Leetcode #503: Next Greater Element II
In this guide, we solve Leetcode #503 Next Greater Element II in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given a circular integer array nums (i.e., the next element of nums[nums.length - 1] is nums[0]), return the next greater number for every element in nums. The next greater number of a number x is the first greater number to its traversing-order next in the array, which means you could search circularly to find its next greater number.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Stack, Array, Monotonic Stack
Intuition
We need the next greater or smaller element efficiently, which is exactly what a monotonic stack offers.
Each element is pushed and popped at most once, yielding a linear-time scan.
Approach
Maintain a stack that is either increasing or decreasing, depending on the query.
When the invariant is broken, pop and resolve answers for those indices.
Steps:
- Scan elements once.
- Pop while the monotonic condition is violated.
- Use stack indices to update answers.
Example
Input: nums = [1,2,1]
Output: [2,-1,2]
Explanation: The first 1's next greater number is 2;
The number 2 can't find next greater number.
The second 1's next greater number needs to search circularly, which is also 2.
Python Solution
class Solution:
def nextGreaterElements(self, nums: List[int]) -> List[int]:
n = len(nums)
ans = [-1] * n
stk = []
for i in range(n * 2 - 1, -1, -1):
i %= n
while stk and stk[-1] <= nums[i]:
stk.pop()
if stk:
ans[i] = stk[-1]
stk.append(nums[i])
return ans
Complexity
The time complexity is , and the space complexity is , where is the length of the array . The space complexity is , where is the length of the array .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.