88. Merge Sorted Array

Description

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?

Solutions

Solution 1: Two Pointers

We use two pointers $i$ and $j$ pointing to the end of two arrays, and a pointer $k$ pointing to the end of the merged array.

Every time we compare the two elements at the end of the two arrays, and move the larger one to the end of the merged array. Then we move the pointer one step forward, and repeat this process until the two pointers reach the start of the arrays.

The time complexity is $O(m + n)$, where $m$ and $n$ are the lengths of two arrays. The space complexity is $O(1)$.

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

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

• class Solution:
def merge(self, nums1: List[int], m: int, nums2: List[int], n: int) -> None:
"""
Do not return anything, modify nums1 in-place instead.
"""
i, j, k = m - 1, n - 1, m + n - 1
# what if j=-1 already but k is not 0 yet? e.g. m=[1,2,0], n=[3]
# => then no more ops needed, rest of m[] already sorted, so this while is good enough
while j >= 0:
# i could be -1, eg. [7,8,9, ] and [1]
if i >= 0 and nums1[i] > nums2[j]:
nums1[k] = nums1[i]
i -= 1
else:
nums1[k] = nums2[j]
j -= 1
k -= 1


• func merge(nums1 []int, m int, nums2 []int, n int) {
for i, j, k := m-1, n-1, m+n-1; j >= 0; k-- {
if i >= 0 && nums1[i] > nums2[j] {
nums1[k] = nums1[i]
i--
} else {
nums1[k] = nums2[j]
j--
}
}
}

• /**
Do not return anything, modify nums1 in-place instead.
*/
function merge(nums1: number[], m: number, nums2: number[], n: number): void {
for (let i = m - 1, j = n - 1, k = m + n - 1; j >= 0; --k) {
nums1[k] = i >= 0 && nums1[i] > nums2[j] ? nums1[i--] : nums2[j--];
}
}


• /**
* @param {number[]} nums1
* @param {number} m
* @param {number[]} nums2
* @param {number} n
* @return {void} Do not return anything, modify nums1 in-place instead.
*/
var merge = function (nums1, m, nums2, n) {
for (let i = m - 1, j = n - 1, k = m + n - 1; j >= 0; --k) {
nums1[k] = i >= 0 && nums1[i] > nums2[j] ? nums1[i--] : nums2[j--];
}
};


• class Solution {
/**
* @param Integer[] $nums1 * @param Integer$m
* @param Integer[] $nums2 * @param Integer$n
* @return NULL
*/
function merge(&$nums1,$m, $nums2,$n) {
while (count($nums1) >$m) {
array_pop($nums1); } for ($i = 0; $i <$n; $i++) { array_push($nums1, $nums2[$i]);
}
asort(\$nums1);
}
}

• impl Solution {
pub fn merge(nums1: &mut Vec<i32>, m: i32, nums2: &mut Vec<i32>, n: i32) {
let (mut m, mut n) = (m as usize, n as usize);
for i in (0..m + n).rev() {
nums1[i] = match (m == 0, n == 0) {
(true, false) => {
n -= 1;
nums2[n]
}
(false, true) => {
m -= 1;
nums1[m]
}
(_, _) => {
if nums1[m - 1] > nums2[n - 1] {
m -= 1;
nums1[m]
} else {
n -= 1;
nums2[n]
}
}
};
}
}
}