Time Complexity - PermMissingElem

Question

An array A consisting of N different integers is given. The array contains integers in the range [1..(N + 1)], which means that exactly one element is missing.

Your goal is to find that missing element.

Write a function:

class Solution { public int solution(int[] A); }

that, given an array A, returns the value of the missing element.

For example, given array A such that:

A[0] = 2 A[1] = 3 A[2] = 1 A[3] = 5

the function should return 4, as it is the missing element.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [0..100,000];
• the elements of A are all distinct;
• each element of array A is an integer within the range [1..(N + 1)].

Report

class Solution {
    public int solution(int[] A) {
        // write your code in Java SE 8
        if(A.length == 0) {
            return 1;
        }
        BitSet bs = new BitSet();
        for (int i = 0; i < A.length; i++) {
            bs.set(A[i]);
        }

        int ret = -1;
        for (int i = 1; i <= A.length + 1; i++) {
            if (!bs.get(i)) {
                ret = i;
                break;
            }
        }
        return ret;
    }
}