[leetcode] 977. Squares of a Sorted Array

题目

Given an integer array nums sorted in non-decreasing order, return an array of the squares of each number sorted in non-decreasing order.

Example 1:

Input: nums = [-4,-1,0,3,10]
Output: [0,1,9,16,100]
Explanation: After squaring, the array becomes [16,1,0,9,100].
After sorting, it becomes [0,1,9,16,100].

Example 2:

Input: nums = [-7,-3,2,3,11]
Output: [4,9,9,49,121]

Constraints:

• 1 <= nums.length <= 10^4
• -10^4 <= nums[i] <= 10^4
• nums is sorted in non-decreasing order.

Follow up: Squaring each element and sorting the new array is very trivial, could you find an O(n) solution using a different approach?

思路

最简单的方式就是先对数组的每个数相乘，然后再为数组排序了，两行搞定，不过这样恐怕不符合这道题的本意。。。

真正的解法是双指针，初始化于数组的最左边和最右边，然后比对两个指针上数值绝对值的大小，其中较大的数值即为整个数组最大的数值，将其乘积取出并保存，随后左（右）移指针。如此循环，取出乘积组成的新数组便是答案。

代码

python版本：

# 双指针（超时）
class Solution:
    def sortedSquares(self, nums: List[int]) -> List[int]:
        i=0
        l=len(nums)
        while i<l:
            if nums[i]<0:
                nums[i]=-nums[i]
                j=i
                while j+1<len(nums) and nums[j]>nums[j+1]:
                    nums[j],nums[j+1]=nums[j+1],nums[j]
                    j+=1
            else:
                nums[i]=nums[i]*nums[i]
                i+=1
        return nums

# map再排序
class Solution:
    def sortedSquares(self, nums: List[int]) -> List[int]:
        nums=list(map(lambda x: x*x,nums))
        return sorted(nums)

# 真正的双指针
class Solution:
    def sortedSquares(self, nums: List[int]) -> List[int]:
        res=[0 for _ in range(len(nums))]
        l,r,now=0,len(nums)-1,len(nums)-1
        while now>=0:
            if abs(nums[l])>abs(nums[r]):
                res[now]=nums[l]*nums[l]
                now-=1
                l+=1
            else:
                res[now]=nums[r]*nums[r]
                now-=1
                r-=1
        return res