renjianbo
beff3fac8d
- Fix delete agent 500: clean up FK records (agent_llm_logs, permissions, schedules, executions, team_members) and unbind goals/tasks before delete - Remove hardcoded personality templates in Android, replace with dynamic system prompt generation from name + description - Set promptSectionsEnabled=false to bypass PromptComposer for personality - Add Tencent Cloud Linux deployment guide (Docker Compose) - Accumulated backend service updates, frontend UI fixes, Android app changes Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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{"content":"所有测试通过 ✅。下面是完整分析：\n\n---\n\n## 时间复杂度详解\n\n### 核心公式：递推关系\n\n每次划分把数组切成两部分，设 pivot 最终位置把 `n` 个元素分成 `k` 和 `n-k-1` 两部分：\n\n$$T(n) = T(k) + T(n-k-1) + \\Theta(n)$$\n\n其中 $\\Theta(n)$ 是分区（partition）的开销——每个元素都要和 pivot 比较一次。\n\n### 三种情况\n\n| 情况 | 条件 | 递推式 | 结果 |\n|------|------|--------|------|\n| **最好** | 每次 pivot 恰好是中位数，均分 | $T(n)=2T(n/2)+\\Theta(n)$ | $\\Theta(n \\log n)$ |\n| **平均** | pivot 随机分布 | $T(n)=\\frac{1}{n}\\sum_{k=0}^{n-1}[T(k)+T(n-k-1)]+\\Theta(n)$ | $\\Theta(n \\log n)$ |\n| **最坏** | 每次 pivot 是最大/最小值，一边为空 | $T(n)=T(n-1)+\\Theta(n)$ | $\\Theta(n^2)$ |\n\n### 直观理解\n\n**最好/平均情况** — $O(n \\log n)$：\n\n```\n每层处理 n 个元素\n┌─────────────────────────┐ ← 第0层: n\n│ partition O(n) │\n├───────────┬─────────────┤\n│ 左 n/2 │ 右 n/2 │ ← 第1层: n\n├─────┬─────┼─────┬───────┤\n│ n/4 │ n/4 │ n/4 │ n/4 │ ← 第2层: n\n└─────┴─────┴─────┴───────┘\n ...共 log₂n 层...\n\n总工作量 = n × log₂n = O(n log n)\n```\n\n**最坏情况** — $O(n^2)$：\n\n当数组已经有序（或逆序）且总选最左/最右作 pivot 时：\n\n```\npivot=1: [1] + 处理 [2,3,...,n] ← 比较 n 次\npivot=2: [2] + 处理 [3,...,n] ← 比较 n-1 次\n...\n总和 = n + (n-1) + ... + 1 = n(n+1)/2 = O(n²)\n```\n\n### 为什么随机化能救回来？\n\n```python\nrand_idx = random.randint(low, high)\narr[rand_idx], arr[high] = arr[high], arr[rand_idx]\n```\n\n随机选 pivot 后，**无论输入是什么**，期望时间复杂度都是 $O(n \\log n)$。因为随机排列下，pivot 的排名等概率落在任何位置，递归树期望深度为 $O(\\log n)$。\n\n### 空间复杂度\n\n| 版本 | 空间 | 说明 |\n|------|------|------|\n| 简洁版（新建数组） | $O(n \\log n)$ | 每层都创建新数组 |\n| 原地版 | $O(\\log n)$ | 递归调用栈深度 |\n| 原地版最坏 | $O(n)$ | 完全偏斜时栈深度=n |\n\n### 与归并排序对比\n\n| | 快速排序 | 归并排序 |\n|------|----------|----------|\n| 时间 | 平均 $O(n \\log n)$，最坏 $O(n^2)$ | 稳定 $O(n \\log n)$ |\n| 空间 | **$O(\\log n)$** | $O(n)$（需辅助数组） |\n| 稳定性 | 不稳定 | 稳定 |\n| 缓存友好 | **好**（顺序访问） | 一般 |\n| 实际速度 | **更快**（常数因子小） | 较慢 |\n\n> 💡 **一句话总结**：快排快在常数因子小 + 缓存友好 + 原地操作，随机化后在实际应用中几乎不会遇到最坏情况，所以成为大多数标准库 `sort` 的默认选择。","iterations_used":3,"tool_calls_made":2,"truncated":false,"session_id":"fe1921f4-d935-491a-8db6-8338ac8c5c64","agent_id":"bdf92fae-27b6-4bfc-8f6a-fdea80d3c0ac","steps":[{"iteration":1,"type":"think","content":"## 快速排序（Quick Sort）\n\n快速排序是分治思想的经典代表，核心步骤：\n1. **选基准（pivot）** → 从数组中挑一个元素\n2. **分区（partition）** → 小于 pivot 放左边，大于放右边\n3. **递归** → 对左右子数组重复上述过程\n\n### 代码实现","tool_name":"code_execute","tool_input":{"code":"\nimport random\nfrom typing import List\n\ndef quicksort(arr: List[int]) -> List[int]:\n \"\"\"快速排序（简洁版，返回新数组，易理解）\"\"\"\n if len(arr) <= 1:\n return arr\n pivot = arr[len(arr) // 2]\n left = [x for x in arr if x < pivot]\n mid = [x for x in arr if x == pivot]\n right = [x for x in arr if x > pivot]\n return quicksort(left) + mid + quicksort(right)\n\n\ndef partition(arr: List[int], low: int, high: int) -> int:\n \"\"\"Lomuto 分区：选最右为 pivot，返回 pivot 最终位置\"\"\"\n pivot = arr[high]\n i = low - 1 # i 指向「小于区」最后一个元素\n for j in range(low, high):\n if arr[j] <= pivot:\n i += 1\n arr[i], arr[j] = arr[j], arr[i]\n arr[i + 1], arr[high] = arr[high], arr[i + 1]\n return i + 1\n\n\ndef quicksort_inplace(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"快速排序（原地版，空间 O(log n)，工程常用）\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n pivot_idx = partition(arr, low, high)\n quicksort_inplace(arr, low, pivot_idx - 1)\n quicksort_inplace(arr, pivot_idx + 1, high)\n\n\ndef quicksort_randomized(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"随机化快排：随机选 pivot 防最坏情况\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n # 随机选 pivot 并换到最后\n rand_idx = random.randint(low, high)\n arr[rand_idx], arr[high] = arr[high], arr[rand_idx]\n pivot_idx = partition(arr, low, high)\n quicksort_randomized(arr, low, pivot_idx - 1)\n quicksort_randomized(arr, pivot_idx + 1, high)\n\n\n# ====== 测试 ======\nif __name__ == \"__main__\":\n # 测试用例\n test_cases = [\n [3, 6, 8, 10, 1, 2, 1],\n [5],\n [],\n [1, 2, 3, 4, 5], # 已排序\n [5, 4, 3, 2, 1], # 逆序（最坏情况）\n [random.randint(0, 100) for _ in range(15)],\n ]\n\n for i, tc in enumerate(test_cases):\n a1 = quicksort(tc[:])\n a2 = tc[:]; quicksort_inplace(a2)\n a3 = tc[:]; quicksort_randomized(a3)\n py_sorted = sorted(tc)\n ok = (a1 == a2 == a3 == py_sorted)\n print(f\"测试 {i+1}: {tc[:8]}{'...' if len(tc)>8 else ''}\")\n print(f\" 简洁版: {a1}\")\n print(f\" 原地版: {a2}\")\n print(f\" 随机版: {a3}\")\n print(f\" 结果: {'✅ 通过' if ok else '❌ 失败'}\\n\")\n","language":"python"},"tool_result":null,"reasoning":"The user wants me to write a quicksort algorithm in Python and explain its time complexity. Let me:\n\n1. Write a clean, well-commented quicksort implementation\n2. Execute it to verify it works\n3. Explain the time complexity thoroughly\n\nLet me write a comprehensive quicksort with multiple variants and good explanations."},{"iteration":1,"type":"tool_result","content":"工具 code_execute 返回结果","tool_name":"code_execute","tool_input":{"code":"\nimport random\nfrom typing import List\n\ndef quicksort(arr: List[int]) -> List[int]:\n \"\"\"快速排序（简洁版，返回新数组，易理解）\"\"\"\n if len(arr) <= 1:\n return arr\n pivot = arr[len(arr) // 2]\n left = [x for x in arr if x < pivot]\n mid = [x for x in arr if x == pivot]\n right = [x for x in arr if x > pivot]\n return quicksort(left) + mid + quicksort(right)\n\n\ndef partition(arr: List[int], low: int, high: int) -> int:\n \"\"\"Lomuto 分区：选最右为 pivot，返回 pivot 最终位置\"\"\"\n pivot = arr[high]\n i = low - 1 # i 指向「小于区」最后一个元素\n for j in range(low, high):\n if arr[j] <= pivot:\n i += 1\n arr[i], arr[j] = arr[j], arr[i]\n arr[i + 1], arr[high] = arr[high], arr[i + 1]\n return i + 1\n\n\ndef quicksort_inplace(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"快速排序（原地版，空间 O(log n)，工程常用）\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n pivot_idx = partition(arr, low, high)\n quicksort_inplace(arr, low, pivot_idx - 1)\n quicksort_inplace(arr, pivot_idx + 1, high)\n\n\ndef quicksort_randomized(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"随机化快排：随机选 pivot 防最坏情况\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n # 随机选 pivot 并换到最后\n rand_idx = random.randint(low, high)\n arr[rand_idx], arr[high] = arr[high], arr[rand_idx]\n pivot_idx = partition(arr, low, high)\n quicksort_randomized(arr, low, pivot_idx - 1)\n quicksort_randomized(arr, pivot_idx + 1, high)\n\n\n# ====== 测试 ======\nif __name__ == \"__main__\":\n # 测试用例\n test_cases = [\n [3, 6, 8, 10, 1, 2, 1],\n [5],\n [],\n [1, 2, 3, 4, 5], # 已排序\n [5, 4, 3, 2, 1], # 逆序（最坏情况）\n [random.randint(0, 100) for _ in range(15)],\n ]\n\n for i, tc in enumerate(test_cases):\n a1 = quicksort(tc[:])\n a2 = tc[:]; quicksort_inplace(a2)\n a3 = tc[:]; quicksort_randomized(a3)\n py_sorted = sorted(tc)\n ok = (a1 == a2 == a3 == py_sorted)\n print(f\"测试 {i+1}: {tc[:8]}{'...' if len(tc)>8 else ''}\")\n print(f\" 简洁版: {a1}\")\n print(f\" 原地版: {a2}\")\n print(f\" 随机版: {a3}\")\n print(f\" 结果: {'✅ 通过' if ok else '❌ 失败'}\\n\")\n","language":"python"},"tool_result":"{\"stdout\": \"<22><><EFBFBD><EFBFBD> 1: [3, 6, 8, 10, 1, 2, 1]\\r\\n <20><><EFBFBD><EFBFBD>: [1, 1, 2, 3, 6, 8, 10]\\r\\n ԭ<>ذ<EFBFBD>: [1, 1, 2, 3, 6, 8, 10]\\r\\n <20><><EFBFBD><EFBFBD><EFBFBD>: [1, 1, 2, 3, 6, 8, 10]\\r\\n\", \"stderr\": \"Traceback (most recent call last):\\r\\n File \\\"C:\\\\Users\\\\86181\\\\AppData\\\\Local\\\\Temp\\\\tmp83pxiw_q.py\\\", line 73, in <module>\\r\\n print(f\\\" <20><><EFBFBD>: {'\\\\u2705 ͨ<><CDA8>' if ok else '\\\\u274c ʧ<><CAA7>'}\\\\n\\\")\\r\\nUnicodeEncodeError: 'gbk' codec can't encode character '\\\\u2705' in position 6: illegal multibyte sequence\\r\\n\", \"returncode\": 1}","reasoning":null},{"iteration":2,"type":"think","content":"Windows 编码小问题，去掉 emoji 重新跑：","tool_name":"code_execute","tool_input":{"code":"\nimport random\nfrom typing import List\n\ndef quicksort(arr: List[int]) -> List[int]:\n \"\"\"快速排序（简洁版，返回新数组）\"\"\"\n if len(arr) <= 1:\n return arr\n pivot = arr[len(arr) // 2]\n left = [x for x in arr if x < pivot]\n mid = [x for x in arr if x == pivot]\n right = [x for x in arr if x > pivot]\n return quicksort(left) + mid + quicksort(right)\n\n\ndef partition(arr: List[int], low: int, high: int) -> int:\n \"\"\"Lomuto 分区方案\"\"\"\n pivot = arr[high]\n i = low - 1\n for j in range(low, high):\n if arr[j] <= pivot:\n i += 1\n arr[i], arr[j] = arr[j], arr[i]\n arr[i + 1], arr[high] = arr[high], arr[i + 1]\n return i + 1\n\n\ndef quicksort_inplace(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"快速排序（原地版）\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n pi = partition(arr, low, high)\n quicksort_inplace(arr, low, pi - 1)\n quicksort_inplace(arr, pi + 1, high)\n\n\ndef quicksort_randomized(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"随机化快排 -- 防最坏情况\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n rand_idx = random.randint(low, high)\n arr[rand_idx], arr[high] = arr[high], arr[rand_idx]\n pi = partition(arr, low, high)\n quicksort_randomized(arr, low, pi - 1)\n quicksort_randomized(arr, pi + 1, high)\n\n\n# ====== 测试 ======\ntest_cases = [\n [3, 6, 8, 10, 1, 2, 1],\n [5],\n [],\n [1, 2, 3, 4, 5],\n [5, 4, 3, 2, 1],\n [random.randint(0, 100) for _ in range(15)],\n]\n\nfor i, tc in enumerate(test_cases, 1):\n a1 = quicksort(tc[:])\n a2 = tc[:]; quicksort_inplace(a2)\n a3 = tc[:]; quicksort_randomized(a3)\n expected = sorted(tc)\n ok = (a1 == a2 == a3 == expected)\n print(f\"Test {i}: input={tc[:6]}{'...' if len(tc)>6 else ''}\")\n print(f\" simple : {a1}\")\n print(f\" inplace: {a2}\")\n print(f\" rand : {a3}\")\n print(f\" result : {'PASS' if ok else 'FAIL'}\\n\")\n","language":"python"},"tool_result":null,"reasoning":"Unicode encoding issue on Windows with GBK. Let me fix the emoji issue and also check why the output looks garbled. Let me use simpler ASCII-safe output."},{"iteration":2,"type":"tool_result","content":"工具 code_execute 返回结果","tool_name":"code_execute","tool_input":{"code":"\nimport random\nfrom typing import List\n\ndef quicksort(arr: List[int]) -> List[int]:\n \"\"\"快速排序（简洁版，返回新数组）\"\"\"\n if len(arr) <= 1:\n return arr\n pivot = arr[len(arr) // 2]\n left = [x for x in arr if x < pivot]\n mid = [x for x in arr if x == pivot]\n right = [x for x in arr if x > pivot]\n return quicksort(left) + mid + quicksort(right)\n\n\ndef partition(arr: List[int], low: int, high: int) -> int:\n \"\"\"Lomuto 分区方案\"\"\"\n pivot = arr[high]\n i = low - 1\n for j in range(low, high):\n if arr[j] <= pivot:\n i += 1\n arr[i], arr[j] = arr[j], arr[i]\n arr[i + 1], arr[high] = arr[high], arr[i + 1]\n return i + 1\n\n\ndef quicksort_inplace(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"快速排序（原地版）\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n pi = partition(arr, low, high)\n quicksort_inplace(arr, low, pi - 1)\n quicksort_inplace(arr, pi + 1, high)\n\n\ndef quicksort_randomized(arr: List[int], low: int = 0, high: int | None = None):\n \"\"\"随机化快排 -- 防最坏情况\"\"\"\n if high is None:\n high = len(arr) - 1\n if low < high:\n rand_idx = random.randint(low, high)\n arr[rand_idx], arr[high] = arr[high], arr[rand_idx]\n pi = partition(arr, low, high)\n quicksort_randomized(arr, low, pi - 1)\n quicksort_randomized(arr, pi + 1, high)\n\n\n# ====== 测试 ======\ntest_cases = [\n [3, 6, 8, 10, 1, 2, 1],\n [5],\n [],\n [1, 2, 3, 4, 5],\n [5, 4, 3, 2, 1],\n [random.randint(0, 100) for _ in range(15)],\n]\n\nfor i, tc in enumerate(test_cases, 1):\n a1 = quicksort(tc[:])\n a2 = tc[:]; quicksort_inplace(a2)\n a3 = tc[:]; quicksort_randomized(a3)\n expected = sorted(tc)\n ok = (a1 == a2 == a3 == expected)\n print(f\"Test {i}: input={tc[:6]}{'...' if len(tc)>6 else ''}\")\n print(f\" simple : {a1}\")\n print(f\" inplace: {a2}\")\n print(f\" rand : {a3}\")\n print(f\" result : {'PASS' if ok else 'FAIL'}\\n\")\n","language":"python"},"tool_result":"{\"stdout\": \"Test 1: input=[3, 6, 8, 10, 1, 2]...\\r\\n simple : [1, 1, 2, 3, 6, 8, 10]\\r\\n inplace: [1, 1, 2, 3, 6, 8, 10]\\r\\n rand : [1, 1, 2, 3, 6, 8, 10]\\r\\n result : PASS\\r\\n\\r\\nTest 2: input=[5]\\r\\n simple : [5]\\r\\n inplace: [5]\\r\\n rand : [5]\\r\\n result : PASS\\r\\n\\r\\nTest 3: input=[]\\r\\n simple : []\\r\\n inplace: []\\r\\n rand : []\\r\\n result : PASS\\r\\n\\r\\nTest 4: input=[1, 2, 3, 4, 5]\\r\\n simple : [1, 2, 3, 4, 5]\\r\\n inplace: [1, 2, 3, 4, 5]\\r\\n rand : [1, 2, 3, 4, 5]\\r\\...","reasoning":null},{"iteration":3,"type":"final","content":"所有测试通过 ✅。下面是完整分析：\n\n---\n\n## 时间复杂度详解\n\n### 核心公式：递推关系\n\n每次划分把数组切成两部分，设 pivot 最终位置把 `n` 个元素分成 `k` 和 `n-k-1` 两部分：\n\n$$T(n) = T(k) + T(n-k-1) + \\Theta(n)$$\n\n其中 $\\Theta(n)$ 是分区（partition）的开销——每个元素都要和 pivot 比较一次。\n\n### 三种情况\n\n| 情况 | 条件 | 递推式 | 结果 |\n|------|------|--------|------|\n| **最好** | 每次 pivot 恰好是中位数，均分 | $T(n)=2T(n/2)+\\Theta(n)$ | $\\Theta(n \\log n)$ |\n| **平均** | pivot 随机分布 | $T(n)=\\frac{1}{n}\\sum_{k=0}^{n-1}[T(k)+T(n-k-1)]+\\Theta(n)$ | $\\Theta(n \\log n)$ |\n| **最坏** | 每次 pivot 是最大/最小值，一边为空 | $T(n)=T(n-1)+\\Theta(n)$ | $\\Theta(n^2)$ |\n\n### 直观理解\n\n**最好/平均情况** — $O(n \\log n)$：\n\n```\n每层处理 n 个元素\n┌─────────────────────────┐ ← 第0层: n\n│ partition O(n) │\n├───────────┬─────────────┤\n│ 左 n/2 │ 右 n/2 │ ← 第1层: n\n├─────┬─────┼─────┬───────┤\n│ n/4 │ n/4 │ n/4 │ n/4 │ ← 第2层: n\n└─────┴─────┴─────┴───────┘\n ...共 log₂n 层...\n\n总工作量 = n × log₂n = O(n log n)\n```\n\n**最坏情况** — $O(n^2)$：\n\n当数组已经有序（或逆序）且总选最左/最右作 pivot 时：\n\n```\npivot=1: [1] + 处理 [2,3,...,n] ← 比较 n 次\npivot=2: [2] + 处理 [3,...,n] ← 比较 n-1 次\n...\n总和 = n + (n-1) + ... + 1 = n(n+1)/2 = O(n²)\n```\n\n### 为什么随机化能救回来？\n\n```python\nrand_idx = random.randint(low, high)\narr[rand_idx], arr[high] = arr[high], arr[rand_idx]\n```\n\n随机选 pivot 后，**无论输入是什么**，期望时间复杂度都是 $O(n \\log n)$。因为随机排列下，pivot 的排名等概率落在任何位置，递归树期望深度为 $O(\\log n)$。\n\n### 空间复杂度\n\n| 版本 | 空间 | 说明 |\n|------|------|------|\n| 简洁版（新建数组） | $O(n \\log n)$ | 每层都创建新数组 |\n| 原地版 | $O(\\log n)$ | 递归调用栈深度 |\n| 原地版最坏 | $O(n)$ | 完全偏斜时栈深度=n |\n\n### 与归并排序对比\n\n| | 快速排序 | 归并排序 |\n|------|----------|----------|\n| 时间 | 平均 $O(n \\log n)$，最坏 $O(n^2)$ | 稳定 $O(n \\log n)$ |\n| 空间 | **$O(\\log n)$** | $O(n)$（需辅助数组） |\n| 稳定性 | 不稳定 | 稳定 |\n| 缓存友好 | **好**（顺序访问） | 一般 |\n| 实际速度 | **更快**（常数因子小） | 较慢 |\n\n> 💡 **一句话总结**：快排快在常数因子小 + 缓存友好 + 原地操作，随机化后在实际应用中几乎不会遇到最坏情况，所以成为大多数标准库 `sort` 的默认选择。","tool_name":null,"tool_input":null,"tool_result":null,"reasoning":"All tests passed. Now I need to provide a thorough explanation of time complexity. Let me give a comprehensive answer."}]} |