly prints $0$ without a special case.\n\n### Why it works\n\nLet $k=\\min(y-x,z-y)$.\n\nIf $k=0$, there is already a tie, so exactly zero rounds are played.\n\nOtherwise, after any $r<k$ rounds, the counts are\n\n$$x+r,\\quad y,\\quad z-r.$$\n\nBecause $r<y-x$ and $r<z-y$, we have\n\n$$x+r<y<z-r.$$\n\nThus all three counts remain distinct, the same players remain the minimum and maximum, and another round is played.\n\nAfter exactly $k$ rounds, at least one of $x+k=y$ or $z-k=y$ holds. A tie now exists, so the game ends before another round begins.\n\nTherefore, the game lasts exactly $k$ rounds, which is what the algorithm prints.\n\n### Complexity\n\nSorting exactly three integers takes $O(1)$ time and $O(1)$ space. Each test case therefore uses **$O(1)$ time** and **$O(1)$ auxiliary space**, with $O(t)$ total time. Ordinary `int` values are sufficient.",
              "solution": "#include <bits/stdc++.h>\nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n    ios::sync_with_stdio(false);\n    cin.tie(nullptr);\n}\n\nint main() {\n    setIO();\n\n    int t;\n    cin >> t;\n    while (t--) {\n        array<int, 3> a;\n        cin >> a[0] >> a[1] >> a[2];\n        sort(a.begin(), a.end());\n        cout << min(a[1] - a[0], a[2] - a[1]) << '\\n';\n    }\n}\n"
            },
            "output": "Structured output captured successfully.",
            "metadata": {
              "valid": true
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            "title": "Structured Output",
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