31. Next Permutation
Array, Two Points, AMateList ·Problem Statement
link: https://leetcode.com/problems/next-permutation/ https://leetcode.cn/problems/next-permutation/
A permutation of an array of integers is an arrangement of its members into a sequence or linear order.
For example, for arr = [1,2,3], the following are all the permutations of arr: [1,2,3], [1,3,2], [2, 1, 3], [2, 3, 1], [3,1,2], [3,2,1]. The next permutation of an array of integers is the next lexicographically greater permutation of its integer. More formally, if all the permutations of the array are sorted in one container according to their lexicographical order, then the next permutation of that array is the permutation that follows it in the sorted container. If such arrangement is not possible, the array must be rearranged as the lowest possible order (i.e., sorted in ascending order).
For example, the next permutation of arr = [1,2,3] is [1,3,2]. Similarly, the next permutation of arr = [2,3,1] is [3,1,2]. While the next permutation of arr = [3,2,1] is [1,2,3] because [3,2,1] does not have a lexicographical larger rearrangement. Given an array of integers nums, find the next permutation of nums.
The replacement must be in place and use only constant extra memory.
Example:
Input: nums = [1,2,3]
Output: [1,3,2]
Input: nums = [3,2,1]
Output: [1,2,3]
Input: nums = [1,1,5]
Output: [1,5,1]
Solution Approach
Find the first decreasing element from the end, swap it with a slightly larger element, and reorder the subsequent numbers.
Algorithm
- Identify the first decreasing element nums[i] from the end.
- Swap it with the next greater element found from the end.
- If no swap occurs, reverse the entire array; otherwise, reverse the sequence after i.
Implement
class Solution:
def nextPermutation(self, nums: List[int]) -> None:
""" Do not return anything, modify nums in-place instead. """
n = len(nums)
i = n - 2
while i >= 0:
if nums[i] >= nums[i + 1]:
i -= 1
else:
for j in range(n - 1, i, -1):
if nums[j] > nums[i]:
nums[i], nums[j] = nums[j], nums[i]
nums[i + 1:] = sorted(nums[i + 1:])
return
nums.reverse()