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Exercise 14

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

function test(n) {
  let count = 0;
  for (let i = n; i > 1; i = Math.floor(i / 2)) {
    for (let j = 0; j < n; j++) {
      count++;
    }
  }
  return count;
}

Solution

The time complexity is O(NlogN). The outer loop runs logN as it halves i in each iteration. The inner loop runs n times so the overall time complexity is O(logN) * O(N) or O(N*logN).

Space Complexity is O(1) as we are not using any additional space.

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