以下搜索算法的时间复杂度是多少

Question

I am trying to make a program that recursively searches for an element by dividing the array into half, can you tell what will be time complexity of the below code?

public  boolean search(List<Integer> A, int B,int l,int r) {
        if(l==r) {
            if(A.get(l)==B) {
                System.out.println("Found at index : "+l);
                return true;
            }else {
                return false;
            }
        }
        int mid = (l+r)/2;
        boolean a = search(A, B,l,mid);
        boolean b = search(A, B,mid+1,r);
        return a||b;
    }

above code, l is left most index and r is right most index for example

List A = new ArrayList<>(Arrays.asList(2,5,1,65,8,4));

for the above arraylist we are searching element 4 so the method will be-

search(A, 4,0,A.size()-1)

Answer 1

The time complexity of this algorithm is O(n) because it will go through each element in the list.

The space complexity is O(log(n)) because of the recursive calls putting in the stack at most log(n) recursive calls before backtracking. Why? Because each recursive call will 'divide' the list in half until the last element in that search (sub-list) is processed. Then it will return/backtrack and continue the search on another part of the list. Since it backtracks while halving until there is one element left in that sublist, it will never put all the elements in the stack of the recursive calls at once.