{
  "slug": "balanced-accuracy-macro-recall",
  "title": "Balanced Accuracy 类别不平衡二分类平衡准确率",
  "difficulty": "Easy",
  "difficulty_breakdown": {
    "concept": 2,
    "implementation": 2,
    "math_derivation": 2,
    "boundary_complexity": 2
  },
  "category": "ML",
  "tags": [
    "Metrics",
    "BalancedAccuracy",
    "ImbalancedLearning",
    "TorchLeet"
  ],
  "description_md": "### 题目描述\n计算类别不平衡二分类任务中的敏感度（Sensitivity ($\\text{TPR} = \\frac{TP}{TP + FN}$)）、特异度（Specificity ($\\text{TNR} = \\frac{TN}{TN + FP}$)）以及平衡准确率 $\\text{BalancedAcc} = \\frac{1}{2}(\\text{TPR} + \\text{TNR})$，返回 `(tpr, tnr, balanced_acc)`。\n\n### 函数签名\n```python\ndef balanced_accuracy_binary(\n    tp: int,\n    tn: int,\n    fp: int,\n    fn: int,\n    eps: float = 1e-12,\n) -> Tuple[float, float, float]:\n```\n\n### 示例\n```python\n# 输入\ntp = 0\ntn = 990\nfp = 0\nfn = 10\neps = 1e-12\n\n# 输出 (tuple)\n(0.0, 1.0, 0.5)\n```\n\n### 参数规格与约束\n- **`tp`**：`int`\n- **`tn`**：`int`\n- **`fp`**：`int`\n- **`fn`**：`int`\n- **`eps`**：`float`（默认 `1e-12`）\n- **返回值**：`Tuple[float, float, float]`，输出规格 `Tuple` (`float` (示例值: `0.0`), `float` (示例值: `1.0`), `float` (示例值: `0.5`))\n- **精度容差**：`atol=0.0001, rtol=0.0001`\n> 题目来源：改编自 [TorchLeet](https://github.com/Exorust/TorchLeet)（MIT License），已改写为函数式评测接口与中文题面。",
  "entry_point": "balanced_accuracy_binary",
  "starter_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ndef balanced_accuracy_binary(\n    tp: int,\n    tn: int,\n    fp: int,\n    fn: int,\n    eps: float = 1e-12,\n) -> Tuple[float, float, float]:\n    # 请在此处编写你的实现代码\n    pass\n",
  "reference_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ndef balanced_accuracy_binary(tp: int, tn: int, fp: int, fn: int, eps: float = 1e-12) -> Tuple[float, float, float]:\n    tpr = float(tp) / (float(tp + fn) + eps)\n    tnr = float(tn) / (float(tn + fp) + eps)\n    return tpr, tnr, 0.5 * (tpr + tnr)\n",
  "test_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ncases = [\n    (\"多数类全预测为负时 BalancedAcc 仅为 0.5\", 0, 990, 0, 10),\n    (\"完美预测 1.0\", 50, 500, 0, 0),\n    (\"均衡错误\", 40, 80, 20, 10),\n    (\"高召回低特异度\", 95, 50, 50, 5),\n]\nfor idx, (name, *args) in enumerate(cases, 1):\n    t0 = time.time()\n    try:\n        exp = ref_obj(*args)\n        act = user_obj(*args)\n        match, err, max_diff = compare_outputs(act, exp, atol=atol, rtol=rtol)\n        passed, msg = match, err\n    except Exception as e:\n        passed, msg = False, f\"Runtime Exception: {str(e)}\"\n        act, exp, max_diff = None, None, None\n    cases_results.append({\n        \"case_id\": idx, \"case_name\": name, \"passed\": passed,\n        \"time_ms\": round((time.time() - t0) * 1000, 2), \"message\": msg,\n        \"user_output_summary\": summarize_obj(act) if act is not None else None,\n        \"expected_summary\": summarize_obj(exp) if exp is not None else None,\n        \"max_diff\": max_diff,\n    })\n",
  "test_cases": [
    {
      "name": "多数类全预测为负时 BalancedAcc 仅为 0.5",
      "input_desc": "真实参数契约用例 (tp, tn, fp, fn, eps)",
      "params": [
        {
          "name": "tp",
          "type": "int",
          "value": "0"
        },
        {
          "name": "tn",
          "type": "int",
          "value": "990"
        },
        {
          "name": "fp",
          "type": "int",
          "value": "0"
        },
        {
          "name": "fn",
          "type": "int",
          "value": "10"
        },
        {
          "name": "eps",
          "type": "float",
          "value": "1e-12"
        }
      ],
      "raw_inputs": {
        "tp": "0",
        "tn": "990",
        "fp": "0",
        "fn": "10",
        "eps": "1e-12"
      }
    },
    {
      "name": "完美预测 1.0",
      "input_desc": "真实参数契约用例 (tp, tn, fp, fn, eps)",
      "params": [
        {
          "name": "tp",
          "type": "int",
          "value": "50"
        },
        {
          "name": "tn",
          "type": "int",
          "value": "500"
        },
        {
          "name": "fp",
          "type": "int",
          "value": "0"
        },
        {
          "name": "fn",
          "type": "int",
          "value": "0"
        },
        {
          "name": "eps",
          "type": "float",
          "value": "1e-12"
        }
      ],
      "raw_inputs": {
        "tp": "50",
        "tn": "500",
        "fp": "0",
        "fn": "0",
        "eps": "1e-12"
      }
    },
    {
      "name": "均衡错误",
      "input_desc": "真实参数契约用例 (tp, tn, fp, fn, eps)",
      "params": [
        {
          "name": "tp",
          "type": "int",
          "value": "40"
        },
        {
          "name": "tn",
          "type": "int",
          "value": "80"
        },
        {
          "name": "fp",
          "type": "int",
          "value": "20"
        },
        {
          "name": "fn",
          "type": "int",
          "value": "10"
        },
        {
          "name": "eps",
          "type": "float",
          "value": "1e-12"
        }
      ],
      "raw_inputs": {
        "tp": "40",
        "tn": "80",
        "fp": "20",
        "fn": "10",
        "eps": "1e-12"
      }
    }
  ],
  "time_limit": 5.0,
  "memory_limit_mb": 512,
  "atol": 0.0001,
  "rtol": 0.0001,
  "forbidden_modules": [
    "os",
    "sys",
    "subprocess",
    "socket",
    "shutil",
    "pathlib",
    "ctypes",
    "multiprocessing"
  ],
  "forbidden_calls": [
    "eval",
    "exec",
    "compile",
    "open",
    "__import__",
    "input",
    "breakpoint"
  ],
  "is_featured": false,
  "editorial_md": "#### 💡 核心算法原理与数学推导\n**Balanced Accuracy 类别不平衡二分类平衡准确率**（`balanced_accuracy_binary`）聚焦于 **ML** 中的关键计算逻辑：\n\n计算类别不平衡二分类任务中的敏感度（Sensitivity ($\\text{TPR} = \\frac{TP}{TP + FN}$)）、特异度（Specificity ($\\text{TNR} = \\frac{TN}{TN + FP}$)）以及平衡准确率 $\\text{BalancedAcc} = \\frac{1}{2}(\\text{TPR} + \\text{TNR})$，返回 `(tpr, tnr, balanced_acc)`。\n\n在实现中，函数接收参数 `tp` (`int`)、`tn` (`int`)、`fp` (`int`)、`fn` (`int`)、`eps` (`float`)，目标是计算出类型与形状严格符合 `Tuple[float, float, float]` 契约的结果。\n\n#### 📐 输入输出张量变换与步骤拆解\n- **输入基准规格**：`tp` 规格为 `int` (示例值: `0`)，`tn` 规格为 `int` (示例值: `990`)，`fp` 规格为 `int` (示例值: `0`)，`fn` 规格为 `int` (示例值: `10`)。\n- **期望输出规格**：`Tuple` (`float` (示例值: `0.0`), `float` (示例值: `0.999999999999999`), `float` (示例值: `0.4999999999999995`))。\n\n**具体推导与计算步骤如下：**\n1. 计算中间量 `tpr`：通过表达式 `float(tp) / (float(tp + fn) + eps)` 完成张量或数值变换。\n2. 计算中间量 `tnr`：通过表达式 `float(tn) / (float(tn + fp) + eps)` 完成张量或数值变换。\n3. 返回最终结果：输出 `tpr, tnr, 0.5 * (tpr + tnr)`，严格对齐函数签名要求的返回类型与维度。\n\n#### 📊 复杂度分析\n- **时间复杂度**：$O(1)$，仅涉及标量代数运算或闭式公式求值，执行耗时与规模参数大小无关。\n- **空间复杂度**：$O(1)$，仅使用常数级标量局部变量，无额外张量显存分配。\n\n#### ⚠️ 关键实现细节与易错点\n- **除零保护与数值平滑 (`eps`)**：在执行分母归一化、标准差缩放或对数运算时，需加上 `eps` 或执行 `clamp_min` 防止除零产生 `NaN` / `Inf`。\n- **边界输入鲁棒性**：注意单样本（`Batch=1`）、零值输入或极端超参数下的计算行为，禁止硬编码特定测试用例常量。\n- **向量化算子优先**：优先使用 PyTorch 原生向量化张量算子，避免低效的逐元素循环。\n\n#### 💻 官方标准参考实现\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ndef balanced_accuracy_binary(tp: int, tn: int, fp: int, fn: int, eps: float = 1e-12) -> Tuple[float, float, float]:\n    tpr = float(tp) / (float(tp + fn) + eps)\n    tnr = float(tn) / (float(tn + fp) + eps)\n    return tpr, tnr, 0.5 * (tpr + tnr)\n```"
}