时间/空间复杂性 - 如何弄清楚这个功能？

Question

I need to calculate the time and space complexity for this problem, can anyone help me figure out what it is and why?

I believe the time complexity for this problem would be O(n^2) because of the 2 filter functions. Essentially, it would be similar to having 2 for-loops that iterate over the array and because they are looping for a set amount of time, we know that it will be O(n) for the first filter and adding another would make it O(n^2)?

Not sure about space complexity.

let arr = [1, 2, 2, 4, 4, 5, 6, 7, 7, 8, 9];
const result = arr.filter(x => arr.filter(y => y === x).length > 1)
console.log(result);
// 2, 2, 4, 4, 7, 7

Answer 1

Yes, time complexity is O(n^2) - for example, if arr has 10 items, the algorithm needs to make ~100 comparisons before finishing.

Space complexity is O(n) . For example, consider the last iteration of the outer .filter - the result that's almost finished being constructed takes up O(n) space at that time (worst-case; equivalent to the side of the input arr ). The inner array inside the callback being filtered (which will then have its length checked, and returned) will also be, worst-case, the side of the input n . So, the most space that will be being currently used at any point in time is O(2n) , which is equivalent to O(n) .

Answer 2

I think you are right about the time complexity, it is O(n^2) due to the two nested loops.

IMO space complexity is O(n) as you need only n units of space to keep the array and no additional memory is allocated.