From 3cf3e1fc69de883601345e666390ab468adf6c6f Mon Sep 17 00:00:00 2001 From: Chiayi Date: Fri, 28 Jan 2022 00:36:00 +0800 Subject: [PATCH] problem: 0977 squares of a sorted array --- .../0977 Squares of a Sorted Array.md | 147 ++++++++++++++++++ 0977 Squares of a Sorted Array/Untitled 1.png | Bin 0 -> 66603 bytes 0977 Squares of a Sorted Array/Untitled 2.png | Bin 0 -> 37395 bytes 0977 Squares of a Sorted Array/Untitled.png | Bin 0 -> 19002 bytes 4 files changed, 147 insertions(+) create mode 100644 0977 Squares of a Sorted Array/0977 Squares of a Sorted Array.md create mode 100644 0977 Squares of a Sorted Array/Untitled 1.png create mode 100644 0977 Squares of a Sorted Array/Untitled 2.png create mode 100644 0977 Squares of a Sorted Array/Untitled.png diff --git a/0977 Squares of a Sorted Array/0977 Squares of a Sorted Array.md b/0977 Squares of a Sorted Array/0977 Squares of a Sorted Array.md new file mode 100644 index 0000000..278ef24 --- /dev/null +++ b/0977 Squares of a Sorted Array/0977 Squares of a Sorted Array.md @@ -0,0 +1,147 @@ +# 0977. Squares of a Sorted Array + +* Difficulty: easy +* Link: https://leetcode.com/problems/squares-of-a-sorted-array/ +* Topics: Array-String + +# Clarification + +1. Check the inputs and outputs + - INPUT: List[int] + - OUTPUT: List[int] + +# Naive Solution + +### Thought Process + +1. squares of each number +2. sort it +- Implement + + ```python + class Solution: + def sortedSquares(self, nums: List[int]) -> List[int]: + """ + 1. squares of each number + 2. sort it + """ + for idx, num in enumerate(nums): + nums[idx] = num ** 2 + nums.sort() + return nums + ``` + + +### Complexity + +- Time complexity:$O(nlogn)$ + + ![Untitled](./Untitled.png) + +- Space complexity:$O(1)$ + +### Problems & Improvement + +- **Follow up:** Squaring each element and sorting the new array is very trivial, could you find an `O(n)` solution using a different approach? + +# Improvement + +### Thought Process + +- `nums` is sorted in **non-decreasing** order. +1. split the array into two array + 1. negative array + 2. positive array + + ```python + [-4,-1,0,3,10] + ^^^^^ ^^^^^^ + ``` + +2. Reverse the negative array +3. begin to traverse two array + 1. square the num and check which element is larger, insert the larger one +- Implement + + ```python + class Solution: + def sortedSquares(self, nums: List[int]) -> List[int]: + # split the array into two array (by linked list) + positive = [] + negative = nums + for idx, num in enumerate(nums): + if num >= 0: + positive = nums[idx:] + negative = nums[:idx] + break + + # reverse the negative array + negative = negative[::-1] + + # traverse the array + result = [] + p, n = 0, 0 + while p < len(positive) and n < len(negative): + if abs(negative[n]) < abs(positive[p]): + result.append(negative[n] ** 2) + n += 1 + else: + result.append(positive[p] ** 2) + p += 1 + for i in range(p, len(positive)): + result.append(positive[i] ** 2) + for i in range(n, len(negative)): + result.append(negative[i] ** 2) + + return result + ``` + + +### Complexity + +- Time complexity: $O(n)$ + + ![Untitled](./Untitled%201.png) + +- Space complexity:$O(n)$ + +# Improvement + +### Thought Process + +- 可以不用 Reverse Array,因為 **non-decreasing** order,兩側最大,從兩側往內夾擊 +- implement + + ```python + class Solution: + def sortedSquares(self, nums: List[int]) -> List[int]: + # split the array into two array (by linked list) + right = len(nums) - 1 + left = 0 + # traverse the array + result = [0] * len(nums) + resultIdx = len(nums) - 1 + while resultIdx >=0 : + if abs(nums[left]) > abs(nums[right]): + result[resultIdx] = nums[left] ** 2 + left += 1 + else: + result[resultIdx] = nums[right] ** 2 + right -= 1 + resultIdx -=1 + + return result + ``` + + +### Complexity + +- Time complexity: $O(n)$ + + ![Untitled](./Untitled%202.png) + +- Space complexity:$O(1)$ + +# Note + +- **[Python: A comparison of lots of approaches! 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