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Exercise 9

What is the time complexity of the function test? What is its space complexity?

function test(n) {
  let matrix = [];
  for (let i = 0; i < n; i++) {
    matrix[i] = [];
    for (let j = 0; j < n; j++) {
      matrix[i][j] = i + j;
    }
  }
  return matrix;
}

Solution

The time complexity of the function test is O(N^2) because it involves two nested loops, each running n times. As a result, the number of operations is proportional to n * n = n^2.

The space complexity is also O(N^2) because it creates a matrix of size n * n. The space required grows quadratically with the input size.

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