[LeetCode] 88. Merge Sorted Array 合并两个有序数组

You are given two integer arrays nums1 and nums2, sorted in non-decreasing order, and two integers m and n, representing the number of elements in nums1 and nums2 respectively.

Merge nums1 and nums2 into a single array sorted in non-decreasing order.

The final sorted array should not be returned by the function, but instead be stored inside the array nums1. To accommodate this, nums1 has a length of m + n, where the first m elements denote the elements that should be merged, and the last n elements are set to 0 and should be ignored. nums2 has a length of n.

Example 1:

Input: nums1 = [1,2,3,0,0,0], m = 3, nums2 = [2,5,6], n = 3
Output: [1,2,2,3,5,6]
Explanation: The arrays we are merging are [1,2,3] and [2,5,6].
The result of the merge is [1,2,2,3,5,6] with the underlined elements coming from nums1.

Example 2:

Input: nums1 = [1], m = 1, nums2 = [], n = 0
Output: [1]
Explanation: The arrays we are merging are [1] and [].
The result of the merge is [1].

Example 3:

Input: nums1 = [0], m = 0, nums2 = [1], n = 1
Output: [1]
Explanation: The arrays we are merging are [] and [1].
The result of the merge is [1].
Note that because m = 0, there are no elements in nums1. The 0 is only there to ensure the merge result can fit in nums1.

Constraints:

nums1.length == m + n
nums2.length == n
0 <= m, n <= 200
1 <= m + n <= 200
-109 <= nums1[i], nums2[j] <= 109

Follow up: Can you come up with an algorithm that runs in O(m + n) time?

混合插入有序数组，由于两个数组都是有序的，所有只要按顺序比较大小即可。题目中说了 nums1 数组有足够大的空间，说明不用 resize 数组，又给了m和n，那就知道了混合之后的数组的大小，这样就从 nums1 和 nums2 数组的末尾开始一个一个比较，把较大的数，按顺序从后往前加入混合之后的数组末尾。需要三个变量 i，j，k，分别指向 nums1，nums2，和混合数组的末尾。进行 while 循环，如果i和j都大于0，再看如果 nums1[i] > nums2[j]，说明要先把 nums1[i] 加入混合数组的末尾，加入后k和i都要自减1；反之就把 nums2[j] 加入混合数组的末尾，加入后k和j都要自减1。循环结束后，有可能i或者j还大于等于0，若j大于0，那么还需要继续循环，将 nums2 中的数字继续拷入 nums1。若是i大于等于0，那么就不用管，因为混合数组本身就放在 nums1 中，参见代码如下：

解法一：

class Solution {
public:
    void merge(vector<int>& nums1, int m, vector<int>& nums2, int n) {
        int i = m - 1, j = n - 1, k = m + n - 1;
        while (i >= 0 && j >= 0) {
            if (nums1[i] > nums2[j]) nums1[k--] = nums1[i--];
            else nums1[k--] = nums2[j--];
        }
        while (j >= 0) nums1[k--] = nums2[j--];
    }
};

我们还可以写的更简洁一些，将两个 while 循环融合到一起，只要加上 i>=0 且 nums1[i] > nums2[j] 的判断条件，就可以从 nums1 中取数，否则就一直从 nums2 中取数，参见代码如下:

解法二：

class Solution {
public:
    void merge(vector<int>& nums1, int m, vector<int>& nums2, int n) {
        int i = m - 1, j = n - 1, k = m + n - 1;
        while (j >= 0) {
            nums1[k--] = (i >= 0 && nums1[i] > nums2[j]) ? nums1[i--] : nums2[j--];
        }
    }
};