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Exercise 12

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

function test(n, m) {
  for (let i = 0; i < n; i++) {
    console.log("Hello!");
  }
  for (let j = 0; j < m; j++) {
    console.log("World!");
  }
}

Solution

In this example, we have two separate loops, one iterating n times and the other iterating m times. The time complexity of the first loop is O(N), and the time complexity of the second loop is O(M). Since the loops are iterating over different collections, we cannot directly combine or simplify their time complexities.

Therefore, the time complexity is expressed as O(N) + O(M). This notation emphasizes that the time taken by the algorithm increases linearly with the size of n and m separately.

Remember that if the values of n and m are not related or do not have a fixed relationship, we cannot further simplify the time complexity expression.

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

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