简单function的大O

Question

I am learning data structure and pretty new to this game. I know a single loop running for n-iteration has O(n) time complexity. But if I use a splice inside the for loop, is it going to be O(n ² ) time complexity? I am positive it's O(n ² ) but want to make sure.

Here is the sample code that I was working on:

var createTargetArray = function(nums, index) {
    let target = []
    for (let i=0; i< index.length; i++){
        let idx = index[i]
        target.splice(idx,0,nums[i])
    }
    return target
};

Answer 1

You are correct. Worst case for the splice method should be O(n). That call is occuring inside the iteration of a foreach loop O(n); So the big o-notation of the whole script is O(n^2)

Answer 2

Since big O notation is asking how many iterations your function takes to perform f(x) to your array as input, when you loop over all the elements the general time complexity of O(n). However using the.splice() function in JavaScript also has ideally a time complexity of O(n) and thus when you put a O(n) in another O(n) then it effectively becomes O(n^2). As a good rule of thumb you can think of nested O(n) increasing the power of n by one. For example if you were to loop to have a triple nested loop doing 1 operation to each element of an array it would become O(n^3) and so on.