Problem

Given an array contains N numbers of 0 .. N, find which number doesn't exist in the array.

Example

Given N = 3 and the array [0, 1, 3], return 2.

Note

找第一个缺失的数，可以用求和相减或二分法查找，也可以用位运算XOR来做。
求和相减是先求出0到N这个等差数列的和，再减去实际数组的和，就是缺失的数，
第二种方法是，只要先按顺序排列好[0, 1, 2, 3, 4, ...]，用二分法找到第一个和A[i]不相等的数i就可以了。

Solution

1. 二分法

public class Solution {
    public int findMissing(int[] A) {
        int len = A.length;
        Arrays.sort(A);
        int left = 0, right = len - 1;
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (A[mid] > mid) {
                right = mid - 1;
            }
            else {
                left = mid + 1;
            }
        }
        return A[left] == left ? left + 1 : left;
    }
}

2. 求和相减法

public class Solution {
    public int findMissing(int[] A) {
        int len = A.length;
        int sum = 0;
        for (int i = 0; i < len; i++) {
            sum += A[i];
        }
        int targetsum = len * (len + 1) / 2; //0, 1, 2,...,len, 共len+1个数，多加了一个len
        return targetsum - sum;
    }
}

3. 异或法

public class Solution {
    public int findMissing(int[] nums) {
        int x = 0;
        for (int i = 0; i <= nums.length; i++) {
            x ^= i;
        }
        for (int i = 0; i < nums.length; i++) {
            x ^= nums[i];
        }
        return x;
    }
}