121.json

{
  "id": "121",
  "title": "Vector Element-wise Sum",
  "difficulty": "easy",
  "category": "Linear Algebra",
  "video": "",
  "likes": "0",
  "dislikes": "0",
  "contributor": [
    {
      "profile_link": "https://github.com/moe18",
      "name": "Moe Chabot"
    }
  ],
  "description": "Write a Python function that computes the element-wise sum of two vectors. The function should return a new vector representing the resulting sum if the operation is valid, or -1 if the vectors have incompatible dimensions. Two vectors (lists) can be summed element-wise only if they are of the same length.",
  "learn_section": "## Understanding Vector Element-wise Sum\n\nIn linear algebra, the **element-wise sum** (also known as vector addition) involves adding corresponding entries of two vectors.\n\n### Vector Notation\nGiven two vectors $a$ and $b$ of the same dimension $n$:\n\n$$\na = \\begin{pmatrix} a_1 \\\\ a_2 \\\\ \\vdots \\\\ a_n \\end{pmatrix}, \\quad b = \\begin{pmatrix} b_1 \\\\ b_2 \\\\ \\vdots \\\\ b_n \\end{pmatrix}\n$$\n\nThe element-wise sum is defined as:\n\n$$\na + b = \\begin{pmatrix} a_1 + b_1 \\\\ a_2 + b_2 \\\\ \\vdots \\\\ a_n + b_n \\end{pmatrix}\n$$\n\n### Key Requirement\nVectors $a$ and $b$ must be of the same length $n$ for the operation to be valid. If their lengths differ, element-wise addition is not defined.\n\n### Example\nLet:\n\n$$\na = [1, 2, 3], \\quad b = [4, 5, 6]\n$$\n\nThen:\n\n$$\na + b = [1+4, 2+5, 3+6] = [5, 7, 9]\n$$\n\nThis simple operation is foundational in many applications such as vector arithmetic, neural network computations, and linear transformations.",
  "starter_code": "def vector_sum(a: list[int|float], b: list[int|float]) -> list[int|float]:\n\t# Return the element-wise sum of vectors 'a' and 'b'.\n\t# If vectors have different lengths, return -1.\n\tpass",
  "solution": "def vector_sum(a: list[int|float], b: list[int|float]) -> list[int|float]:\n    if len(a) != len(b):\n        return -1\n    return [a[i] + b[i] for i in range(len(a))]",
  "example": {
    "input": "a = [1, 3], b = [4, 5]",
    "output": "[5, 8]",
    "reasoning": "Element-wise sum: [1+4, 3+5] = [5, 8]."
  },
  "test_cases": [
    {
      "test": "print(vector_sum([1, 2, 3], [4, 5, 6]))",
      "expected_output": "[5, 7, 9]"
    },
    {
      "test": "print(vector_sum([1, 2], [1, 2, 3]))",
      "expected_output": "-1"
    },
    {
      "test": "print(vector_sum([1.5, 2.5, 3.0], [2, 1, 4]))",
      "expected_output": "[3.5, 3.5, 7.0]"
    }
  ]
}