消失的两个数字

// 思路：
// 1. 使用Stream计算实际总和和平方和。
// 2. 使用相同的公式计算期望的总和和平方和。
// 3. 使用公式求解出两个缺失数字。

import java.util.stream.IntStream;

public class FindMissingNumbersStream {
    public static int[] findMissingNumbers(int[] nums) {
        int n = nums.length + 2;

        int actualSum = IntStream.of(nums).sum();
        int actualSquareSum = IntStream.of(nums).map(x -> x * x).sum();

        int expectedSum = n * (n + 1) / 2;
        int expectedSquareSum = n * (n + 1) * (2 * n + 1) / 6;

        int sumDiff = expectedSum - actualSum;
        int squareSumDiff = expectedSquareSum - actualSquareSum;

        int sumXY = (sumDiff * sumDiff - squareSumDiff) / 2;

        int x = (sumDiff + (int) Math.sqrt(sumDiff * sumDiff - 4 * sumXY)) / 2;
        int y = sumDiff - x;

        return new int[]{x, y};
    }

    public static void main(String[] args) {
        int[] nums1 = {1};
        int[] nums2 = {2, 3};

        System.out.println(Arrays.toString(findMissingNumbers(nums1))); // 输出: [2, 3]
        System.out.println(Arrays.toString(findMissingNumbers(nums2))); // 输出: [1, 4]
    }
}